Multi-Play Video Poker Primer

  

            This past week, I received an e-mail from a reader who had some questions about Multi-Play video poker.  For those who are not familiar with it, Multi-Play allows Players to play out the result of a draw multiple times.  The Player is dealt five cards as per normal video poker.  He then decides which cards to hold/discard.  The draw is then played out from 2 to 100 times depending on which version he is playing and how many hands he chooses to play.  Generally speaking, the casinos offer 3-Play, 5-Play, 10-Play, 50-Play and 100-Play.  The underlying video poker game may be any of the ones offered on a regular video poker machine – jacks or better, Bonus, Double Bonus, Deuces Wild, etc…

            The game was invented about 15 years ago by Ernie Moody of Action Gaming.  If you’ve never heard of Mr. Moody, well, I guess multi-play didn’t make him a household name, but it sure did make him a lot of money.  There are thousand, if not tens of thousands of these games across the casinos of the world.  While it seems that the game may be off its peak (in terms of popularity, not necessarily total machines), it is still an immensely popular game.

            The good part about Multi-Play is that you don’t need to learn any new strategies.  It does not matter if you are playing 1 hand, 2 hands, 100 hands or theoretically a million hands at a time.  The proper strategy is still Expert Strategy which will look at the expected values of each possible way you can play the hand.  The number of times the draw is played out does NOT change this one bit.  The payback of Multi-Play is NOT dependent on the number of hands being played, but rather is based on the underlying video poker variation being played and the paytable being used.

            The bad news about Multi-Play is that you had best be prepared to bring a larger bankroll or to lower the denomination that you are used to playing, which can have its problems too.  Ideally, you want to keep playing max-coin to help ensure being paid 800 for 1, instead of 250 for 1 if you hit a Royal.  Assuming you do this, then the amount you are wagering per game is multiplied by the number of hands you are playing.  If you play Five Play then you are going to have to wager 5 coins (for max-coin) times 5 hands or 25 units.  If you’re a Quarter Player, you just went from wagering $1.25 per game to $6.00 per game.  This does not necessarily mean you need to have 5 times the bankroll (for reasons I’ll get to shortly), but you will need something close to this.

            To help with the bankroll issue, you could lower the denomination you normally play at.  If you go from Quarters to Nickels, you’ll still be wagering $1.25 even though you will now be playing five hands instead of one.  The only thing you need to watch out for is that sometimes the paytable for Nickels will be different (i.e. lower) than the one for Quarters.  This is true even when you are on the same physical machine but merely switch denomination.  You’ll get away with a lesser bankroll by switching to nickels, but if the payback is cut by 1% (or more), you’ll pay for it in other ways.

            So, how does playing multiple hands effect our bankroll requirements?  The more hands you play simultaneously (in the manner of Multi-Play), the less volatile the game can be.  When you play a single hand and are dealt a Low Pair, the number of possible outcomes is relatively small.  You might lose, get a Two Pair, Trips, Full House or Quads.  Your payout will be exactly equal to zero (losing) or one of the payouts of a winning hand.  None of these are very close to the actual expected value.  However, as you play more hands at the same time, you’ll find that you’ll approximate the actual expected value far more often.  This is especially true if you play 50-Play or 100-Play.  It is amazing how many times you’re dealt a Low Pair in 100-Play only to find that you win 80-85 coins back (per unit wagered) and that this hand has an EV of 0.82.  In essence you bring the long run to your game much quicker.   This is why I said earlier that you don’t necessarily need 5 times the bankroll.  But, don’t be fooled into thinking that you don’t need a larger bankroll if you’re playing 5 times the amount of money per game.

            So, one of the questions my reader asked is, “Is there a "best" number of multiple hands to play out of: Triple, Five Play, Ten Play Video Poker?”  The answer is not really.  As always you have to play the one you feel most comfortable playing based on bankroll, paytable and enjoyment.

How Did That Happen?

            I have been analyzing casino games for about 30 years.  Given that I’m in my mid-40’s, that is quite a statement.  When I first learned to program computers in High School, my father asked me to create a program that would analyze blackjack.  That was the beginning of it all for both of us.  Through the years, between the two of us, we would analyze the most popular games in the industry – video poker, Three Card Poker, Let It Ride, Mississippi Stud, Ultimate Texas Hold’em and many more. 

            Despite all of this, there is still one burning question that I simply cannot answer.  How did the casinos ever allow video poker machines paying over 100% to get to the casino floor?  When I work on a table game, questions always come up about whether there are ways to count cards or use knowledge of other Player’s cards to get a Player advantage.  Generally speaking, most games do allow for the Player to reduce the house edge if he knows other Player’s cards and can alter his strategy accordingly.  To date, I have not yet discovered a case where the Player can turn the tables on the house, but rather reduce somewhat the house advantage.  The response I invariably get from the inventor is – as long as he can’t push the payback over 100%, we’re good.

            So, if a bunch of friends head over to a Let It Ride table and start sharing information about their cards and by doing so can push the payback of Let It Ride all the way up to 99.9%, that’s okay.  But, if it goes to 100.01% there is a problem.  At 99.9%, the Player will still lose in the long run.  At 100.01%, in theory, he will win in the long run.  This is a line the casinos (and inventors) do not want to cross.

            So, given this, how did so many video poker machines hit the floor with a payback of over 100% and while they have been greatly reduced, how do so many still exist today?

            For the first part of the previous question – I haven’t a clue.  I can only speculate.  My best guess says that somehow it eluded the inventors, gaming companies and even the Nevada Gaming Control Board that there was a discrete mathematical solution to the perfect payback of video poker.  Or, based on the computers readily available at the time, they believed that calculating such a payback was nearly impossible.

            Of course, as we all know, my father proved them wrong.  Despite relatively limited programming skills and a computer that by today’s standards would seem to be less powerful than most of our phones, he managed to determine the best way to play each hand and calculate an exact payback for most of variations of video poker that existed at the time.  Much to his surprise, many of these variations would have paybacks well over 100%.  Even the most popular variation (jacks or better) had a payback of about 99.6%, which seemed high.  However, as I stated earlier it was still below 100%, so while perfect play might cut into profits it would not eliminate them.  Games with a payback of over 100% might slice into profits.

            So, one train of thought could be that so few people would play the game correctly, what harm could it cause?  Let’s take a look at just how much someone could win.  If we use Deuces Wild paying 100.76% as an example and use a $1 machine, an expert Player would wager about $4000 per hour (800 hands times $5 – max coin).   With a 0.76% Player advantage, a Player would win about $30.40 per hour.  If someone were to choose to make this a profession, he could win more than $1200/week or about $60K per year.  You won’t become a millionaire this way, but it’s not a bad wage.  Now, what if someone were to train a team of people and play an entire bank of 8 or 10 machines paying out 100.76%.  He would reduce the volatility and could pay people $20-30K to play video poker per year and keep  $200K+ for himself!  Take it one step further and imagine if he can find a $2 machine or a $5 machine or even a higher denomination.  Throw in cashback and comps and someone could take the casinos for a lot of money.

            Of course, one the casinos figure all this out, they’re just going to lower the payouts on these machines, right?  Well, that certainly happened too.  It is much more difficult to find machines paying over 100% today than it was 10-15 years ago.  However, they still exist in rather large amounts.  What has changed then?  Mostly the denomination.  The casinos have made it so that it is very difficult to find a machine playing more than quarters paying out over 100%.

            If we perform our earlier calculation using a quarter machine, we find that a Player can earn an average of about $7.50/hour.  This translates to a yearly income of $15,000 which isn’t exactly a living wage.  Thus, it isn’t likely to attract ‘professionals’.  Instead, casinos get to scream how they have video poker machines paying over 100% knowing that 90% of the Players who play it will probably not use the proper strategy and will actually play it a lower payback.

            This is truly the definition of a win-win scenario.  The casinos are willing to leave the machines on the floor which gives the knowledgeable Player the opportunity to take advantage of them.  What is interesting is that virtually all of the positive machines can be found at casinos frequented by locals – i.e. not the Strip casinos.  As I’ve discussed many times before, it would seem that many (too many?) people would rather make a donation to Caesar’s than a withdrawal from Red Rock Canyon.

            To find machines with top paybacks, I highly recommend the database at http://www.vpfree2.com.   I have absolutely no affiliation with this site and do not profit in any way if you choose to use the database.  I just find it a very good resource to find full-pay machines.  Of course, another good resource is our “Expert Video Poker for Las Vegas” which is an excellent beginner’s guide to video poker.  For the month of May, it is available at special price of $7.95 (reg. $9.95) for Gaming Today readers.  If you would like to order, please send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603.

A Slot Upgrade?

             This past weekend, we had some friends over for lunch.  Invariably, the conversation winds up on my relatively unique profession.  Somewhat ironic in this case as one of the other guys is a hedge fund manager who counts as one of his clients one of the top poker players in the world.  Then again, some would argue that we’re both in the same general profession – casino gambling!

            I got asked the usual question of what the best games to play are and how I got started in the profession.  At one point, the subject turned to slot machines.  There was both good news and bad news to report here.  On one hand everyone seemed to agree that these were amongst the worst payers in the casino.  On the other hand, not everyone admitted that they would never play one.  For those whom are intimidated by the table games, the slots still are the mainstay – no matter how bad they pay.

            I remarked how I had just read an article talking about a comeback that is being made by ‘old fashioned’ mechanical slots.  Everyone in the room agreed that the older slots were better than the newer ones.  A few reasons were cited.  One was that they actually had a handle to ‘pull’.  Another was the clinking of the coins coming out when you won.  I actually commented that I wasn’t sure if the machines making the comeback are ticket-in/ticket-out or truly old-fashioned in that they accept and pay out real coins. 

            One of the reasons I cited for the popularity of the mechanical machines was that you could actually tell when you won or lost.   As I’ve written many times in my column in Gaming Today, I have occasionally put a $5 machine into a penny or nickel video slot machine in order to kill some time.  I then press a button that says “Play max lines” and press another that says “Spin”.  When the reels are done ‘spinning’, the machine then tells me that I either won some number of coins or that I lost.  No matter how many times I try to figure it out, I can’t tell on my own WHY I’ve won when I do!

            I’ll see several identical symbols on the same line only to find that’s not really a line to this 5 ‘reel’, 27-line machine!  Someone should tell some of the slot manufacturers that a ‘line’ usually denotes a STRAIGHT line between two points, not an up and down line that looks more like a heart monitor!  Is it any wonder that people are not having fun playing slots anymore?  It wasn’t good enough when the casinos were essentially taking the Player’s money with 92-93% slot machines, now they have to do it in a way that most Players have absolutely no idea what is going on?  For anyone reading this, please tell me – are you really having fun playing the newer video slots?  I’m sure it’s a lot of fun when you get to a Bonus Round on something like Wheel of Fortune, but do you even know why you got there? 

            I remember playing one slot machine that put me into some sort of Bonus Round.  I won about $25 (on a nickel machine) in under 5 minutes.  I couldn’t tell you why I wound up in the Bonus Round or what I was trying to do while in it!  It just kept telling me to pick boxes and I did.  Each time it opened one, I won more coins.  Hey, I was very happy to win $25 in a few minutes, but I have to be honest.  I can’t really say I had any fun doing it.  I could’ve just as easily lost my bankroll (okay, it was only $5 for the slot machine) and been just as clueless.

            As I raised this point to my guests, there was universal agreement.  While some of them admitted to still playing them, none said they had fun while doing it.  My hedge fund manager friend does all he can to dissuade his wife from playing the slots at all – just based on their horrible paybacks.

            Of course, I have mixed emotions about a comeback for the mechanical slots.  They still have the worst paybacks in the casinos and I would much prefer that slot machines go the way of the dodo bird.  There are SO many better games to play in the casino with better paybacks and that are more fun.  I know that one of the reasons people avoid them is sometimes they are intimidated to play new games that they don’t know how to play.  So, we try to make it a bit easier with our books and booklets.

            Today, May 12^th, 2011 would have been my father’s (Lenny Frome’s) 85^th birthday.  So, for the rest of May, we’re offering some special prices on our titles:

•         Winning Strategies for Video Poker and Video Poker: America’s National Game of Chance (both books) for $19.26 (his birth year)
•          Expert Video Poker for Las Vegas or Expert Video Poker for Las Vegas for just $5.12 each.
•          Any of the Expert Strategy series books (Three Card Poker, Four Card Poker, Let It Ride, Spanish 21, Caribbean Stud Poker, Mississippi Stud or Blackjack Switch)  - 1 for $4.85, 2 for $8.85, 3 for $11.85 or all 7 for $19.26

            To learn more about any of these titles, go to my website at www.gambatria.com and click on the “Products” tab.  If you would like to order any products, just send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603.

Coming Up Aces

            When it comes to video poker, I think there is no doubt that the Ace is by far the most enigmatic card in the deck.  In the old days when we only had jacks or better video poker, the Ace was actually worth far less than most people gave it credit for.  In video poker an Ace High Flush or Ace High Straight has no more value than a 7-High hand of the same rank.  Whereas a Full House with three Aces is nearly unbeatable in table poker, it has no more value than 3’s over 2’s in video poker.

            The only additional value an Ace has is as a High Card.  In this regard, it has the same value as a Jack, Queen or King.  These four cards give extra weight to the expected value of our partial hands because of the opportunity to pick up a High Pair.  Once you have a High Pair or better, they provide no additional value.  This is where the irony starts to build.  A single Ace actually has the lowest expected value of any single High Card (tied with a King).  This is because an Ace inherently creates only INSIDE Straights.  With a single Ace you still have two shots at a Straight (10 – A or A-5), but if you add an Ace to any other High Card (i.e. J-A) you leave yourself only once chance to make a Straight.  Whereas, if you hold a J-Q, you can make a Straight multiple ways (8-9-10, 9-10-K, 10-K-A). 

            We overlook this weakness when we have an opportunity to hold two suited High Cards (i.e. a 2-Card Royal).  We would rather hold a suited J-A then an off-suit J-Q.  However, when we have three unsuited High Cards and one of them is an Ace, we do NOT keep the Ace.  Thus, if dealt J-Q-A, J-K-A or Q-K-A (offsuit), we keep the two NON-Ace cards.  The reduction in our chances of grabbing a Straight by keeping the Ace is greater than the benefit of keeping the third High Card.

            Thus, we see from all this that the almighty Ace is really not so almighty.  From an expected value perspective it is the weakest of all the single High Cards.  Fortunately for the Ace, someone invented the Bonus Poker variations of video poker restoring it to its full glory.

            The Bonus Poker variations turned the values of cards a bit upside down.  Pairs of Jacks or Better still paid 1 so this kept the extra value of the single High Card.  However, the 2^nd tier of Bonus Payouts for Quads went to 2’s – 5’s.  This gave extra weight to these cards as they started to Pair up.  No one discards three of a kind so that wasn’t an issue, but all of a sudden ‘Low Pairs’ had to be split between ‘very’ low (2’s – 5’s) and just low (6’s – 10’s).  The top Tier (Aces) is what restored the Ace to the top of the pecking order.  Not only did it have value as a singleton above the low cards, it now had the top value as it began to Pair up and Players hoped to collect all four of them. 

            In reality, the paytable of the original bonus poker doesn’t do much for the Aces.  Obviously a Pair of Aces has a higher expected value, as does that of the single Ace – but not enough to really change how we play our hands.  However, as we move up the ladder of bonus games, this begins to change.  In Double Bonus Poker, a Pair of Aces outranks a 3-Card Royal, but a Pair of J-Q-K’s does not outrank all of them.  If you’ve got Trip Aces with another Pair (i.e. a Full House), you’ll throw away the Pair to go for the fourth Ace.  Don’t do that with any other Three of a Kind!

            If we move up to Double Double Bonus, we now find that if we’re dealt a Pair of Aces with another Pair (Two Pair) that we discard the other Pair hoping to get dealt the remaining two Aces.  The power of the Ace is complete!

            The most important lesson in all of this is that you need to learn the strategy table for whatever game you are playing.  You also need to discard your pre-conceived notions about cards and their values.  In table poker an Ace is a very powerful card.  In most versions of video poker, it is just another High Card and not even the most valuable of them.  Video poker is not about kickers and eking out a better hand.  It’s a game about cold calculated math.  

Take A Stroll Through the Casino

It has been more than 20 years since my father, Lenny Frome, began writing about video poker. I think he had two goals when he started. The first was to tell people about this relatively new casino game which had paybacks about as high as any in the casino – and in some cases over 100%. The second goal was to get people away from slots which have arguably the absolute worst paybacks in the casino. Two decades later, it would appear that while much good work has been done, much more is needed.


The most common question I’m asked by friends is “what is the ‘best’ game to play in the casino?” In this case, ‘best’ means having the highest payback. Usually, most people start to answer the question before I can and start with blackjack – which is essentially a correct answer. With a payback of 99.5% (give or take, depending on the rules), blackjack must be described as being one of the ‘best’ games to play. Of course, the original version is a bit slow and requires a significant degree of strategy, but that really isn’t part of the equation at the moment.


Frequently, the next answer that comes up is Craps. This is a bit tougher to size up. Craps is really dozens of different independent wagers so determining the ‘payback’ of Craps is not only difficult (if not impossible), it is also meaningless. Avoid all the proposition wagers with horrible paybacks and you’ll have a much higher payback than the guy constantly buying ‘hard ways’ bets. Craps can be a really fun game with a lively table and when a shooter gets hot. Playing with just a couple of Players and/or during only cold or slightly warm streaks and it I prefer games where you can sit down!


After blackjack and Craps, the person who asked the question finally goes silent. It is almost as if the casino still only has about 4 options – blackjack, Craps, Roulette and slots. Well, I guess the good news is that the silence means the most people have figured out that you’re not going to win money playing slots. As for Roulette, well, it is a bit like Craps, but almost every wager has the same so-so payback. But what about the rest of the casino? Over the past 20 years, the casino floor has changed tremendously. Many of the people who ask me the question do go to the casino. Have they not noticed all the other games?


I don’t know who is more surprised. The person I’m talking to when I say “video poker” or me when they respond “what’s that?” I guess if you’ve always been a table game person maybe you haven’t noticed that not all the ‘slot machines’ look alike. Of course, this was truer when slot machines still had handles and video poker machines didn’t. With the advent of video slots, the casual observer may just see lots of lights and colors on a computer screen and think they are all the same. I’ve spent many columns explaining the vast differences between slots and video poker to need to do so again today.


Once I explain what video poker is to the person who asked the original question, they are even more surprised to find out that a ‘routine’ payback can be about the same as blackjack and that there are still a fair number that can be found that have paybacks over 100%. This, of course leads to an explanation of what it takes to exploit such a Player advantage. Yes, you can probably make 30k-40K a year playing quarter video poker, but it would take playing 40 hours a week in a smoky casino, playing very disciplined and it would be a lot like having a very streaky commission job. You might earn nothing one year and earn 50-60K the next. This is not necessarily an easy job or one suited for anyone. The ultimate irony comes when I find out the person I’m talking to is an attorney, here in the NYC area, who is probably pulling down at least a few hundred thousand a year. I don’t think he’s giving up his day job!


So, I guess after more than 20 years of trying to get people to break the slot habit, we can confidently say we have achieved some success. I think the number of people who think that they have a shot at the slots has gone way down. At the same time, the campaign to keep teaching people about all the other games in the casino goes on. From video poker to blackjack to many of the newer table games that offer higher paybacks than the traditional casino games – many while offering a good deal more excitement too. The next time you head out to the casino, before you sit down to play, just walk the casino floor and check out all the games you may not have known existed. Then, to learn more about it, head over to my website and there’s a good chance I already have written about it. If not, feel free to drop me a line and I’ll do my best to cover it in the near future.

The Case For War

            No, not the War in Iraq or Afghanistan or even Libya.  To be honest, I can’t believe I’m writing about this game.  I can’t believe people now gamble on a game I used to play with my grandmother when I was 4.  What next, Casino Candyland?

            But, if people are going to play it, I have a responsibility to write about it and inform the players about what they are playing, what to expect and what strategy to use.  Much to my surprise, when I was done with the analysis, I found that the payback for Casino War really wasn’t that bad given the type of game it is.  So, if you’re looking for a simple game, requiring very little strategy and no knowledge of Poker, maybe this game is for you.

            For those who are not familiar with the game, it doesn’t get any easier than this.  The Player makes a wager.  The Player gets one card.  The Dealer gets one card.  High Card wins.  If the Player wins, he gets even money on his wager.  In case of a tie, the Player can either surrender half of his original wager or make an additional wager equal to the first one.  If he makes this wager, the Player and the Dealer each get an additional card.  Again, High Card wins.  If the Player wins at this point, he will win even money on his 2^nd wager and push on the original wager.  If the Dealer wins, the Player loses all wagers.  If they Tie again, the Player WINS even money on both wagers.  There is also a sidebet that pays 10 units if the Player and Dealer Tie.

            Casino War is usually played with a shoe of 6 or 8 decks.  From the Player’s perspective, there really isn’t much difference between the two.  The overall payback of the game is little higher with 6 decks, but not enough to get worked up over.  The sidebet pays about 1% more with the 8 deck shoe because ties are more common, but as we’ll soon see, this is immaterial.

            The entire house advantage comes from Ties.  Without them, Casino War would be a 100% game with no advantage to the Player or the House.  As such, we can calculate the house advantage by calculating the frequency of Ties.  Once a Tie occurs, the Player and the Dealer will still each win with the same frequency, but when the Player wins, he will win even money on one bet and push on the other.  In essence, he will be wagering 2 units to win one.  The casino gives a small advantage back to the Player by paying even money on both wagers if they Tie again after the initial tie.

            When all the math is done, we find that the overall payback of Casino War is a rather respectable 97.8%.  Obviously, this is not what we can expect to achieve from Blackjack, Spanish 21 or even Four Card Poker, but it is in the same range as Three Card Poker.  Given that there is almost no strategy involved, this is not too bad.  The only strategy question that does exist for Casino War is whether the Player should ever surrender half of his original wager after the first tie.  Although the player has a significant negative expectation once the first tie has occurred, he is still better off wagering instead of Folding.  This is essentially because of the possibility of the Double Tie which will allow the Player to win even money on both wagers.

            Personally, I prefer games with tougher strategy that provide more of a challenge, but I believe that no matter what game you’re going to play, you should go in with your eyes open, play with the best strategy and know what to expect.            

Bankroll Considerations

  

            Recently, I answered a question from a reader about what to do when you win ‘big’ early in your session.  Of course, both ‘big’ and ‘early’ are rather subjective terms.  Ironically, the definition of big probably has less to do with the denomination you are playing and more to do with the size of your bankroll.  If you showed up with $20 and you hit a $100 hand, you’re more likely to stop than if you came to the casino with $1000 and hit a $100 hand.  In the first case, the Player was probably bankrolled too small and in the latter case, it was overkill.  But it is just a normal human reaction to place the size of the winnings next to the amount of money we show up with to determine what ‘big’ is.

            This, of course, leads to an important question - and one that I’m frequently asked.  What is the right size bankroll for video poker?  To answer that, we need to define some things.  First – what is bankroll?  I’m going to drive my English teachers nuts by telling you what it isn’t.  It isn’t the amount of money you put into the machine.  It’s not the amount of money you head off to the casino with.  It (hopefully) is NOT your life savings.  Bankroll is the amount of money that is the maximum you are willing to lose before calling it quits over some period of time.  So, if you go to the casino with $100 in your pocket, but know full well that if you lose it, you’re going to head to the ATM to get more – then $100 is NOT your bankroll.  Conversely, if you’ve got $1000 in your pocket and if you drop $200 you are heading for your hotel room, then the $200 is your real bankroll and not the $1000.

            So, what does this bankroll really do for us?  Well, it sets a maximum that we can lose over some defined period of time.  Maybe it is a single session over a single day/night.  Or, maybe it is the amount we are willing to lose over a week-long vacation.  Why is it important?  Well, besides setting some limits for ourselves, it is also tells us that at the point we’ve lost that much, we are done.  There is no coming back from that loss with a hot streak.  So, if we were to sit at a $5 blackjack table with $5, we have to realize that if we lose that very first hand, we’re done.  If we sit down with $20, then we have to lose 4 more hand than we win (ignoring doubling and splits) to be ‘broke’.  If we sit down with $1000 then we’d have to lose 200 more hands than we won.  With a $5 bankroll, you have a greater than 50% chance of going bust just on the first hand.  With a $1000 bankroll, you might be able to play weeks or months before going bust.

            While we assign a payback to every game, and we can calculate the anticipated loss over a period of time for that game, this is just a theoretical average over time.  Most casino games are fairly volatile which is simple terms means STREAKY.  So, if you play an hour of $5 blackjack, you can realistically expect to lose about $8.  If you start with $100, you’re almost guaranteed to get thru that hour.  If, however you start with $10, your chances of playing the entire hour go down considerably, which ironically means that you would lose MORE than the ‘average’.  By not allowing yourself a reasonable opportunity to come back from a cold streak, you in essence do yourself a grave disservice.  This is why showing up with the right size bankroll is so important.

            One could thus argue that the right size bankroll is one that makes sure that you have ZERO chance of going bust before you are done playing the amount of time you want to play.  There is a certain amount of truth to this notion, but it removes the human element.  It is too easy for us ‘greedy’ human to decide to play longer or up our wager if we have too much cash on hand.  Also, sometimes it is not so practical to do this.  To play an hour at $5 blackjack, we would merely need to show up with $150-$175.  If, however, we wish to play 3 hours of video poker – max-coin quarters – we would need almost $2000 (assuming 500 hands per hour).  This is probably overkill if you’re playing a full-pay jacks or better machine.

            I created a program that simulated video poker.  It started with different bankroll amounts.  If at any point in the 1500-hand session the Player lost more than his bankroll, he was considered to have ‘busted’ and the session ended.  For the moment, I just focused on the percentage of busts and did not bother keeping track of how far into the session the Player was or how he would’ve done had he decided to go beyond his bankroll (i.e. how often does he recover his initial bankroll by using yet more money).

            If the Player starts with 200 wagers ($250 for a max-coin quarter machine), he went bust only 1.39% of the sessions.  If we cut our bankroll down to 120 wagers ($150), our Player went bust just a smidge under 20% of the time.  If the bankroll is reduced to 80 wagers ($100), we find that the bust rate goes up to over 43%.  If the Player tries to get away with a mere $50 bankroll, he’ll find that he’ll lose it all about 73% of the time.  Try and get away with only $25 and you’ll lose the entire bankroll more than 87% of the time.

            So, what’s the right amount of bankroll?  There is no absolute right answer for that.  You have to decide how much you’re willing to risk that your session ends prematurely.  But, if you’re looking for some advice, based on the numbers presented here, I’d go with 120 wagers ($150).   You’ll go bust only 20% of the time, and if you’re night is going that bad, you might just be best off calling it a night.

What To Do When You Win Early

            A couple of weeks ago, a reader sent me a note asking what he should do when he finds himself up significantly very early in a session when he expected to play 4-5 hours.  This is not an easy question to answer as it is really isn’t a math question.  The bottom line is that if you are playing a game with a payback below 100% (you can choose to throw in comps and cashback if you want) then you are playing a game in which you will lose over the long run.  The more you play, the greater the likelihood that you will lose and the amount you are likely to lose (from the beginning of time) continues to go up. 

            Of course, using this logic, you should never play any game with a payback below 100%.  So, if your only reason for playing is winning then you should stop now unless you are playing some of the video poker machines that pay over 100%.  However, as I have long surmised, most of you play in the casino for entertainment purposes.  We all want to win when we play, and the games are created to allow you to win some of the time over short sessions.  So, what is the answer when we’re up $100-$200 after 20 minutes of play after taking a long drive to the casino and expecting to play deep into the night?

            I’ve already explained the mathematical answer, but I don’t think that’s the one my reader was looking for.  So, the question has to be answered more from an emotional standpoint.  First of all, it is good for the psyche to win some of our sessions.  So, it might not be a bad idea to just walk away for the evening.  If you make these trips on a regular basis, giving up the few extra hours of play and driving home may be one solution.  Another possibility is to take your winnings and find something else to do in/around the casino.  Most have some other form of entertainment available.  Go see a show or a movie.  Go bowling.  Head to the video arcade (Pac-man, not video poker!).  This latter one is one of my personal favorites.  I can make a dollar last pretty long on a pinball machine! 

            Another possibility is to take it down in denomination.  If you’ve been playing quarters, maybe you want to try nickels for a little while.  If you’ve been playing multi-play, go back to playing a single hand.  The simple fact is that the math is against you and you can’t change that.  The key is to not allow yourself to lose your psychological edge.  You hold in your hand the casino’s money.  There is no reason to give it back. 

            The last thing you want to do is losing your composure.  It is human nature to get frustrated when the winning streak stops.  We start losing some of what we won and we want to get it back.  So, we start increasing our wager or taking bigger chances in the hopes of recovering some of what we started to give back.  If we were already on a downswing, our bankroll may be dwindling which limits the downside.  Or the credits may almost be gone from the machine so it will give us a reason to stretch our legs.  If, however, we just had a big win, these braking mechanisms won’t be there. 

            At the very least, I advocate hitting the “Cash Out” and taking your ticket out and going to cash it in.  Start with a new $20 after taking a little breather.  We’ve all seen the little disclaimer on advertising (when talking about stocks and the like) that past performance is not necessarily and indication of future gains.  Nothing could be more true for gambling.  In fact, it may be even more true for gambling.  What happened in the past is meaningless.  The game you are playing has a particular payback and that is what you can expect to happen over the long run going forward.  You simply cannot change this.  But, you CAN change how you let it effect you.

                    

Who Isn't Crazy 4 Poker?

             Shortly after  Four Card Poker was being launched, another similar, yet different, game hit the marketplace.  It was called Crazy 4 Poker.  In a recent conversation with Roger Snow, Executive Vice President at Shuffle Master, he revealed that Crazy 4 Poker was invented on January 28, 2002.  How does he remember the specific day?  It was the same day that Four Card Poker went live at Jackson Rancheria in California.  Fearful that Four Card Poker was going to flop, he immediately went to work on its successor game.  As it turns out, he got them both right.

            For reasons not fully known, the game was a big hit in Nevada.  There are currently about 100 Crazy 4 Poker tables, of which 40 are in Nevada.  Virtually every major casino in Las Vegas has one.  Crazy 4 Poker is an important piece in the history of table games.  It introduced the concept of a ‘Super Bonus’ (now more commonly referred to as the “Blind” wager) in Shuffle Master games.  This has become a staple of their more recent games.

            Crazy 4 Poker is broken down into two separate wagers.  The first is called Queens Up is like Pair Plus.  If the Player is dealt a Pair of Queens or better he wins according to the paytable in use.  The second portion of the game is like Ante/Play.  It requires that the Player make both an Ante wager and a Super Bonus wager.  The Player and the Dealer are each dealt FIVE cards to make their best FOUR card hand.

            Once the Player has reviewed his hand, he can either Fold, forfeiting his Ante and Super Bonus wagers, or he can Play.  If the Player has a Pair of Aces or better, he may Play 3 times his Ante wager.  If he has less than a Pair of Aces, he can only wager 1 times his Ante.  Thus, when the Player has a strong hand, he can really sock it to the casino. 

            After all Players have decided what they want to do, the Dealer reveals his hand.  If the Dealer does not have at least a King High, his hand does not qualify.  In this case, the Ante wager is pushed and the Play wager is paid even money.  This means that if you have a strong hand and Play 3x you will still win even money on this when the Dealer does not qualify.  If the Dealer’s hand IS a King High or better, his hand qualifies.  In this case, if the Player’s hand outranks the Dealer’s hand, he will be paid even money on both his Ante and Play wagers.  If the Dealer’s hand outranks the Player’s hand, the Player will lose his Ante and Play wagers.

            The payouts on the Super Bonus wager are a bit more complex.  If the Player has a Straight or better (keep in mind with a 4-card hand, Trips outrank Straights and Flushes), he is paid according to the paytable regardless of the Dealer’s hand.  If the Player beats the Dealer, but with a hand less than a Straight, the wager pushes.  If the Player loses to the Dealer with a hand less than a Straight, the wager loses.

            The strategy for Crazy 4 Poker is rather similar to that of Three Card Poker.  The Player must remember only a single strategy to master the game – K-Q-8.  If the Player’s hand is K-Q-8 or higher, he should Play.  Technically, he must also remember to Play 3x if he has a Pair of Aces or better, but I consider this part of the strategy to be more than a little obvious.  The Player will win 90% of these hands.  It should be noted that K-Q-8 is not actually ‘perfect strategy’.  There are a handful of hands which should be Folded above K-Q-8 and a few that should be Played below.  However, these require taking into account the specific suit makeup of the hand and are more likely to cause errors by the Players than they are worth.  The difference between ‘perfect’ and ‘expert’ strategy is a mere 0.01% of payback.

            Speaking of payback, if you follow the simple strategy provided here, you’ll find Crazy 4 Poker affords a 98.91% payback on the Ante/Play portion of the game.  Given the relatively easy strategy, this is a very strong payback to offer.   As a side note to those that like to play games like this and never Fold.  Never folding in Crazy 4 Poker will take the payback down to 96.5%.  Considering an average wager of more than 3 units per hand, a $5 Player will be throwing away about $15 per hour more by following this wayward strategy.

            Stick to the K-Q-8 and before you know it, you’ll be Crazy 4 Poker too!  You can read more about Crazy 4 Poker and many other games at my website – www.gambatria.com.

The Storm After the Calm

            After Three Card Poker takes the casinos by storm, there is a bit of a lull in activity of new games.  That’s not to say that there weren’t many attempts, some with some success.  Up until Three Card Poker, casinos were not exactly chomping at the bit to put in new games.  Of course, as Three Card Poker grew in popularity and casinos started making that much more money even AFTER paying for the table, they probably began to realize that there was more money to be made with yet newer games.

            Enter Four Card Poker.  My initial reaction to hearing the name of the game was that I hoped it was NOT just Three Card Poker with four cards.  Fortunately, it is not.  Four Card Poker holds an interesting place in my heart.  On one hand, it is one of the few successful table games that was NOT analyzed by my father or myself.  It was developed after my dad passed away and before I jumped into the profession.  Nonetheless, it helped speed my entry into the profession. 

            Shortly after starting to write for Gaming Today in 2003, I received an e-mail from a reader about my Three Card Poker article.  He asked me if I had ever heard of Four Card Poker.  I had just read about the game earlier that day and the gentleman and I had an exchange of a few e-mails.  I finally asked him if he had a financial interest in the game (based on his questions) and he told me that he had just become the President of Shuffle Master (Paul Meyer).  Obviously, he had not been using his company e-mail address.  A few months later, after completing an analysis of Four Card Poker, I wrote an article about it in Gaming Today.  Again, I received an e-mail from Paul, this time commending me on nailing the math for the game.  I had accurately repeated the original analysis of the game.  Paul wound up putting me in touch with Roger Snow, then Manager of Table Games for Shuffle Master.  Roger gave me a few small projects to ‘test’ me and the rest is as they say ‘history.’  Roger and I have been working together ever since.

            Four Card Poker does have some similarities to Three Card Poker.  It is broken down into two games – the Ante/Play and the Aces Up wagers.  The latter is like Pair Plus.  The Player is paid if dealt a Pair of Aces or better.  Despite the name of the game, neither Player NOR Dealer get dealt four cards.  The Player is dealt five cards to make his best four card hand.  The Dealer, in the meantime, is dealt SIX cards to make his best four card hand.  One of his cards is dealt face up, but this makes only a minor amount of difference to our strategy.  To help compensate the Player for the Dealer’s ‘extra’ card, the Player has the opportunity to bet up to 3 times his base wager as part of Ante/Play.  So, he can Fold (forfeiting his Ante), Play 1 times his Ante or Play 3 times his Ante.  Also, there is no qualifying in Four Card Poker.  Once you decide to Play it is your hand vs. the Dealer hand.  There is one additional benefit to the Player in Four Card Poker.  The Player wins all ties.  Ties mean identical four card hands.  The cards not used to make the four card hands are NEVER taken into consideration.  If the Player’s hand beats or ties the Dealer’s hand, he is paid even money on his Ante and Play Wagers.  Additionally, the Player is paid an Ante Bonus if he has a Three of a Kind or better.

            With 5 Player cards and 6 Dealer cards, there are 28 TRILLION possible hands that can be dealt.  This makes creating a program to run all of them impractical.  Instead, we go in search of the beacon hands.  These are the hands that are at the strategy points.  In the case of Four Card Poker, we need to find two of them.  We need to know when to Fold vs. Play 1x and we need to know when to Play 3x instead of 1x.  Much to my surprise, Shuffle Master provided a basic strategy for the game on their information card.  When I simulated this strategy, I found a payback of 98.41%.  When I performed a more complete analysis, I found that I could push this up to 98.60%, but it requires memorizing a strategy that is a bit more complex.

            The basic strategy is as follows:

• Play 3x if you have a Pair of 10’s or Better
• Play 1x if you have a Pair of 3’s through 9’s
• Fold if you have a Pair of 2’s or less

            The Expert Strategy I developed has 6 rules for when to Bet 3x which more fully takes into account the Dealer upcard.  While the additional 0.19% might not sound like a lot, it cuts the house edge by about 12%, which is significant.  If you’re interested in learning more about Four Card Poker, you can order Expert Strategy for Four Card Poker for $5.95.  Send a check or money order to Compu-Flyers, P.O. Box 132, Bogota NJ 07603.

            Four Card Poker was an important milestone in table game development as it showed that Three Card Poker wasn’t just a fluke success.  The Players were looking for more games with more excitement than the casino standards of Blackjack, Craps and Roulette.  Four Card Poker would soon lead to Crazy 4 Poker and then the Texas Hold’em craze started to build.  You can read about some of these other games on my website at www.gambatria.com or you can just stay tuned here and I’ll be covering them in the coming weeks.

Don't Call It Spanish Blackjack

Until the recent emergence of Blackjack Switch, Spanish 21 was the only blackjack variant to make a significant impact to the casino floor. The trash heap is filled with the names of games using only numbers (i.e. 7, 11, 31, 41 and probably everything in between).

Spanish 21 (NEVER call it Spanish Blackjack!) is owned by Masque Publishing, a company you’ve probably never heard of. They are predominately a software company (www.masque.com) and license numerous variations of casino software. For fair disclosure, they have two titles (Video Poker Strategy Pro and Caribbean Stud Knowledge Pro) that were done in concert with my father’s strategies.

Spanish 21 is essentially a very liberal form of Blackjack. Here are some of the highlights of these rules:

Player Blackjack beats a Dealer Blackjack (and is still paid 3 to 2)

Player 21 beats a Dealer 21 (all other ties are pushes)

Player may Double Down on ANY number of cards

Player may Double Down after splitting

Late Surrender is allowed

Numerous Bonus 21 payoffs – 5-plus card 21, 6-7-8 and 7-7-7

‘Free’ Super Jackpot Bonus of $1,000 if player has suited 7-7-7 and dealer has 7 upcard.

As is always the case with table games, rules may vary a bit from one casino to the next, so keep your eyes open for the specific set of rules you’re playing.

So, how does Spanish 21 manage to give the player such a liberal game? Very easily. It uses a big shoe (six to eight decks) and removes the 10’s (NOT the face cards) from the shoe. For anyone who plays blackjack regularly, you know the big cards are good for the player and the little cards are good for the dealer. So, removing 24-32 10’s from a shoe can’t be good for the player.

The rule and deck changes combine to make significant shifts in how we play many hands. The removal of the 10’s causes the dealer to bust far less frequently. Thus, we find the player hits much more frequently against traditional "bust" upcards.

The 5-plus card 21 bonus causes us to hit some very ugly hands, IF we have 4-plus cards, in attempt to secure one of these bonuses. It should be noted, however, that we NEVER hit a hard 17 or greater to go for one of these bonuses. The payouts are simply not compelling enough in these cases.

The removal of the 10’s also causes us to re-think some of our double down situations. We don’t double on a 10 vs. 8 or 9 as we would in regular blackjack. At the same time, we have to be alert to the cases where we have three or more cards and get to a 10 or 11. In Spanish 21, you get to double in these cases.

The bottom line is you have to take your strategy for regular blackjack and throw it out the window.

 While there are, of course, similarities, the differences are significant. They affect every part of the game – when to hit, when to stick, when to double down and when to split.

 Spanish 21 offers the player a livelier version of the game at about the same payback as regular blackjack (99 percent-plus depending on the exact rules) but only if you learn the proper strategy. Fortunately, we’ve already done the hard part!

 Availability: For $4.95 you can order Expert Strategy for Spanish 21 with a full-color pocket-sized strategy card. Send check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603.

How About a Comp System that works?

            A lot of noise was made recently by Las Vegas Sands announcing that they were making significant changes to their comps program.  They were going to greatly reduce the number of free rooms and other things they give out to the masses.  A couple of months ago, I wrote a column about this, expressing that under the conditions that the Sands operates, it really may not be a bad move on their part.  While I think it is a bad idea for casinos that cater to locals to cut back on things like this, I think that the casinos that rely on the out-of-town tourists should have a very different model.

            A few weeks ago, I saw an article that talked about how the Sands was changing its cashback as well.  If I recall correctly, they would now be giving video poker Players back 8% of the theoretical house advantage.  So, if the machine you’re playing has a 1% house edge (99% payback), you be getting back 0.08% of your total wager.  If you’re a max-coin quarter Player, playing 800 hands per hour, you’ll get 80 cents back for each $1000 you drop into the machine.  The expectation is that you’ve lost $10 of that $1000 over the hour.

            I saw a tweet that commented on this, using a full-pay jacks or better as an example.  With a house edge of just 0.4%, the Player will be getting back 0.032% of his total wager.  In my prior example – 32 cents per hour or just under $1 for a 3-hour session.  So, if you go to Las Vegas and play at the Sands, you’ll get back just over $6 if you play every night for 3 hours per night.   I responded to the tweet that this case was non-existent.  Las Vegas Sands does not offer full-pay machines, so their Players will get back far more.  This really is not a good thing, on the whole, for Players.  I’d rather play a full-pay machine then get 3 times the cashback by playing a poor machine.

            That said, I have to go on the record as saying that I think this is the most ridiculous way to calculate cash back.  I’m not blaming the Sands.  Casinos have used ‘cash in’ as the deciding factor for years.  They combine this with a more generic ‘payback’ of a game to determine a percent of ‘cash in’ that Player should receive as a rebate.   To figure out a better system, we should first ask, what is the point of such a rebate?

            Over the past decade or two, many companies have instituted similar such rebates of one type or another.  I have a key ring full of ‘loyalty cards’ that I carry – from my supermarket, drug store and other retailers.  One drugstore gives me a 2% rebate on most of my purchases.  Does this really make me go there for my purchases?  I don’t think so.  But, once a quarter, I get a coupon for a couple of dollars and I feel compelled to use it before it expires.  If I’m disciplined, I buy only things I truly need or buy something that costs only the amount of the coupon.  Of course, we know that it doesn’t always work out so well.  The goal of this cash back is to get me back into the store at a time when I may not really need much of anything and then spend more than the coupon is worth.  This would seem to be similar to the casino model.

            There is, of course, one major difference.  When I buy something in a store, I bring home something tangible.  In the casino, it is not quite the same.  I hope you all enjoy the entertainment you get there, but you’re not bringing a specific item home.  Also, the need for discipline is far greater in the casino.  $2 is $2 in the drugstore.  In the casino, some can make their money last much longer than others.

            So, if we have two players who play identical video poker machines and one plays it ‘Expertly’ and plays at 99% and the other plays it rather poorly and plays only 95%, why should they receive the same cashback.  Mind you, I’m not talking about how they ACTUALLY do with their bankroll.  I’m talking about the theoretical payback of how they play each hand.  The machine can be easily programmed to keep tabs on this.  In this scenario, the Player who plays poorly will actually receive more money than the one who plays properly.  From a casino perspective, I would think this would be a no-brainer!

            Let’s be real, here.  If I’m playing the machine, why would the casino want to give me much money back?  I’ll drop $30 in 3 hours and then they’ll give me $2.40 cents back.  Realistically, they can’t give me much more.  Also, if I’m a good Player, I’m losing relatively little and just how much incentive do I need to come back?  Will $2.40 really bring me back to this casino?

However, if I’m a bad player and my play would dictate that I should lose $150 in those 3 hours, I would now get back a $12 rebate.  If I’m that casino, I want to bring back this Player more than the Expert Player.  Give him $12 to play with.  He’ll likely lose far more than that while playing at 95%. 

            So, yes, I AM advocating that bad Players get more cashback than good Players.  However, I’d still rather be a good Player getting less in cash back than a bad Player getting more.  Some of you may wonder about a system that pays cashback based on how much the Player actually wins or loses.  In a future column, I’ll discuss my thoughts on that.

            I’d like to hear what you have to say about this, so PLEASE feel free to leave comments – but let’s all be civil!

How About That Strategy? It Works!

            This pretty much speaks for itself:

http://fbg.me/App/Posts/BlogPost.aspx?pstid=29444&pstaid=462

             Someone playing a $2 full-pay max-coin Double Double Bonus Poker hits an $8000 Royal Flush starting from a 2-Card Royal!  Without knowing who hit it (and I don’t), we really don’t know to what extent this Player follows Expert Strategy.  For all I know, he discarded a Pair of Jacks to go for the 2-Card Royal.  But, lacking this information, I’m going to use this picture to demonstrate some key components of Expert Strategy.

            Play the right machine – Well, Double Double Bonus isn’t exactly the ideal machine to play with its 98.8% payback.  However, it multiple jackpots (Royal and 4 Aces w/kicker) has made it immensely popular.  From the picture we can see that the Player chose to play one that is full-pay (1/1/3/4/6/9).  Before the payout on this hand, the Player had about $535 remaining in their bankroll.  If they play a short-pay machine, perhaps the bankroll is exhausted before they have the opportunity to win the $8000!

            Know the right strategy – This is really the crux of this column.  We don’t know what hand the Player was dealt, but we do know that he held the suited J-A.  2-Card Royals make up about 7-8% of our playable hands.  Misplaying them can be rather dangerous to your bankroll.  When my father, Lenny Frome, developed his first strategies for video poker, one of things that surprised him was that most 2-Card Royals outranked 3 High Cards.  Given the unlikely odds of hitting a Royal, intuitively, one might think that you’re better off having 3 High Cards increasing your chances of a Jacks or Better or a Straight.  But by holding 3 off-suited cards, you eliminate all chances of a Flush, reduce the likelihood of Trips and eliminate Quads and the Royal.

            ‘Unlikely’ is also a relative term.  The actual odds of hitting a Royal from a 2-Card Royal is ‘only’ 16,215 to 1.  In the grand scheme of the casino, this isn’t really all that rare.  If one out of 13 hands is a 2-Card Royal and 1 in 16,215 of these will result in a Royal Flush, then we’re talking about 1 in 210,000 hands will have this ‘fate’.  At 700 hands per hour, this means about 300 hours of play.  Depending on how serious of a Player you are, this might take weeks or months, but in a casino with hundreds of video poker machines being played 10-15 hours day each, it’s happening every day all over the place.  So, why not you?

            Of course, you increase your chances of it being you if you play your 2-Card Royals correctly.  This will, of course, depend on the specific game and paytable you are playing.  In the case of Double Double, here are some key pointers:

            -  A 10-A 2-Card Royal is NOT playable.  We hold only the Ace if we have no alternatives.

            -  We Play J-Q-K-A (off suit) over a 2-Card Royal

            -  Pay attention to all of your cards and don’t just focus on the 2-Card Royal.  You might be dealt 4-5-6 of one suit and a J-Q of another.  The 3-Card Straight Flush outranks the 2-Card Royal by a considerable margin.

            -   Do NOT discard any Pairs to go for a 2-Card Royal

            This list is hardly meant to be comprehensive.  If while reading it you realized that you didn’t know these things, you might want to brush up on your game before you spend real money.  As always, it is important to learn the strategy table of the game you intend to play and stick to it. 

            This way, maybe next time I post up a picture of a big jackpot, you can sit back and say “That’s MINE!”

Lenny Frome Left a Legacy to Casino Gambling World

(the following is a re-print of my column in this week's edition of Gaming Today)  

            There are days in our lives that we all have burned into our memories – weddings, births of our children and regrettably, the passing of someone dear.  As this article goes to print in Gaming Today, I will be remembering one of those days – the 13^th anniversary of my father’s passing.  I will never forget my brother telling me that my dad had had a heart attack.  When I asked him how he was doing, he responded “he isn’t.”

            I could fill up this entire edition of stories about my dad as a dad.  I’m not sure exactly how long he wrote for Gaming Today, but I believe it was 8 or 9 years, which means we could fill this edition with the hundreds of articles he wrote.  But, why think small?  If one wants to see the legacy my father left to the casino world, one only needs to walk into virtually any casino in the world.

            A good gaming analyst doesn’t just crunch the numbers.  He works with the inventors to create the game.  You need the creative side to envision the cards and the betting, but the math is the glue that holds it all together.  So, the analyst may not have his name on the patent and he may not get technical credit for inventing the game, but there is no doubt that a good analyst helps to invent each game he works on.  So, try to walk into a casino and not see Lenny Frome’s handiwork. 

            You see some Let It Ride tables?  He worked with the founders of Shuffle Master to save that one from a horrible fate (a math error).  How about some Caribbean Stud tables?  Yep, his name is on the math for that one too.  Three Card Poker?  Yes, he worked with Derek Webb to refine the math and rules of the game.  He worked on Boston 5 from New Vision Gaming.  He worked on Spanish 21 with Masque Publishing.  He worked on dozens of other games that hit the casino floor but didn’t quite make it to success.  But even these failures opened up the doors to dozens more.  Imagine walking into a casino and having none of these games be there?  It would be like Las Vegas circa 1980!

            Of course, on the other half of the floor, we’d all be stuck with nothing but slot machines!  Oh, the horror!  Where would the casino of 2011 be without Lenny Frome’s contributions to video poker?  I don’t know who first called him the ‘godfather of video poker’ but it’s a nickname that has stuck through the years.  You can even find this on his Wikipedia page (http://en.wikipedia.org/wiki/Lenny_Frome) – which, by the way, I DID NOT create!

            Despite the accolades, when it came time for my father to choose an e-mail address – he didn’t choose “vpgodfather”, “vpguru” or “vpexpert”.  He chose “Playerspal”.  He tried very hard to create games that while they obviously had house advantages, at least gave the Player a fighting chance.  What he loved about table games and video poker was that everything was known and could be calculated using finite math.  He hated the slots because everything about them was a deep dark secret.  He called himself Playerspal because that’s how he saw himself.  He was there to educate the Players about how to play the games.

            Well, so far this has been about my father as a gaming analyst.  As I said earlier, I could fill up this entire edition of Gaming Today with stories about my dad as a dad.  Of course, there would be some similarities.  Education was very important to my father.  It didn’t really matter what the topic was.  Shortly after arriving in Las Vegas, he wound up teaching at UNLV.  Here was a guy who could ace my AP Physics tests at the dinner table without a calculator and he was teaching a relatively low level algebra course in college.  Still, he had the patience to teach the kids to the best of his ability and he took it far more seriously than many full-time professors I had in college.  It meant so much to him.  This is one of the reasons why my family started the Leonard Frome Memorial Scholarship at UNLV after he died. 

            Another thing very important to my father was his family.  He adored his children and grandchildren.  So, in an attempt to put together two very important things in my father’s life – children and education, I’m asking my readers to help me with a little project.  I found out via twitter (@gambatria) that my friends at Shuffle Master are having a book drive to help a Las Vegas based organization called “Spread the Word Nevada” which promotes literacy by distributing books to elementary schools throughout Nevada.   My wife and I will be shipping to them a few dozen gently-used books  from my kids’ home library.  I’m asking my readers to check out their website and if you are so inclined to assist them in any way you can – whether via a monetary donation, donating books or volunteering. 

            I’ll get back to gaming tips next week.  

What Would You Do? A VP mini-quiz

            There are few games in the casino that require learning a strategy as complex as video poker.  Really, only blackjack (and its variants like Blackjack Switch and Spanish 21) comes to mind.  Fortunately, as complex as the strategy is, about 75% of video poker hands become fairly obvious after a little bit of time spent studying and some time spent practicing.  The tough part is the remaining 25% of the hands.  Some require a bit of thought and some require some serious concentration.  It is these hands that separate the average Player from the true Expert Player.

            Consider the following hand in full-pay jacks or better:

3♣       8♦        10♥      J♦         Q♦

            It is not a very pretty hand and I dare say that most beginners are probably not going to play this one correctly.  If they do, it may be more by accident than by design.  So, which way should you play it?  If you say “the way which gives you the highest expected value”, you’re right, but you’re cheating a bit.  Which way has the highest expected value?

            I think we can all agree that we’re NOT going to hold onto that 3♣ under any condition.  So, that leaves us with 4 hands to consider:

            1)         8♦        10♥      J♦         Q♦

            2)         10♥      J♦         Q♦

            3)         J♦         Q♦

            4)         8♦        J♦         Q♦

            Option 1 is a 4-card Inside Straight with 2 High Cards.  If you look for it on the strategy table, you won’t find it.  The expected value is about 0.47.  By itself this doesn’t make it unplayable, but  at least one subset of these 4 cards always has a higher expected value.

            Option 2 is a 3-card Straight.  The expected value is 0.44.  Again, you won’t find it on the strategy table, meaning some subset of these cards always has a higher expected value. 

            Option 3 is a 2-Card Royal.  A J-Q Royal is categorized as a V3 for the highest ranking Royal as it consists of 2 out of JQK.  If the two cards consists of an Ace and one of JQK, then it is V2.  If it consists of a 10 and one of JQK, it is a V1 and if it is an A10, it is a V0.  We WILL find this one on the strategy table.  It has an expected value of 0.60.  The expected value of this specific situation is 0.59 as a result of discarding the 10 and the 8 reducing changes for Staights, Flushes and even a Straight Flush.  The fact that we find it on the strategy table, at least means that this MIGHT be the right answer.

            Option 4 is a 3-Card Double Inside Straight Flush with 2 High Cards.  It almost sounds like something you would order at Starbucks!  When we look on the strategy table, we’ll find that it has an expected value of 0.64.  Discarding the 10 brings the actual expected value of this hand to 0.63, which is still a bit higher than Option 3.  So, in the end, never mind Starbucks, this is the hand you want to ‘order’ if dealt the five cards described earlier.

            I’d like to say that there is some sort of easy way to remember that this is the right way to play the hand, but there isn’t.  To make matters worse, if you were playing a Progressive with the Royal paying 1600 instead of the usual 800, Option 3 would actually have the higher expected value and become the proper play.

            Will you obliterate the payback if you always play Option 3?  No.  The hand is infrequent enough and the impact small enough that you will only cost yourself marginally.  You’ll also hit a few extra Royals (over a lifetime), so this might make up for the lost bankroll.  But, Expert Strategy is about playing the right hand all the time and avoiding playing any sort of hunches or going for the big kill.

            There is one other lesson from this example.  One of the most forgotten hands in video poker is the Straight Flush.  Players are quickly taught to ignore 3-Card Straights and 3-Card Flushes in most versions of video poker.  However, the 3-Card STRAIGHT FLUSH (and all its variations) are quite playable in most games.  While they all have expected values below 1.00 and thus are ‘losing hands’, this doesn’t mean that playing them incorrectly is okay.  It is just as important to play the losing hands correctly as it is the winning hands.  Perhaps more so as there are far more losing hands than winning hands.  

Is that Harry Potter playing Blackjack?!

            A couple of months ago, my son, who is a college freshman , and I were walking through a local mall when he was telling me about some of the interesting people on his campus.  Apparently, there is one young man who wears ‘wizard’ clothing every day.  My son remarked “maybe if you’re buying all your clothes at Party City, you need to change your wardrobe.”  Maybe the kid was just hoping to land the job as official spokesman of the new game Blackjack Switch.

            We’ve all sat down at a Blackjack table at some point and watched as we are dealt a series of bad hands.  After a while, we notice the person next to us is being dealt hands just as bad, but like a mirror image.  We’re getting 5-10, he’s getting face-6.  Sooner or later, one of you joke how you wish you could switch your 2^nd cards with each other.  Geoff Hall decided to do something about it.  He invented Blackjack Switch.

            It’s a very simple concept.  You play two Blackjack hands (equal wagers).  The Dealer deals you your regular 2 cards for each hand.  When it is your turn, you can ask him to switch the 2^nd cards of the two hands.  So, if you’re dealt a 5-10 and a face-6, you now have a 5-6 and a 10-Face.  Two really lousy hands just became two killer hands!  So, what’s the catch?

            Well, being able to switch your cards like this is a pretty big advantage for the Player, so the house has to take a few things back.  First, a Natural Blackjack pays only even money.  A switched Blackjack only counts as a regular 21.  The ‘biggie’ is that a Dealer 22 (i.e. a busted hand) will PUSH against all Player non-busted hands EXCEPT a Player Natural Blackjack.  Other than that, the rules are pretty standard and moderately liberal.  The Player can double down on any two cards.  He can split until 4 hands.  (It should be noted that you should verify these rules before sitting down to play as casinos can sometimes choose to tighten up the rules a bit).

            Blackjack Switch gives the Player the opportunity to spend a lot more time playing good hands.  In order to get to this position, however, you’ll need to learn a whole new layer of strategy dealing with WHEN to switch cards.  Unfortunately, there is no simple strategy I can provide you.  The only way to know when to switch is by comparing the expected values (EV) of your initially dealt hands with the expected values of your potentially switched hands.  On a positive note, I’ve already done the hard part – calculating these expected values.  So, you just need to look up your hands on a simple chart.

            The second part of the strategy is knowing when to hit, stick, double and split.  The bad news is that if you attempt to use standard Blackjack strategy for Blackjack Switch, you’ll DOUBLE the house advantage even if you switch at all the right times.  The Dealer pushing on 22s greatly alters our strategy.  Doubling on soft hands is nearly nonexistent.  A Dealer upcard of a ‘2’ is transformed from a so-so upcard into a rather powerful one for the Dealer.  The bottom line is you need to throw out everything you learned about regular Blackjack strategy and replace it with a new Blackjack Switch strategy.  Again, I’ve done the hard part and figured out when to hit, stick, etc…

            When all is said and done, if you learn when to switch and you learn the right strategy, Blackjack Switch will afford you a payback right up there with regular Blackjack (about 99.4+%).  At the same time, you’ll be playing a more entertaining version of the game that keeps you involved in the play because you will be busting less often as you will have much better hands on average.

            Shuffle Master is the worldwide distributor of Blackjack Switch and from what I’m told you can now find more than 100 tables in the marketplace, and it is growing monthly.  You can read more about the game and where to find it on their Blackjack Switch Facebook page (www.facebook.com/pages/Blackjack-Switch/167559943295302)

            I just picked up from the printer my brand new booklet Expert Strategy for Blackjack Switch.  It comes with a full-color 4-panel double sided strategy card which has both the expected values to help you decide when to switch AND the hit/stick strategy.  It will also go into far more detail on how the strategy was developed (and why it is mathematically sound!) and what to expect from this new Blackjack variant.  The booklet and strategy card sell for $6.95, but I’m running an introductory special for the month of March of just $5.95.  Additional strategy cards can be ordered for just $1.50 if you order the booklet or for $2.95 alone.  Head on over to my website at www.gambatria.com and download the order form to order or just send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603

You can be a Three Card Poker expert too!

            This past week, I posted something on the Facebook page for Three Card Poker.  Shuffle Master asked people to relate their best story about Three Card Poker.  So, to get the ball rolling, I posted the following true story:

I'll get the ball rolling: A few years ago, my wife and I sat down at a Three Card Poker table (I think we were at Sunset Station). It was the first time my wife ever sat a casino table game. We had covered the basics of how to play the game (strategy-wise), but after the Dealer gave her her chips, she looked at me and said "now what do I do" - meaning just where to put the wagers. The woman to her right struck up a conversation by telling my wife exactly where to put the chips and how to play. She told my wife that you "'usually play with Queen or better, but sometimes you 'Play' with a Jack and can beat the Dealer." It took all my wife's strength to not respond to the woman, "Do you have any idea who my husband is? He WROTE THE BOOK on Three Card Poker!" (literally). This is an absolutely true story, and unless someone recognizes me - I don't tell anyone who I am in the casino so that's why my wife didn't say anything.

            In response, another reader, posted the following:

‎^^^ little cocky huh? 

By the way Q-6-4 is a great strategy - if you work for Shuffle Master.

Q-J, Q-10 isn't even a good one. King high only, but you did write a book on it so you must know what you're talking about.

            I couldn’t really argue with the ‘cocky’ part.  When it comes to gaming math, I am one of the experts.  Nearly every successful proprietary table game in the casino has had either my father’s work or my work behind it.  The rest of this person’s response had me a bit befuddled.  Queen – Six – Four is not a great strategy if you work for Shuffle Master.  It’s a great strategy (and the best strategy) if you play Three Card Poker.  In fact, it really is ALL you need to know to be an expert at the game.

            This poster seems to have it backwards.  It is not because I wrote a book about Three Card Poker that I know what I’m talking about.  It is because I know what I’m talking about that I wrote the book Expert Strategy for Three Card Poker.  My father worked with the inventor of Three Card Poker.  Several years ago, when Shuffle Master had a Three Card Poker tournament, they came to me to write a strategy booklet on the best way to play for Tournament Play.  But, it’s not because of all this that I know what I’m talking about.  It is because I can prove mathematically that Q-6-4 is the best strategy that I know what I’m talking about.

            How does one go about proving this?  In the case of Three Card Poker, it is very simple.  There are 22,100 unique 3-card hands you can receive from a 52-card deck.  For each of these, there are 18,424 possible Dealer hands.  Using a computer program, I run every one of these hands (just over 400 MILLION hands) and determine for each of the 22,100 Player hands whether the Player is better of Playing or Folding.  If the Player wins back at least the 18,424 units he would wager playing against each of the Dealer’s 18,424 possible hands, then he should Play.  If not, he will lose less by Folding than he would by making an additional wager.  When you analyze the results of this program, you find that the decision point is at Q-6-4.

            At Q-6-4, the Player will wager 18,424 additional units, but win back 18,546.  His net loss will be 18,302 which is still a bit better than Folding and losing 18,424.  At Q-6-3, he will win back only 18,377 creating a net loss of 18,471 which is a bit more than he would if he just Folded.

            So, the poster, seemingly attempting to mock my answer, suggests three other possible strategies – QJ, Q10 and even King High.  How do these stack up?  Well, QJ will get you a payback of 97.61%.  Q10 will get you a payback of 97.28%.  If you want simplicity and go with King High then the payback falls to 96.84%.  The payback for Q-6-4 is 97.98%.  So, there is a clear difference, but it may not seem so big to some of you.  So, let’s flip this around to look at the house advantage (100%-payback).  For Q-6-4, we give up 2.02% to the house.  For QJ it become 2.39% or nearly a 20% increase.  For Q10 it goes up to 2.72% for a 35% increase.  Last but not least, for King High, the house advantage goes to 3.16% or a 55% increase. 

            There are times when you may want to simplify the strategy to reduce errors with a tradeoff of some payback.  However, I really don’t think remembering Q-6-4 should push anyone’s brain to the limit.  It’s your money, you can lose 20-55% more by picking a different strategy or you can become an expert and remember Q-6-4.  Not because I wrote the book and not because I ‘must know what I’m talking about’, but because it IS the BEST strategy.

Everyone's a Joker!

            I’m continuing last week’s column by continuing the discussion of Joker Wild video poker.  This game is still available in numerous casinos around Las Vegas and offers a 100.65% payback.  As always, of course, it offers this payback ONLY if you find the full-pay paytable.  You should be looking for the following:

Hand	Pays*
Royal Flush (Natural)	800
Five of a Kind	200
Royal Flush (Joker)	100
Straight Flush	50
Four of a Kind	20
Full House	7
Flush	5
Straight	3
Three of a Kind	2
Two Pair	1
High Pair (K’s or A’s)	1

* With Max-Coin play

            There are a total of 50 entries on the strategy table for this version of Joker Wild.  However, they are split up between Joker hands (23) and non-Joker hands (27).  When thought of this way, the process of learning the strategy table becomes much simpler.  First let’s focus on the non-Joker hands which make up almost 90% of the total hands.

            The top half of the non-Joker strategy table has few surprises.  Most of the hands are the pat hands for which there is little to decide.  One key point is that you will discard a Straight to go for any 4-Card Straight Flush.  You do NOT break up a Flush, however, for these cases.  A 3-Card Royal ranks above a High Pair, but below Two Pair and 4-Card Straight Flushes. 

            The bottom half of the non-Joker strategy table contains the hands with an expected value less than 1 so these are the messier partial Straights, Flushes and Straight Flushes.  The key points here are NO 3-Card Straights are playable and NO 3-Card Flushes are playable.  3-Card Straight Flushes, however, are quite playable, but generally below a Low Pair (except for a non-inside 3-Card Straight Flush), but ABOVE the equivalent 4-Card Straight.  So, if you have a 3-Card Straight Flush that is also a 4-Card Straight, you stick with the 3-Card Straight Flush most of the time.  The payout of only 3 on the Straight makes a significant difference for these hands.  If you have a 2-Card Royal that is A-K, K-Q, K-J or K-10, it will outrank holding only the single High Card.  However, it is preferable to hold a single A or K over a 2-Card Royal of 10-J-Q (2 of the three).  A 2-card Royal consisting of an Ace but not a King is not playable.

            It probably is no surprise that on the non-Joker half of things, 3 hand types make up about 70% of all our hands dealt – Low Pair, 1 High Card and Razgu.  This last hand – where we throw all 5 occurs about 12.5% of the time for hands without a Joker, which is 4 times more frequent than in jacks or better.

            On the Joker side of things, we find that the lowest playable hands are 4-Card Straights and 4-Card Flushes.  If after accounting for the Joker you still have an Inside 4-Card Straight, you do NOT play this (i.e. 4-5-JKR-8-Q).  As in non-Joker hands, a 3-card Straight Flush is played over a 4-Card Straight.  Since every hand with a Joker is by its very definition at least a Pair, which one of the 4 remaining cards to you decide to keep if dealt nothing much but the Joker?  You don’t!  Over 10% of our Joker hands will result in a Joker Razgu where we throw the other four cards.  There is no Joker Low Pair hand in Joker Wild.

            There are three secrets to winning at Joker Wild video poker.  The first is to find the right game to play.  There are a lot of different paytables out there and even a variation of Joker Wild that pays beginning at Two Pair, albeit harder to find and not nearly as lucrative.  The second secret is learning the strategy.  It’s really not that hard of a strategy to learn, but if you go in trying to adapt your jacks or better of your Bonus Poker strategy to Joker Wild, you’re going to get killed.  Last, but not least, you need to get your fair share of Jokers.  The payback is all in the Joker hands and if you don’t get your fair share of them, you’re not likely to have a winning session.  The good news is that the payback is above 100%, so you only need your fair share.  If you happen to get even more – all the better for you.

A Wild Ride on the Positive Side

            Frequently, people come up to me asking what is the best game to play in the casino and then answer it themselves by saying, “blackjack, right?”  By saying ‘best’, I usually assume they mean the best paying.  As table games go, they are essentially correct, although it may depend on the exact rules being used.  As for the best paying games (not just table games), the answer to that one is without a doubt video poker.  A decade ago, finding a video poker machine paying 99.6% or better in Las Vegas was easier than finding those little sheets of paper with semi-naked girls on them strewn on the strip.  Today, you have to search a little harder, but they are still there.

            While my father, Lenny Frome, added greatly to the popularity of video poker through his hundreds of articles and numerous books, he is also probably partly responsible for the disappearance of these ‘positive’ games.  Let’s be real.  The casinos don’t exactly purposefully put out games over 100% very often.  No one knows exactly why ANY were allowed to hit the casino floor.  We can only assume that because so many players played so poorly in the early days that the casinos never bothered to notice the few who might take advantage of the situation.

            Also, unlike a table game, which focuses more on a table minimum, video pokers focus on a machine maximum.  A $5 blackjack table allows the player to frequently play up to at least $500.  If that table were somehow created to allow a Player advantage, the Player could win a lot of money at $500 per hand.  With a mere 0.65% Player advantage and playing 30 hands per hour, a $500 blackjack Player could win $110 per hour.  Not a bad salary.  A 25-cent video poker machine allows for the Player to play $1.25 per hand.  At 800 hands per hour, this is still only $1000.  A machine paying 100.65% will afford the player a $6.50 per hour profit.  It beats losing, but tough to make a living off of it. 

            Why did I pick 0.65% as the Player advantage?  This happens to be the advantage for a relatively common form of video poker – Joker’s Wild (A-K).  When I say ‘common’, I don’t mean that you’ll find it at every casino.  I’m not sure you can find any 100+% payback machines along the mid-strip area of Las Vegas.  So long as the Players there are in awe of the marble statues while they play short-pay machines, there is no reason for the casino to offer anything but.  According to my friends at VPFREE, you can find these machines in about a half-dozen casinos in Las Vegas. 

            Now, before you go giving up your day job to go play these Player-friendly machines, I have to tell you that the highest denomination you’re going to find is a quarter machine – which will generate the $6+ per hour I mentioned earlier.  The casinos have figured out that a quarter machine will not attract the professional video poker Players and thus they don’t care much if a couple of people walk away a winner every now and then.  But as I said earlier, it beats losing.

            Learning Joker games can appear to be a bit challenging at first.  The strategy table has 50 entries on it which makes it rather long.  However, when you realize that the hands are broken down to Joker vs. Non-Joker, you realize that you actually have 2 relatively short tables to learn.  The fact that game pays for a Pair of Kings or Better (and not Jacks) means that the need to keep track of the number of High Cards is greatly diminished. 

            One of the toughest parts about playing a Joker’s Wild game is the volatility.  If you don’t get your Jokers frequently enough, you don’t stand much of a chance.  Joker hands account for just under 10% of the total number of hands.  The payback when you have a Joker is a whopping 286%!  For the other 90+% of the hands it is a mere 81.3%.  Expect to see wild swings in your bankroll with this one.

Happy Birthday to the Father of our Country!

Many years ago, I remarked to a high school classmate that I shared a birthday with George Washington. He looked at me and said, "you were born on the third Monday in February?". I just didn't know how to respond!

Today is the 279th anniversary of the birth of George Washington - and my 45th birthday. I'm trying not to think too much about being "mid 40's". I'd rather just go with you're only as old as you feel! Um, er...On second thought that may not be a good idea either. How about, you're only as old as your children make you feel? No, that doesn't work either - I have a teenager who keeps telling me how old I am. How about, you're only as old as your YOUNGEST child makes you feel? I like that one. My four-year old likes to jump on me like I'm still 20-something, so I'll stick with that one.

Well, all over the country they have been having President's day sales this past weekend. The cool part about being the 'President' of a company is I get to have a President's day sale in my own honor! For this week only, we are offering our best-selling books at a very special price of $4.50 (for my 45th birthday!), which includes shipping and handling (in the U.S.). Pick from Winning Strategies for Video Poker, Video Poker: America's National Game of Chance or Expert Video Poker for Las Vegas. You can order one or as many as you'd like. Send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603. Please make sure it is postmarked by 3/1/11.