Thursday, October 11, 2012

New Games at Global Gaming Expo from SHFL

            It is hard to believe that a year has gone by since the last Global Gaming Expo.  Last year, I previewed three games that were on display - Cincinnati Stud, Six Card Poker and Money Market.  To date, one of those (Six Card Poker) has had some success while the other two continue to try and make inroads into the casino.  As I've written many times, no one can guarantee the success of a game.  It is far easier to predict failure.  This is because some attributes of a game are likely to result in the game failing and because 99+% of all games developed fail.

            Because of the extensive analysis and development work that I do with Shuffle Master, I often get to provide a preview of their games to Gaming Today readers.  This year is no different.  I have been told that Shuffle Master will be showcasing both existing successful games, such as Ultimate Texas Hold'em and Mississippi Stud and some very new games like House Money (both Blackjack and Baccarat versions), 6-Card Fortune Pai Gow, Raise It Up, Straight Jack Progressive, Face Up Stud Poker and Free bet Blackjack.  I can't cover all of these games in detail in this column, but I'll do my best to give a little synopsis of each. 

House Money -  I've written about this game twice in the past few months.  Obviously, I'm not the only one who thinks this game is a winner.  This week, House Money Blackjack won an award as the Best Table Game Product or Innovation as determined by Global Gaming Business magazine.   It is a very simple blackjack sidebet, but with a twist.  If you are dealt a Pair, a 2-Card Straight or a 2-Card Straight Flush, you win.  Now you have the option to add your winnings to your base blackjack wager.  So, if you're dealt a Pair of 10's looking into a Dealer 6, you can add your winnings to your base wager and take home even more money.  A similar concept has been developed for Baccarat, but here you win if the Player or the Banker hand is dealt a Pair, and even more if both are dealt Pairs.  You may then take your winnings and place it on the Banker or Player hand  - your choice - regardless of how you played your original wager.  So, if you originally bet Player and the Banker is dealt a Pair of 9's and the Player is dealt a Pair of Jacks, you can STILL take your winnings and put in on the Banker hand - which has already won the hand!

6-Card Fortune Pai Gow -  Have you ever found the House Way to be confusing at Pai Gow?  Well, those days are gone.  In this version of the popular game, the Player and the Dealer each get 6 cards to make a 5-card hand and a 1-card hand.  The Dealer CANNOT break apart any sets (i.e. Pairs, Trips) unless he has 2 Three of a Kinds, a Straight, a Flush or a Straight Flush.  Also, the Player does not LOSE all 1-card hand ties with the house.  It is Pai Gow but even simpler.

Straight Jack Progressive -  This is another blackjack sidebet, but with a Progressive payout.  If your first 2-cards form a 2-card Straight, you win.  You win more if your third card continues the Straight.  If you get dealt a 6-card Straight (A-2-3-4-5-6) you can win a jackpot.  If at any point, your 'hit' card causes the Straight to end, you still win for the longest straight you were dealt, even if the hit card causes you to bust (but the bust card CANNOT extend the Straight).

Free Bet Blackjack-  A new version of blackjack that utilizes the Push 22 rule from Blackjack Switch.  Here you have the opportunity to get certain splits and double downs for free (no additional wagers required to play them). 

Raise It Up - A little like Let It Ride with some Ultimate Texas Hold'em sprinkled in.  This is a 6-card poker paytable game.  You combine your 3 cards with three community cards.  You're not playing against the Dealer, only a paytable.  You win with a Pair of 10's or better.

Face Up Stud Poker - A whole new concept for a table game.  You get to see the ENTIRE hand of the Dealer, but only a portion of your own.  Based on your partial hand, do you think you can beat the Dealer's hand?  If he's got a weak hand, the chances are far greater, so the payout is lower.  If you can beat a strong hand, you can win a lot of money on a single hand - 8 to 1 for beating Trips; 50 to 1 for beating a Flush, etc...

If you make it to the show, I strongly suggest you stop by the Shuffle Master booth and give these games a try.  I find the only way to get a good sense of a game is to sit and play a dozen or two hands.  I'm looking forward to playing these and also wandering around the rest of the Sands Convention Center in search of the next big casino game - almost sounds like a reality tv show, doesn't it?   If you see anything that you find interesting, shoot me an e-mail at and let me know where I can find it. 

Wednesday, September 26, 2012

It is not about the Medium

            I don't think there is a game in the casino more misunderstood than video poker.  Even in the days when slots were mechanical, most people considered video poker to just be another slot machine, but one with a computer screen.  I think many people just think that it was too hard to create a mechanical machine using cards, so they digitized it all, but it still plays like a slot machine - all because the hardware looks roughly the same.  It is NOT the hardware that makes the game.

            This past week, I met a gentleman who told me he likes to play keno slots.  I have to be honest and say I had no idea what he was talking about.  He explained that he picks a certain amount of numbers from 1 to 80 and then the machine picks 20 numbers and he gets paid if the 20 picked includes at least some amount of the ones he picked.  I politely looked at him and said there is nothing 'slots' about what he just described.  He simply was playing keno in video version (hence it is called 'video keno').  He was playing the EXACT same game as if he was playing in a keno parlor marking the little pieces of paper and handing them to the scantily clad woman.  Ironically, the video version of keno tends to pay higher than the old fashioned version because the Player can play far more hands per hour.  I explained to this man that the machine pulls 20 completely random numbers and throws them onto the board.  It does NOT decide ahead of time that you will hit 3 of the 8 you marked and then decide which numbers to pull to make that happen.

            This is in essence the very difference between a slot machine and a video keno machine or a video poker machine or a video blackjack machine.  In the latter three games, the machine uses a random number generator to decide which card to deal or which ball to draw.  You win or lose based on the specific cards/balls it randomly draws.  In a slot machine, the machine first determines whether your will win or lose.  If you are to win, it will decide how much you will win and set the symbols in the appropriate fashion.  If you are to lose, it will decide exactly which symbols to show you - always a losing combination - but potentially set up to make you feel like you almost won. 

            Over the years, when I've been asked what I do for a living and explain that I analyze casino games, a frequent follow up question is if I do it for live games or electronic games.  Since the majority of my work is in table games my response is usually just that, but I tell them it really doesn't matter what medium the game is in.  As long as the game is using essentially a random deck of cards (or ping pong balls) where each card has an equal chance of appearing, it does not matter if you are playing a game with a real life dealer, at a casino on an electronic multi-player table, on a stand-alone machine in the casino or playing at home on some software.

            Video blackjack has existed for years in the casino.  They were not always easy to find, but many Players relished the idea of playing for only $1 per hand and having the same experience (well, mathematically) as playing at a live table.  I would certainly understand those that feel that playing on your own machine is not as sociable as playing at a table, but that's not a mathematical difference. 

            In the past few years, many casinos have added multi-player electronic versions of popular table games (i.e. Shuffle Master's TableMaster games).  These games play identically to the live games.  There are times when for one reason or another the casino chooses to employ different paytables, but the probabilities of winning a hand or losing a hand or being dealt a particular hand remains the same.  Any changes to the payback as a result of paytable changes cannot be sneaked past the Player.  These payouts must all be visible on the machine.   Because the digital cards are as random as real cards, we can always calculate the exact payback of any of these games based on the paytable. 

            While the name "Slot machines" presumably comes from the different slots the wheels are in (well, were in when they were mechanical), and there is a little bit of similarity in the notion that video poker cards are in 'slots' in the machine as well, this is where the similarity ends.  The critical difference between games like video poker and slots is that in video poker your cards are determined randomly and you win or lose based on the pattern of these cards.  With slots, whether your win or lose is determined by the machine and then you are presented with symbols to match the pre-determined outcome.   Slots could never be replicated on a live table, but games like video poker, video keno and video blackjack are (or could be).

Thursday, September 13, 2012

Strategy is Underrated

          I can't stress enough the importance of using the right strategy when playing in the casino.  Over the years, I've heard all sorts of excuses for why people abandon strategy, ranging from it doesn't matter in the short run to some anecdotal story about how someone they know threw strategy to the wind and it paid off massively.  Yeah, that's nice.  If you're a sports fan, you know the importance of having a good coach or manager.  There are reasons why Pat Riley, Joe Torre and Bill Parcells are in such high demand.  Yes, it is because they win.  And they win because the utilize the right strategies for their respective sports.  This doesn't mean that once in a while their strategies won't fall apart.  Nor does it mean that there won't be times that they'll execute their strategy perfectly, yet still the other team will win due to a bad bounce.  I doubt any of these coaches would abandon their strategy over a bad bounce or a single loss.

            The same is true when you walk into the casino.  The coach/manager of your 'team' is you.  You decide which game to play.  This is the first key step in your strategy.  In fact, this leaves you with more power than any of the aforementioned coaches.  I'm sure many of them wish that they could pick their opponent on any given day, but they don't get to.  You on the other hand can decided whether to play slots, video poker or a table game.  If you decide on video poker (always a good choice), you decide which variation and to some degree, which paytable.  You can choose the short-pay paytable or make sure you find the full-pay paytable for the game of your choice.   Joe Torre isn't going to hit the field with only 8 fielders, why should you play jacks or better video poker that pays only 8 for a Full House instead of the full 9?

            Once you decide on your game and paytable, the real nitty gritty part of the strategy begins.  There are 52-cards in the deck.  There are 2,598,960 ways you can be dealt 5 cards from a 52-card deck.  There are 32 ways to play each of these deals, ranging from discarding none of the cards to discarding them all.  You have to make a decision on each of these hands which ones you will keep and which ones you will discard.  Fortunately, in about 75% of the cases, it is fairly obvious which ones you want to keep.  The other 25% is the challenge.  Back to our baseball analogy.  Most of the time, there isn't a lot for the manager to do.  He doesn't really have to tell his leadoff batter to 'get on base' every time he comes up.  I think it is fairly obvious that's what he will be trying to do.

            Unlike the baseball manager who has to outguess the opposing manager and players, the video poker Player doesn't need to outguess anyone or anything.  Video Poker is a game of pure math.  For each of those 32 possible ways to discard, there is a finite number of ways the hand can be completed.  Using computers, we can determine the final hand rank of every one of those hands and determine, on average, how many units the Player can expect to have return to him.  It is true that we don't know exactly which cards will come up this time, but we do know that over time, the actual results will approximate our expected results.  Based on this, we learn that the best play for the Player is to play the hand whichever way results in the highest expected return of units.  We call this 'expected value' or EV for short.

            This concept is used for EVERY single decision made in the casino in every game with any strategy.  The decision to hit or stick in blackjack is decided by which of these two decisions results in the higher expected value.  We Fold on Q-6-3 in Three Card Poker and Play on Q-6-4 because in the case of the Q-6-4, Playing has a higher Expected Value than Folding.  The opposite is true for Q-6-3.

            You are in complete control of how to play these hands.  In the case of video poker, the decisions you make are ones that can result in the machine you are playing having a 100.5% payback or a 96% payback.  One payback means you will win in the long run and the other means you will lose (and lose a lot more) in the long run.

            Does playing the right strategy mean you will win every session?  Absolutely not.  It just means your chances of winning increases greatly.   In today's world, the manager that utilizes matchup charts that show how hitters have done against certain pitchers is likely to be far more successful than one who just feels that now is the right time for a certain pinch hitter - he's due to get a hit.    Utilizing the right strategy is important in a variety of situations.  I can't stress enough that the casino is most definitely one of these situations.

Tuesday, September 4, 2012

House Money Strategy

            A few weeks ago, I discussed a new game that was about to be released called House Money.  Just before the article went to print, I found out that due to a technical snafu, the game did NOT go live in the casino I mentioned in that article.  But, in the ensuing weeks, it has gone live in four casinos (Cannery in LV, Drift on Inn and Great American Casino in Washington and Pala Casino in California) for a total of eight tables.

            As a quick refresher, House Money is a sidebet for blackjack.  On the surface it seems very simplistic.  You make the optional sidebet wager before the hand is dealt.  If you are dealt a 2-Card Straight Flush, a Straight or a Pair, you win.  What makes House Money stand out is what happens next.  You can either just take you winnings and play your blackjack game as normal OR you can take all those winnings and add them to your base blackjack wager.  It then becomes a part of your wager just as if you made it before the hand was dealt.  If you double, you must match the entire wager (unless the casino allows doubling for less).  If you split the hand, you must match the entire wager and be prepared for additional splits and/or doubling.

            Some decisions are rather easy.  If you're dealt a suited K-A (or even an off-suit K-A), there is not much to think about.  You take your winnings and cap your base bet.  If the Dealer has blackjack, no big deal, it all pushes and it is as if you took your winnings in the first place.  If the Dealer DOESN'T have blackjack, then you'll win 3 to 2 for the ENTIRE wager!

            Other decisions will be almost as easy.  If you're dealt a Pair of 10's or Face Cards, you'll always cap your base blackjack bet.  The Dealer will check for blackjack first, so you don't have to worry about losing your sidebet winnings that way.   Sometimes, the decision NOT to cap your wager will be rather easy too.  If you're dealt a 6-7 looking into a 10, you'll gladly take your winnings and know that whatever happens in the base game, the hand can't be an overall loser.

            There are two strategy problems that you are going to come across.  The first are the hands in which the strategy is less obvious.  For example, it may be no surprise that we cap the wager with a 9-10 against a 2 through 8.  But, we also do it against a 9 through Ace.  Yes, you're going to lose some of the hands against a 10 with a 19 but the odds are still in your favor.  It may also be difficult for you to cap your base blackjack wager when you have a 4-5 against an 8.  Yes, you are likely to draw a 10, but there will be times you draw a 6 and are stuck with a 15 against that 8.  You'll have to have the courage to risk busting the hand even with a wager that might be 3-10 times larger than your normal wager!

            The second strategy issue is going to be the double down and even more so, the potential split hands.   If you are dealt a 5-6, you must be ready to cap your base wager and then double the entire amount in order to maximize the payback of the sidebet.   So, if you are a $5 player and you put $5 on the sidebet and are dealt a suited 5-6, you'll win $20 on the sidebet and have $25 to add to your base wager.  You're now a $30 blackjack Player and you have to be ready to put down another $30 in these cases.

            In similar fashion, if you are dealt a Pair of 8's, you cap your base wager against a 2 through 7, which is probably no surprise.  With the Pair of 8's, you'll win $15 on the sidebet and have $20 to add to the base wager, making you a $25 Player.  Now, you have to split those 8's and be ready for the possibility of being dealt a 2, 3 or 8 leaving you with $25 double downs or splits.  You can quickly have $100 on the table.

            But, as the guy who did the math for Shuffle Master for this game, I can tell you that if you want to have a shot at earning the 98.3% payback from the sidebet, you're going to have not only cap your bet at the right times, but once you do, you must play blackjack using standard strategy.  One of the incredible features of House Money is that while it has its own strategy, it does not change basic Blackjack Strategy one bit!

            If you are interested in learning the complete strategy for House Money, I have created a simple 8 1/2" x 11" tipsheet that shows you when to cap your wager and when to take the money.  It is valid for all shoe sizes.  Eventually, I hope to shrink it down to a pocket-sized strategy card that you can bring with you to the casino, but for now, this will have to do.  If you are interested in ordering it, please send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89134.

Wednesday, August 29, 2012

Quads are the Key

For those of you who read my column regularly, you are probably now well aware that a full-pay jacks or better video poker machine pays 99.5%.  Many people are still confused, however as to what this means.  It does NOT mean that if I start with $100 I will walk away with 99.5% or $99.50.  It means that in the long run, you could take the total amount you wager (NOT your bankroll) and multiply it by 0.5% (the 'loss' rate or 100% minus the payback) and this should be the amount you have lost over time.  So, if you play 10,000 hands over the course of a year (or a month or a decade) and you play max-coin $1 machines, you would have wagered $50,000 and can expect to lose about $250. 

            In video poker, however, 10,000 hands isn't really the long run.  Don't get me wrong, it is certainly approaching the long run.  But, given that a Royal Flush should occur about every 40,000+ hands, it would be hard to declare 10,000 hands to be the long run.  If you've hit at least one Royal, you would be ahead of the game.  If you haven't, it would be totally fair to say you are behind because you still have 30,000+ hands to go.  Royal Flushes account for about 2% of our payback.  So, if you were to NEVER hit one, you'd theoretically be playing only a 97.5% game.

            With a hand frequency of 1 in 40,000+, Royals sort of march to their own drummer.  You might hit 2 or 3 in 40,000 hands or you might go 100,000 hands without hitting one.  When you hit one, you're going to have a very good month and when you don't, well, it will be harder to even break even.

            Four of a Kinds, on the other hand, should occur about 1 in about 420 hands.  With the average Player playing hundreds of hands per hour and perhaps thousands in a session, this hand becomes critical to our chances of success over a session or two.  It accounts for 6% of our overall payback.  Relative to the other hands, this is not necessarily large, but it is a hand that is frequent enough that you expect to hit it over a session, but not frequent enough to be sure you'll hit your fair share over a few nights.   If you were to play 10,000 hands, you'd probably find that the frequency of High Pairs and Trips and Straights are very close to what they should be.  Royals will by very definition have to be either more frequent or less frequent than expected, but Quads can be just about anywhere over that period of time. 

            In theory, you should hit about 24 of them over that time.  The math says you very likely could hit only 12 or as many as 36.  If you hit 12, you're about 3% short in payback.  Assuming you haven't hit a Royal and you're now 5% short.  The odds of coming up a winner over that span is very unlikely as you'll be playing at 94.5% and hoping the other hands come up big - which simply isn't very likely.

            Conversely, if you've hit36 of them, you'll be at 100.5% EVEN if you haven't hit a Royal.  A winning session is not guaranteed but certainly more likely.  Over time, the frequency of the Quads will slowly head towards that 24 per 10,000 hands, but your results in the short or medium run is heavily dependent on hitting your four of a kinds.

            As with anything video poker, the number of Four of a Kinds you get is at least partially attributed to luck.  We've all played for hours and been dealt dozens of Three of a Kinds to watch NONE of them turn into Quads.  We've also all sat there and drawn 3 Kings to a single King.  Nothing that happens is truly out of the ordinary.  However, you can increase your chances by playing the right strategy.  If you hold a 4-Card Straight OVER a Low Pair, you are going to greatly reduce your chances of Quads.  If you hold 3 High Cards instead of just the 2 that are suited, you will lower your chances for getting Quads.  The reason why we hold only the 2 suited cards is both to give us a chance to hit the Royal AND to increase the chances of Quads.  Both of these hands are reduced to ZERO CHANCE if you hold 3 off-suit High Cards!

            Of course, if you choose to hold a Low Pair OVER a 4-Card Flush you may increase the frequencies of Four of a Kinds, but you'll do so at your own peril.  Quads are important, but not so important that you should be throwing the proper strategy out the window.

Wednesday, August 8, 2012

Playing with House Money

            Over the years, there have been numerous successful sidebets to blackjack.  Many people have wondered why blackjack Players would bother with a sidebet.  A good blackjack Player can play the game at 99.5%, so why would they want to play a sidebet that might pay anywhere from 75%-90%.  That would seem to defeat the purpose of playing a game with such a narrow house edge. 

            I think the success of blackjack sidebets lie in the volatility of them.  Blackjack is essentially a game of coin tosses.  You win one, you lose one.  You win two, you lose three, you win two more.   It is hard to make a real killing (or get killed) on anyone hand unless you have one of those cases where you split 8's, draw another 8 and then a bunch of 2's and 3's for Double Down situation.   The average wager at a blackjack table is a mere 1.15 (roughly) units.

            The sidebet on the other hand will frequently afford the Player the opportunity to win big on a single hand.  The more frequent payoffs might pay 4 to 1 or even 10 to 1.  The more rare winning hands might pay 100 to 1 or 1000 to 1.  A $5 wager can quickly (so to speak) become $500 or $5000.    The tradeoff for this opportunity is generally the lower paybacks associated with no strategy sidebets.  The casinos can't offer 97-98% paybacks for games with no strategy because they can't rely on human error to help drive the casino edge.

            A couple of months ago, Roger Snow, Chief Product Officer at Shuffle Master brought a game idea to me to analyze.  As is frequently the case when we work together, the game went through multiple iterations before we arrived at the final product.  After we 'ran the numbers', I think Roger liked it but didn't love it.  I, on the other hand, told him I thought we had just come up with a nearly perfect sidebet for blackjack.  It was given the name House Money for reasons which will soon become clear.

            As far as I know, it is the first and only blackjack sidebet that has strategy, yet somehow does not affect base blackjack strategy at all.  As a result, if a Player chooses not to play the sidebet, he gives up nothing to the house by sitting at a table that offers it. Also, the casinos are able to offer a sidebet with a payback in the 95+% range because there is the possibility of human error in the strategy.  With all this, the concept of the sidebet is quite simple.

The Player makes a wager before being dealt his blackjack hand.  The Dealer deals the cards as per normal blackjack rules.  If the Player is dealt a Pair, a Straight or a Straight Flush, he wins.  As always, there may be multiple paytables over time, but for now, this is the most common one for a 2, 6 or 8-deck game:

Pays (TO 1)*
Suited A-K
2-Card Straight Flush
2-Card Straight
            Those payouts may not look all that spectacular.  In all honesty, they are not.  If the game ended right here, the payback would only be about 75% and this would just be another 'nothing special' blackjack sidebet.  But, the game does not end here.  The Player now has two options:

·         Take his winnings and play out his blackjack end per usual
·         Add any/all of his winnings to his base blackjack wager and then play out his hand per usual

            There are NO restrictions on these rules.  If the Player is dealt a Suited A-K, he will be paid 9 to 1 for his sidebet and then can add the entire 10 units to his base Blackjack wager which has ZERO chance of losing.  And YES, the casino will pay 3 to 2 for this additional wagered amount if the Dealer does not also have a Blackjack.

            If the Player is dealt a Pair of Jacks, he will be paid 3 to 1 for the sidebet.  If the Dealer has a 6 up, he can add all 4 units to the blackjack wager.  If the Dealer has a 10 up, he can choose to do so too, but here's where the strategy part comes in.  Is this the right move?  In reality, it is the correct move.  I should add that if the Dealer has Blackjack, the Player NEVER risks his winnings from the sidebet.

            The real fun begins when the Player is dealt a 5-6 (or 5-6 suited) and wins even money (or 4 to 1) and has to decide whether to risk his winnings on his base blackjack wager.  If the Player chooses to do so, it becomes a part of his wager in every sense of the word.  If he decides to double down, he MUST match the ENTIRE wager.  The same applies if he is dealt a Pair and chooses to split.

            Imagine starting with a $5 wager on both the base wager and the sidebet and being dealt a Pair of 8's.  The Dealer pays you 3 to 1 on your sidebet and you now have to decide if you want to add the $20 to your base blackjack wager, making it a total of $25.  Assuming you do and you go ahead and follow standard strategy, you will now split those 8's and you'll have to put up an additional $25 of your own.  Now, you are dealt another 8 and you put up another $25.  Then you're dealt a '3' and you double down and play ANOTHER $25.  You started as a $5 Player and now you have $100 down on the table on essentially one hand!

            For the record, you would only let your sidebet winnings ride if the Dealer has a 2 through 7 as an upcard.  However, whether you cap your bet or take your winnings, you still follow basic blackjack strategy and split those 8's.  You double down on all 11's.

            So far, House Money has been very well received by the casinos that it has been demonstrated in.  It is expected to go live in the next couple of weeks in Reno at the Grand Siena Reno.  It should go live in other casinos shortly thereafter as regulatory approvals are granted.  In a few weeks, after the game has gone live, I'll review the complete strategy for the game.


Friday, July 13, 2012

Eyes Wide Open

            I finally discovered something that has a lower payback than slot machines – New Jersey Turnpike tolls!  As I write this, we’re back on the East Coast for personal business.  After landing at Newark, we had to drive up to the Boston area.  I couldn’t believe the toll from Newark airport to northern end of the Turnpike.  It was $3.60 to go about 20 miles.  Throw in the $12 toll to cross the George Washington Bridge to cross into New York and I was out more than $15 after only being on the road for 25 minutes!  It takes quite a bankroll to drive on these roads, and with NO chance of winning.  We had only left NJ less than a year ago and all these tolls had gone up considerably since we left!

            On a more serious note regarding slots, I received a very good question from a reader this past week.  He acknowledged what I had written several weeks ago that the average slot machines paid only 92-93% and that video poker generally paid 97-100+%.  He asked that given that casino gambling is just a form of entertainment, what is so bad about the idea of taking $100 of your bankroll to go for a huge jackpot on a slot machine, especially given that winning a similar amount at video poker would take a long time with smaller wins along the way.  I have to admit, that it took me a little while for me to come up with a response.

            I think the best I can come up with is that if you go in with your eyes open as to what you are doing then I can’t really say there is anything wrong with it.  Gambling is entertainment and if it brings you enjoyment to take part of your bankroll and put it into a low payback slot machine with a jumbo-sized jackpot, that is your choice.  If I have any issue with the concept it is that it is very hard, if not impossible to go into this with your eyes truly open.  Yes, you can know the size of the jackpot, but you don’t know the probability of actually hitting it. 

            The other issue is that it is standard practice in casino gaming that if the game has a huge jackpot (usually Progressive) then the payback of the game tends to be even lower.  This is true for both slot machines and even table game sidebets.  Outside the casino, this is even truer for things like Lotto.  Most state lotteries have paybacks in the 50-60% range.  Players are willing to play games with very low paybacks in hope of winning that life altering prize.   Again, however, in the case of Lotto, we are able to compute the probability of winning the top prize.  This is not the case for slots.

            While the low payback of regular slots is concerning, and the presumed even lower payback of a Progressive slot is even more concerning, the biggest concern still belongs to the notion that there is no way to know anything about a slot machine.  We don’t know the probability of the jackpot spin or any other result.  We have no way of knowing the overall payback of the machine by a simple glance at the glass.  In a place like Nevada, the payback can be no less than 75% so that is about all we really know.

            So, that all said, if you feel that you want to play a game that has a life-changing jackpot with a portion of your bankroll, I can understand the desire to try your hand at a slot machine.   It is probably the only chance you have for a multi-million dollar prize.  If you are looking for a gigantic jackpot, I would personally recommend a Pai Gow Poker sidebet or the Six-Card sidebet for Three Card Poker.  The prizes will only be in the few hundred thousand to $1 million, but you’ll still be playing games with higher paybacks.

            In the end, it is your money and you have to decide how you want to spend it and what provides you the most enjoyment.  If chasing a mega jackpot on a low paying machines with a portion of your bankroll is what brings you joy, I won’t stop you.

Friday, June 29, 2012

Player Friendly

            This past week, I met someone who was visiting Las Vegas from California.  I told him about my work with video poker and he asked me what is the best game to play.  My natural reaction to that is to just laugh.  How am I supposed to answer that?  Besides the fact that 'best' is a very subjective term.  Admittedly most people want me to answer which games are the best mathematically.  But, as this guy was stating on the strip, the odds (pardon the pun) that the best game is anywhere near is rather slim.  In fact, I'm a bit scared to tell him to play a particular type of machine in fear that he'll find it, but not at anything near full-pay.

            As the conversation continued, he told me that he likes to play Double Double Bonus Poker.  I was certainly not surprised to hear this.  It is a very popular game and he cited the biggest reason that it is - the extra chance to get a huge jackpot with the Four Aces and a kicker.  He also told me about the time that he was playing a ten-play Double Double Bonus machine and was dealt Four Aces plus the kicker on the initial deal.  Multiply that by 10 and it is a NICE payday even if you are playing a relatively small denomination or not max-coin.

            When you get dealt a hand like that, you might just be hooked for life.  It reminds me of the day I was playing golf with a friend.  Neither of us are all that good.  I still had a great time, but he wasn't happy with how poorly he played.  Well, until we got to about the 17th green and he rolled in about 30 foot putt.  Then he wanted to know when we could play next. 

            I suggested to the man that he try to find some Double Bonus machines, which at full-pay have a 100.1% payback.  Double Double Bonus has a payback of only 98.8%, also at full-pay.  I then told him that the best paying machines were variants of Deuces Wild, but only if he played proper strategy.  I really didn't know if he had a clue as to proper strategy for even Bonus games, yet alone Deuces Wild.  I figured that he would still be better off sticking to what he was familiar with than trying to play a game like Deuces without the benefit having attempted to learn the strategy.  While there are differences between Double and Double Double, at least he is still in the same general universe with those two.

            Of course, the real problem with answering his question is that he was going to be playing on the strip, which isn't exactly know nowadays for having too many full-pay machines.   Much to my surprise, I checked my source for video poker inventory - - and found that the casino he was staying in (I won't name it), DOES have a some full-pay machines, but all at denomination of $1 or more.  It took me a second to fully comprehend this.  Usually casinos only put out full-pay machines for low denominations.  If you want to play at nickels they'll allow some winners.  Then it hit me,  NONE of their full-pay machines were over 100%.  If you want to play Double Double at full-pay, they'll be happy to let you at $5 per hand ($1 max-coin).  With a payback of 98.9%, the casino can expect to clear more than $30 an hour!  Of course, they may have some quarter machines to play, but those will be short-pay and you may find the same loss rate as a result. 

            I'm not naive.  I fully realize that most video poker machines have paybacks below 100% and that means that you will lose over the long run.  I have stated many times that gambling is just a form of entertainment for almost everyone.   But given the nature of gambling is that the cost is variable and that sometimes you can win money, your goal should be to minimize the losses and give yourself the best chance to win.

            To do this, you need to find games that have paybacks as close to 100% (or over) being played at a denomination that you feel comfortable with.  If you are okay with playing a $1 machine, that's great, but make sure you have enough bankroll for it.  Don't expect to walk over with $100 and play all night.   If you start with $100 don't be surprised if it is gone in a hurry and once your bankroll is gone, there is no coming back from it. 

            If you don't feel comfortable playing $1 machines or you don't have enough bankroll to do it, make sure that when you step down in denomination that the paytable doesn't take a big step down too.  Or, as I told this gentleman, if he really wants to find good video poker options, he might have to venture to one of the 'locals' casinos where the paytables are known to be a bit more Player friendly.

Wednesday, June 13, 2012

The Penalty Box

            In last week's column, I analyzed a particular hand that could be played multiple ways.  The hand was as follows:

J♠        8♦        Q♦       3♥        9♦

            From a quick glance, one might think to play the hand as a 4-Card Inside Straight with 2 High Cards, a 3-Card Double Inside Straight Flush with 1 High Card or simply as Two High Cards.  As always, the decision comes down to which of the hands has the highest Expected Value (EV).   In last week's column, instead of simply relying on the EV in a strategy table, I used a program that I created that allows me to put in the EXACT 5 cards and tell it which ones I'm holding and which ones I'm discarding.  It then gives me the exact EV of the hand in question.  Why do I do this instead of just using the value in the strategy table?

            The values in the strategy tables are averages of all hands of that particular type.  The accuracy is thus dependent on a few factors, ranging to the nature of the specific hand to the specificity of that hand.  For example, we list the Expected Value of a 4-Card Flush as 1.22.  In reality, there is not a single 4-Card Flush that has that EV.  While there is always the same number of possible ways to draw the Flush (9), the number of High Cards in the hand will impact the exact expected value because it changes the number of ways we can pick up a High Pair.  If we have 0 High Cards, the EV is 1.15.  With 1 High Card it is 1.21 and with 2 High Cards it is 1.28.   We could just as easily list these three hand separately on the strategy table, but it wouldn't change the strategy we would employ at all.  There are no other hands that have an EV between 1.15 and 1.28.  So, in this case we lump all the 4-Card Flushes together and show the average EV for all 85,512 possible 4-Card Flushes.

            In a similar fashion, we have a single entry on our Strategy table called the 4-Card Royal which has an expected value of 18.66.  but not all 4-Card Royals are created equal.  We might have 10-J-Q-K which allows for pulling the suited 9 and picking up a Straight Flush.  Or we can pick up an unsuited 9 for a Straight.  However, we also only have 9 ways to pick up a High Pair.  Thus the EV of this hand is rather different from that of J-Q-K-A which has no way to pick up a Straight Flush and also has only one way to pick up a Straight (both ends are NOT open).  But, we get 3 additional cards that will give us the High Pair.  

            But, there is another item that can affect the specific Expected Value.  What happens if we are dealt a Flush 3-J-Q-K-A.  The Flush has an EV of 6.00 while the 4-Card Royal has an EV of 18.66.  But, when we discard the 3, we lose one opportunity to draw the Flush.  This will certainly NOT drop the EV of the 4-Card Royal to below that of a Flush, but we should recognize the impact of the specific card we discard.  When we discard a card that could help improve the final hand, it is called a 'penalty card'.  In this particular case, there is no impact to our strategy as a result of discarding the 3, so we are safe to lump all 4-Card Royals together.

            However, as we go down further on our strategy table, we begin to break apart the hands into smaller groupings.  We don't have all the 4-Card Straights listed together the way we do the 4-Card Flushes.  Because a Straight only pays 4 and there are only 8 ways to complete them, the EV of Straights drops to the point where it is very close to many 3-Card Straight Flushes, 2-Card Royals and even High Card hands.  Many of these hands also tend to overlap a lot, as in the example at the beginning of this article.  The hand is 2 High Cards, a 3-Card Straight Flush and a 4-Card Inside Straight all at the same time.  Slight changes in the hand make up could make it other hands all at the same time.

            When a hand overlaps as this one does, there is usually at least some penalty card situations.  In this case, if we choose to play the hand as 2 High Cards, discarding the 8 and 9 create the penalty card situation.  We wouldn't want to draw an 8, 9 and 3, but we wouldn't mind drawing an 8, 9 and 10.  While this may not be the most common outcome, it is one that would complete the Straight and give us one of the highest possible payouts for the 2 High Cards.  So, discarding them may reduce the ACTUAL Expected Value slightly from the one we may find under 2 High Cards in the strategy table.

            Likewise, when we hold the 8, 9 and Q, we are discarding the Jack which is a penalty card.  It can be used to complete a Straight or we might pick up another Jack to make a High Pair.  So, I calculate the exact Expected Value in last week's column to make sure the result was 100% accurate.

            As I've said many times in my column, you don't need to memorize the Expected Value of any hand because the value itself is meaningless.  What matters is the relative value.  You need to know which hand has the higher EV.   Once in a while, a penalty card situation will cause a hand as it is shown on the strategy table to have an ACTUAL Expected Value that actually drops it to below that of another playable hand from that same 5-card draw.  This in essence creates an exception condition to how the hand should be played when using a strategy table.  The hand should STILL be played according to which has the higher Expected Value, but because we are using the 'average' shown on a strategy table, we don't actually do this.

            When my father, Lenny Frome, developed Expert Strategy, he was well aware of this situation.  He felt that the impact on the payback of these exceptions was too small to be concerned with relative to the idea of listing out what could be several to dozens more lines on the strategy table.  Learning Expert Strategy can be enough of a challenge.  He didn't want to complicate it further by trying to list out hands that might look something like this:

·         4-Card Straight with 2 High Cards, EXCEPT if there is a 3-Card Straight Flush, but ONLY if the 2 High Cards are part of the 3-Card Straight Flush

            I tend to agree with my father and learning these extra rules are only for diehards and even then, the risk of error might be more than the extra 0.001% it might yield in payback.

Thursday, June 7, 2012

Rare Gems - Straight Flushes

            One of the ironies about video poker paytables is that they don't always reward hands more for being more rare.  If I were to ask you which occurs more often in video poker - a Flush, a Straight or a Full House, I'm guessing most of you would say a Straight, followed by a Flush and lastly a Full House.  It is really a trick question.  Without knowing what the paytable is, there is no way to answer the question accurately.  The only thing we know is that, in general, a Full House outranks a Flush, which outranks a Straight. 

            On a full-pay video poker machine, assuming you use Expert Strategy, you will actually hit more Full Houses than either of the other two.  A Straight will occur just slightly more often than a Flush.  Upon close inspection, we realize that this is by far a product of the payouts for each hand than it is a product of the hands themselves.   If we take a look at the game of All American Video Poker - which would appear to now be obsolete - we will see a very different pattern develop.  In All American, a Straight, Flush and Full House all pay 8.  With no reason to go for one or the others, the pure probabilities of hitting each hand begin to show up.  As a result, the frequency of Straights and Flushes increase dramatically, to the point where they occur nearly twice as often as a Full House.

            A similar phenomenon occurs with a Straight Flush.  Generally speaking, it occurs just about 4 times as frequently as a Royal Flush, while paying only 1/16th of the amount.  Or we can look at it the other way and say that it is more than 20 times as rare as a Four of a Kind while only paying twice as much.  When we throw in the Bonus Video Pokers, it only looks worse.  This far more rare hand might actually pay LESS than many of the Quads we can hit, which are far more common.

            Of course, I'm wondering how many of you have hit nearly as many Royal Flushes as you've hit Straight Flushes.  I doubt you remember your Straight Flushes as vividly.  Winning $62.50 on a max-coin quarter machine isn't quite as memorable as a cool $1000, but that isn't my point.  If you use Expert Strategy on a jacks or better machine, you should hit a Royal every 40,400 hands or so and a Straight Flush every 9200 hands.  The key phrase is "if you use Expert Strategy."  Since most Players, at best, use pieces of strategy, I'm guessing that the Straight Flush shows up far less often because the partial Straight Flush is frequently overlooked when the Play.

            If dealt the following, what's the right play?

J♠        8♦        Q♦       3♥        9♦

            Do you play the 4-Card Inside Straight with 2 High Cards, the 3-Card Double Inside Straight with 1 High Card or the 2 High Cards?  As always, there is just one way to determine the right play.  We go to the Expected Values of each.

            Calculating the Expected Value for the 4-Card Inside Straight is fairly easy.  We can draw the Straight with 4 cards and we can draw a High Pair with 6 more.  This will return 22 units to us.  Divide by 47 and we get a result of just below 0.47.  For the other two, I ran them through a program I have that calculates the exact Expected Value given the specific discards.   The Two High Cards have an Expected Value of just below 0.50 and the 3-Card Double Inside Straight Flush has an Expected Value of just below 0.53.  This is the proper play. 

            While the odds of hitting the Straight Flush are 1 in 1081, this is still far greater than hitting it with either of the other two hands (it is zero in these cases).  Ironically, it is not the tremendous payout of the Straight Flush that causes us to play the hand this way.  By holding a 3-Card Straight Flush, we give ourselves numerous chances to hit just Straights and Flushes - a combined 1 in 20 (roughly).  Throw in opportunities for Three of a Kind and Two Pairs and this hand simply beats the others.

            Now, no one expects you to calculate the Expected Value of even the 4-Card Inside Straight on the fly or to carry a small computer to run my program that calculates the exact Expected Value for each hand.  It is much easier to simply use a strategy table that lists out each playable hand.   If we look up the three hands in a strategy table, we find a 3-Card Double Inside Straight Flush has an Expected Value of 0.54, the Two High Cards have an Expected Value of 0.49 and the 4-Card Inside Straight with 2 High Cards doesn't even make it onto our strategy table because the Two High Cards always outranks it.  These values are the average of all hands of that type so they don't always equal the exact Expected Value taken into account the exact discards.

            In the end, the frequency of a hand occurring is a product of the paytable and following the right strategy.  If you want to get your share of Straight Flushes, you can't do a lot about the former, but the latter is fully in your control.

Tuesday, May 29, 2012

Boston 7 Invades Taj Mahal in Atlantic City

            Almost everyone is familiar with what a heavy Boston accent sounds like.  Or should I say Bah-stun?  I'll never forget a story I heard while a freshman in college.  A classmate had visited one of the Boston colleges the year before to check it out.  The student giving the tour told him that "Freshman are not allowed to have cars on campus."  What he heard was "cahs: and not "cars."   A bit confused he asked the student leading the tour - "why would a freshman want to have a cow on campus?"

            Less well known about Bostonians is that they have taken the word 'wicked' and turned it upside down.  Wicked doesn't mean evil in Boston.  It means 'very'.  A wicked bad headache is a very bad headache.  So, when I say that John Feola of New Vision Gaming has invented one wicked cool game, it means it is a game worth playing! 

            The new game is called Boston 7 Stud Poker and it just opened at the Trump Taj Mahal in Atlantic City.  It is a wicked simple game and if you're familiar with Mr. Feola's Boston 5 Stud, you'll notice some similarities.  Boston 7 Stud just takes advantage of the on-going popularity of the 7-card Poker games.

            To begin with, the Player makes 2 equal size wagers, called the Ante and the 1st Wager.  He then receives 3 cards.  The Player now has a choice to make.  He can either Fold, forfeiting his Ante and 1st Wager or he can make a 2nd Wager - equal in size to the other two wagers - and receive 4 additional cards.

            If the Player decides to make the 2nd Wager, his hand will go head-to-head against the Dealer's hand.  The Player will make his best 5-Card Poker hand from his 7 cards.  The Dealer is also dealt 7 cards to make his best 5-card Poker Hand.   If the Player's hand beats the Dealer's hand, his 1st and 2nd Wager will pay even money.  The Ante will push unless the Player's hand is a Three of a Kind or better, in which case it will pay an Ante Bonus according to the following paytable:

7 - Card Royal
6 - Card Royal
5 - Card Royal
Straight Flush
Four of a Kind
Full House
Three of a Kind

            Note that the top two hands actually consist of 6-card and 7-card hands, respectively and are fixed pays, not odds pays.

            If the Dealer's hand beats the Player's hand, all wagers are taken, BUT the Player will still be paid according to the above paytable if he has a Three of a Kind or better.  So, while he will still lose his Ante Wager itself, he will still be paid for the hand.  If the Player's hand and Dealer's hands tie, all wagers push, but the Player can still earn an Ante Bonus.

            There is also an optional 3-card Bonus Sidebet that the Player can make that is based on his first three cards.  The Player MUST show his first three cards to the Dealer if he has a Pair or better in order to claim his win.  The paytable for the 3-Card Bonus is as follows:

Royal Flush
Straight Flush
Three of A Kind
* Pays are "TO 1"

            As I did the analysis on this game for the regulatory agencies, I'm quite familiar with the math.  The overall payback of the base game is 97.59% which is fine for a game with essentially no strategy.  While the Player has to make a decision, in theory, there really is no decision in reality.  The Player should NEVER Fold.  Even the worst possible 3-card starter hand can come back to beat the Dealer often enough to make it not worth Folding.  As a result, what we really have is a game in which the Player and Dealer will each win 50% of the time.  The House edge is created from the fact that the Ante Pushes unless the Player's hand is Three of a Kind or better.  The Player also gets the advantage of being paid even on losing hands of Trips or better.

            For the 3-Card Bonus Sidebet, the payback is 93.81%, which is in-line with many other 3-Card paytables that can be found, especially in Atlantic City.  The game was developed with numerous Ante Bonus and 3-Card Bonus paytables, so pay careful attention to the actual paytables before you sit down and play. 

            If you do make it down to Atlantic City and play Boston 7, I'm sure you're in for one wicked good time.  You can go to and check out more of their games, including Imperial Pai Gow

Tuesday, May 22, 2012

What to Play

            Last week, I wrote about Four Card Poker and mentioned how I would cover it's 'crazy' cousin - Crazy 4 Poker in an upcoming column.  I started to work on this column this past week when I got to the point of discussing why a Player would choose to play one of the games over the other.  The overall paybacks are fairly similar.  The reality is, that I can't really suggest to Players to play one of these games instead of the other.  This is because casino games are (or at least should be) a form of entertainment and we can't overlook this factor in our choices.

            So much of what I write is all about the math.  Years ago, my father, Lenny Frome, described Expert Strategy as a three-legged stool, with each leg equally important.  After all, we know what happens if one leg of a stool is shorter than the other two!   These three legs were:

·         Know which game to play
·         Know how to play that game
·         Know what to expect

            The first of these legs essentially referred to the payback of the game.  Don't play short-pay machines when you can find full-pay machines.  On the surface, it might mean play only the game(s) with the absolute highest payback.  But, if that were the case, everyone should be clamoring for the one type of video poker machine in the casino with the highest payback - probably some Deuces Wild variant. 

            If this were what my father intended, why did he bother to write about all the other games in detail - not just video poker but all of the proprietary table games too?  This is why a few years back, I added a concept to my father's three-legged stool.  I called it the comfy cushion.  It means you have to ENJOY playing whatever game you choose as well.  There are two significant reasons why I added this explicity to Expert Strategy.

            The first reason is because, as I said earlier, gambling should be a form of entertainment.  By this definition, you should enjoy it your time doing it.  Yes, I fully understand that it is a somewhat unique form of entertainment in that you might walk away with more money than you started, but with rare exception, these are not life-altering amounts of money we are talking about.  I'm sure no one minds being miserable while they are winning thousands (or hundreds of thousands of dollars), but more often than not, your win will be far smaller than this and you will lose more often than you will win.  No one likes to lose, but if you're absolutely miserable while you are losing $20 over 3 hours, something is very wrong.   When you go to a movie theater, there is a good chance you'll spend $20 too.  You'll have no chance of getting that money back.  You probably won't mind if the movie was good.  If the movie was a rotten tomato, it might bother you a bit more.  This is the same attitude you should take with you to the casino.

            The second reason is that if you're not having any fun while playing, there's a pretty good chance you are going to forget all about the other two legs of the stool.  You may know how to play a game, but in your frustration you'll start doing things you shouldn't be doing.  You may know what to expect, but while you're not having fun, you'll start imagining the cards are all against you or that the casino must be cheating and again, you'll go away from the strategy that you are supposed to be using.  So, on a theoretical level, you might be playing a game with a higher payback, but if you don't adhere to the strategy you may find that on a reality level, you've lowered the payback to the point where you'd be better off playing a different game.

            Undoubtedly, some of you may take what I'm saying as carte blanche to now go off and play any game in the casino.  In the end, of course, it is your decision.  But, please don't take this as my endorsement of playing slots or sitting down at a Craps table and simply playing the Hardways bets for hours at a time.  The other two legs of Expert Strategy remain full in force, so I suggest you certainly know what to expect in these cases.  Your chances of a winning session is greatly reduced.  It is one thing to pick a 99.2% video poker machine over a 99.6% one.  It is quite another to play a 91% payback proposition bet for hours.  If this is the only thing you enjoy in the casino, it might be time to pick a new form of entertainment