Imitation is the Sincerest Form of Flattery

            A couple of weeks ago, I two days walking the halls of the Sands Expo at the Global Gaming Expo.  If I had to pick one word to describe the event, it would definitely be "SLOTS".  Like last year, I think they dominated the show.  For those who have been reading me for years, you know my thoughts on Slots from a Player's perspective.  But, I do give the slot manufacturer's a lot of credit for creativity.  This year, they kept it up, not only in the games that are being developed, but in terms of the marketing.  There were zombies everywhere.  I'm not sure if there was only one manufacturer who had a zombie themed game or if there was more than one.  But there were a lot of zombies in some really good make-up all over the halls.

            As much as I write about video poker in my column, my real love is table games and that's what I'm at the show to really see.   This year, brought a particular trend to its apex (or perhaps more appropriate, its nadir).  Besides the three big table game companies (SHFL, Galaxy and DEQ), there were virtually no new table games.  I did see a couple of other new games, but they were almost afterthoughts from gaming companies involved in other aspects.  I saw exactly ZERO small independent game inventors showing any new games.  I recognize that the cost of a booth at the G2E is not cheap and could easily wipe out the budget of a small inventor, but I always found it fun to talk to someone new about their game.  I didn't get a chance this year.

            I did get introduced to a few inventors who did not have booths at the game who wanted to talk to me about their ideas.  I find that most ideas seem to fall into two categories.  The first is the rather 'far-fetched' category.  These are ideas that aren't necessarily bad, but I have to wonder about their odds of commercial success.  One inventor remarked to me about how all the casino games are poker-based.  He found this to be problematic.  I find this to be indicative of what is likely to be successful commercially.  It is NOT that games that are not poker based haven't been invented and tried, it is that none have ever had the staying power in the casino.  Some might be fun and social for a few hours, but they don't seem to have the ability to create repeat customers the way poker-based games do.

            The second common category of games are the copycats.  People look at a game like Three Card Poker, which is undeniably the most successful proprietary table game (both financially and in terms of number of tables) and try to emulate it in some way.  Now, many table games have some form of patent protection on them (many do not!).  But I am not talking about copying to the point of patent violation.  I'm simply saying that people look at Three Card Poker as some magic formula and try to replicate it.   You know this is happening when they begin describing their game with "It is just like Three Card Poker but......."

            For the past several years, the casinos have been going through a Texas Hold'em craze.  While I think it has peaked overall, it has still left a lasting impression.  Games that might have been developed as 7-card Stud games are being developed with 5 community cards in Texas Hold'em style.  After the dust settled, there are currently 2 very successful Texas Hold'em table games.  The first is Texas Hold'em Bonus Poker - developed by Mikohn/PGIC and purchased by SHFL Entertainment a few years ago, and Ultimate Texas Hold'em - developed directly by SHFL.  I did the original math on UTH for SHFL.  It was by far the most challenging game I had ever worked on to that point and perhaps since.  It was also one of the most rewarding because of the success it has become.  It is generally acknowledged as the 2nd most successful game of all-time with several hundred tables in the market place and is the only game on the horizon that has any chance to knock Three Card Poker out of the number 1 spot.

            Like Three Card Poker, one of the surest signs of the success of UTH is how many times I have heard the phrase in the past few years from an inventor, "It is just like Ultimate, but....."  There is an old saying that imitation is the sincerest form of flattery.  I guess if everyone is trying to create a game just like UTH, then UTH must be a pretty darn good game.   Is it possible to improve upon Three Card Poker or UTH?  I suppose it is possible.  But, 15-20 years after the invention of Three Card Poker, it is not a minor improvement to Three Card Poker that might take it out of the top spot.  It is a game that while still poker-based, introduce many new concepts.  It is a game that has more uniqueness to it than similarity to Three Card Poker.  I think if someone wants to knock UTH out of the number 2 spot, it won't happen because someone tweaks UTH, it will be happen because someone comes up with a new and better idea. 

            To all the inventors out there, don't think of new ways to flatter the existing games by imitating them.  Come up with new games with new ideas if you want to make your mark.

What is the Allure of Progressives

            There is a theory in physics that goes for every action there is an equal and opposite reaction.  In gambling, there is a similar theory.  For every table game there will eventually be a sidebet.  And, for every sidebet there will be a Progressive version of the sidebet.  The math behind Progressives is probably the least understood math of any type of gambling.  It really isn't that hard once it is explained properly, but I've worked with a lot of inventors on a lot of Progressives, and it is fairly obvious to me that few people, even in the industry, understand how a Progressive works mathematically.

            Generally speaking there are 3 components of a sidebet - the fixed pays, the seed and the contribution rate.  Normally when we calculate the payback of a sidebet, we simply multiply the fixed pays by the frequency of each winning hand and sum up these values.  For a Progressive, we have to alter one step slightly and add one.  For the jackpot event, we use the seed amount as the equivalent of the fixed pay for that event.  Each time it is hit, the casino is on the hook to put that money back on the meter, so it is similar to a fixed pay in that regard.  We then need to add the contribution rate - which is the amount of each dollar wagered that goes on the meter - to the total payback calculated.    I'll save more details for another day, as this is not the point of today's column.  What is the point is to discuss how a Progressive differs from other wagers.

            While the top pay for most sidebets are pretty large, the amount they contribute to the overall payback is usually pretty small.  If you pay 1000 for a 1 in a million even, the contribution rate is a meager 0.1%.   In video poker the Royal Flush contributes only 2% to the payback of the game.  If we were to look at most table game sidebets, we'd probably find that most top pays contribute about 1-2% (or less) to the overall payback.  But, when we switch to a Progressive, we find that the top pay frequently contributes 15-20% to the payback when we take into account both the seed and contribution rate.  What does this mean for the Player?

            As I said, the Royal Flush accounts for 2% of the payback of video poker.  What this usually means is that until you hit one, you're only playing at about 97.5% which can be a bit rough.  When you hit one - and if you are a regular player, you WILL hit one, you bring the theoretical payback back to 99.5%.  Hit the Royal more frequently than 'normal' and you're likely up money as you will be above 100%.  With Progressives, it doesn't quite work the same way.  That top hand is either more rare or you'll be playing a game that deals much more slowly than video poker, meaning that there are no guarantees that you will EVER hit it.  So, even if the sidebet were paying 99.5% like video poker, ONE PLAYER is going to wind up winning 15-20% of that payback and everyone else will be playing at 77.5% - 82.5%. 

            When you consider the fact that many sidebets have paybacks far lower than 99.5%, you realize that the picture for those that don't hit the jackpot is even more bleak.  So, why do people play Progressives?  There are two main reasons.  One is a bit emotional and the other a bit more practical.

            First, Players have always been willing to accept low paybacks for a chance to win a life-changing amount of money.  The Lotto has made a lot of money for a lot of states.  Most states payout only 70% on their lotteries.  This is lower than the legal minimum of any casino game here in Nevada.  But, for the chance, however slim, of winning millions of dollars, Players are willing to throw a few dollars in for the hope of getting struck by lightning. 

            The second reason deals with the way Progressives work and makes far more mathematical sense.  To the casinos, the payback of a game is the long-term payback, which is calculated as I described earlier.  You'll note that what I described completely ignores the specific value on the meter at any point in time.   This money is merely an accumulation of the contribution rate over time.  It really doesn't matter to them (mathematically), if a jackpot that is supposed to hit about once a year, doesn't get hit for 3 years.  However, to the Player, the payback of ANY wager is dependent upon the specific payouts for each winning hand at the point in which you make the wager.  It doesn't really matter if the contribution rate is 10% of 20%.  If a Jackpot which is supposed to average $250,000, goes all the way up to $600,000 then the payback at that point in time is WELL above the theoretical payback. 

            It is possible that at a particular point in time that the payback of a wager could be over 100%.  At this point, it makes sense to play the game mathematically.  The problem is, however, that it will be one person that will benefit from this occurrence and it may not be you.  Then again, it might!

Why Play Max Coins?

            Generally speaking, I advise players to play max-coins when playing video poker.  For most versions, this means 5 coins.  The penny Player puts up 5 cents, the nickel player 25 cents, the quarter player puts up $1.25 and the dollar player has to put up $5 per hand.  This is done for one simple purpose.  On most video poker machines, the top payout - the Royal Flush - changes from 250 for 1 to 800 for 1 when that 5th coins is put in.  If you are playing a Progressive, the only way to win that jackpot is to play 5 coins.

            A payout of 800 for 1 on the Royal is worth approximately 2% of the total payback of the machine.  A payout of only 250 reduces this down to about 0.65%.  So, the Player is giving up more than 1.25% of payback if he plays below max-coin.  In similar fashion, if the machine is offering a Progressive, which should push the Royal payout to above 800, then the Player would be surrendering even more payback by playing below the max-coin level.

            The notion of playing max-coin does NOT mean you should wager 5 times the amount you feel comfortable wagering.  Instead it means you should consider lowering your denomination to the next lower level and then play 5 coins.  So, rather than playing 1 quarter, you should play 5 nickels.  This, of course, assumes that all things are otherwise equal.  It is certainly possible that when you go to a nickel machine (or change to the nickel option on a multi-denominational machine) that the paybacks may change as well and you may find that the payback on the nickel machine is well below that of the quarter.   This makes things a bit more complicated.  If the quarter machines pays 99.5% at max-coin, then it will be closer to 98% if you play 1 quarter.  If the nickel machines pays 98.5% at max-coin, then you'll still be better off playing max-coin nickels.

            There are a few times when you may want to play less than max-coin.  The first is when you are first leaning how to play.  As you are more apt to make mistakes at this point, you might be better off simply playing 1 nickel at a time.  Yes, you will be playing at a lower payback, but at this point, your goal is to become a better player while playing on a real machine.  Ideally, you'd spend most of your 'learning' time playing on your computer (or phone or tablet) at home for free ,but I realize that playing for free may be a lot less exciting than even playing for a single nickel.

            Another reason that you may not want to play max-coin is your bankroll.  If your bankroll is not large enough to support playing max-coin then you might be better off playing single-coin.   Once your bankroll is gone, you're done and you need to make sure you have enough money available to ride out the cold streaks.  Of course, one solution to this issue is again to simply drop down in denomination.  So, this advice really only applies if machines of a lower denomination are not available.  Since the advent of the multi-denominational machine, finding machines that play the denomination you want to play has become much easier, however.   So, this second reason may have limited practical applications.  But, if you find yourself in a situation where your bankroll will support 5 nickel play, but you only have quarter machines available, you may want to consider playing a single quarter as opposed to five quarters.

            One critical point to consider.  Just because you switch a machine from quarter play to nickel play, do NOT assume that the paytable is the same even if you are switching to the same variety of video poker.  There are no requirements that state that a machine must use the same paytable when you move from one denomination to another.   In similar fashion, don't assume that a bank of similar (or identical) looking machines all have the same paytable.  Casinos frequently and presumably purposefully mix the machines up, making sure to sprinkle higher paying machines in with lower paying ones.  I dare say that you may find no rhyme or reason to the pattern of machines on the casino floor.

          

Better is Better than Best

            A long time ago, I remember reading an article about product marketing in which it stated that you'll never (rarely?) see a company say that there product is better than a similar product.  Why?  Because if you say something is better you have to prove that it is better.  If you, on the other hand, say your product is the 'best' product then it is possible for the other product to be 'best' too.  Best, in marketing parlance, simply means as good as, whereas, better means superior.  So much for those Run, Spot, Run books which talk about good, better and best.  In marketing it is more like good, best and better.

            As bad as it is in the English language, I think it gets even worse when it comes to math.  You can make numbers say just about anything you want them to.  In the past couple of years, much has been made about the 1% (or is it 2%) of the country that is the wealthiest members of our society.   Then there are those that focus on the remaining 99% (or is it 98%).  I don't get political in this column, so please understand I am making no political commentaries here - only mathematical ones.  A friend of mine posted up on Facebook the other day some statistics about what happens if you look at the top 1% of the world instead of just the U.S.A.  All of a sudden a very significant portion of the country is in the top 1%.   Which statistic is more relevant?  I know people who are millionaires who think they are doing 'ok' and I know people who make very modest salaries who are as happy as can be.   The relevance is more likely in the message that someone is trying to send rather than anything absolute. 

            In the case I just discussed, I'll assume that all data presented was reasonably accurate.  A such, no lies were told.  No misinformation was disseminated.   Data was simply presented in a way to try and get some particular message across.  A few months ago, I wrote a column in which I asked if the U.S. has had a Democrat or Republican President more.  In the past 5 years, it has been a Democrat.  But in the last 8 out of 13 years, we had a Republican.  But, in 13 of past 21 years, a Democrat.  In 20 of Past 33 years, a Republican.  I can keep going backwards through the 20th century.  Someone attempting to make a political point is likely to use whichever statistic backs his point the best, even though it may have only minor relevance to the point.

            When it comes to gambling, the numbers can be manipulated just as much, if not more so.  If I had to take a guess, I'd say that the average video poker machine in Las Vegas probably has a payback of 97%.   Now, if I'm a casino whose average video poker payback is only 96%, I might put together some advertising that simply says 'come to Vegas where the video pokers pay an average of 97%!' .  The implication is that the casino pays this as well, but that's not what they said.  On the other hand, a locals casino that likely has a significantly higher average payback is much more likely to say 'come to the XXX casino, where OUR video poker machines payback 98.5%'.  Of course, we don't really know how they calculate these averages.   With slot machines they simply can present how they paid in the prior month because there is no human error involved.  With video poker machines do they simply take a straight average of all their video poker paytables?  Do they weight $1 machines more than nickel machines?  Maybe there is a uniform method for doing this or maybe they have enough wiggle room to give you whatever number they feel will send the right message. 

            Of course the 'average' payback has very limited value to an Expert Player.  In the simplest example, let's assume we have 2 casinos with 2 video poker machines each.  One casino boasts a 98% average and the other a 97% average.  So, should you head over to the one with the higher average?  What if their 2 machines each have a 98% payback.  But the other casino has one paying 94.5% and the other paying 99.5%.   The only machine out of the bunch worth playing is this last one, even though the casino's average is lower than the others.

            One of the local casinos here boasts of having the most machines paying over 100%.  I'll assume that they are telling the truth with this, but that doesn't mean that their machines don't pay 100.01% and that all of the machines below 100% pay 96%.  Now, to the experienced Player you will still happily seek out the 100.01% machine, but this doesn't mean that you can just show up and sit down at any machine and know that you are playing 100.01%.  At the same time, you would be better off finding a 101% machine at another casino that may have only 3 machines of this type and whose average machine pays 96%!

            So, what's my point?  Don't be sucked in by numbers that can be made to say anything they want.  The payback of a machine is an absolute number, calculated with mathematical certainty.  It doesn't mean that every time you play (even if it is for a few hours), that you will experience this payback.  It does mean that over time, your experience should begin to approximate this theoretical payback, assuming you are using the right strategy.  When you look at the paytable on a machine, that tells you the payback of the machine.  This is all that matters.  Marketing numbers that the casinos produce are just that - numbers they produce.  After all, why trust the group that has actually made better, better than best?

Think Loss Rate

            How much of a difference is there in terms of payback from one casino game to another?  Most table games have a payback between 97 and 99.5%.  Video Poker can range from about 95% to 101%.  Slot machines probably range from about 85% up to 95%.  Sidebets, quite frankly are all over the place, ranging from just over the legal limit of 75% and going up to the low-mid 90%.  While there is a lot of overlap, one of the largest determining factors is strategy.  More complex strategy means a combination of more human error and/or Players not even trying to follow it.  Simple strategy is much easier to learn and follow.  Three Card Poker has one simple strategy rule.  Follow it and you should approach the theoretical payback of about 98%.  Don't follow it and you can only do worse.

            Video Poker has paybacks considerably higher.  Not all of the versions, but you can still find plenty of them well above 98%.  Video Poker's strategy, however, is far more complex than Three Card Poker's strategy.  The average Video Poker machine has more than 30 different strategy items that need to be memorized and in the appropriate order so that you know how to play the hand.  So, first you need to review the hand and determine the realistic ways the hand can be played and then you have to know which of these ways has the highest expected value, which tells us which way the hand should be played.

            In most games, many of the hands are pretty obvious even if you knew little.  If you're dealt a 6-7-8 in Three Card Poker, I don't think you need to have read a book to know what to do.  What if you are dealt K-3-2?  What about Q-8-2?  What about Q-3-2?   For each hand, the Player is really asking himself if he is better off Playing or Folding.  Those are the only two options in Three Card Poker.  The answer is pretty obvious for the Straight and a good deal less obvious for the other three hands.  The strategy is determined by the math behind the question of whether the Player is better off Folding or Playing.  By Folding, the Player forfeits his original wager (one unit).  By Playing, he wagers an additional unit.  If Playing can return at least that additional unit (on average), then the hand is worth Playing.   The Player does not have to perform some complex calculation on each hand.  The decision is to Play or Fold and the math works out very neatly.  For every hand stronger or equal to Q-6-4 the Player is better off Playing.  For Q-6-3 or less, he is better of Folding.  You've just become an expert at Three Card Poker strategy.

            Video Poker is not nearly this simple.  First of all, there is no folding and no additional wagers.  You make an original wager and your only goal is to maximize the amount of money you get back on average for each hand.  If you're dealt a Straight off the deal, there isn't much to think about - unless of course it is also a 4-Card Straight Flush or a 4-Card Royal - then what?  What if you're dealt Three of a Kind and 3-Card Royal?  How about a Pair and a 4-Card Flush?  Does it matter if it is a High Pair or a Low Pair?  (Yes, it does!)  

            In Video Poker, the hands are categorized into about 30-40 different hand ranks and partial hand ranks.   Each of these is assigned an expected value.  This expected value is calculated by looking at ALL the possible draws for that hand and tabulating the total units won for each final winning hand.  We then divide this total by the number of possible draws so that we can compare apples to apples.  So, to look at a simple example.  Suppose you are dealt the following hand:

4♥        5♥        6♥        7♥        8♦

            The decision here should NOT be driven by your favorite Clint Eastwood line ("are you feeling lucky, punk?").  It should be driven by the math.   The straight has an expected value ("EV") of 4.00.  There is no draw in this case and the EV is simply the payout of the hand.  If you decide to discard the 8, there are 47 possible draws.  2 will result in a Straight Flush, 5 will result in a Straight (remember that you would have discarded a card that could also have made it a Straight) and 7 that will result in a Flush.  All other cards result in a losing hand.  So, do you throw away the sure 4 units to go for the Straight Flush?  When we add up the payouts of the winning hands, we get 162 units (2 x 50, 5 x 4, 7 x 6).  We divide this by 47 (the number of possible draws) and get 3.45.  As this is less than the EV of the Straight, we keep the Straight.  In the long run, this will be the better move.

            While most Player would play this correctly (I guess?), the simple reality is that except for those that learn the right strategy, there will be a significant number of Players who will NOT play this correctly.  Throw in the roughly 25% of hands that require a real decision and the casinos can count on Player error to help pad their winnings.  This is why they can offer the 99.5% paybacks on so many full-pay jacks or better Video Poker.   Someone like myself might sit down and get the 99.5%, but the vast majority of Players will play well below this level.   They are likely to play in the 97-98% range if they have some idea of what is going on and perhaps as little as 95% if they just 'wing it'.   The difference between 99.5% and 96% may not seem like a lot, but I always suggest you turn that around to the loss rate - 0.5% vs 4%.  Now there is a 700% increase from one to the other.  The impact to your bankroll could be staggering.

Frustration

            I consider myself to be a very competitive person.  Anybody who has ever played against me in a board game or on a sports field is pretty aware of this.   I play fair and hard.  I'll never cheat and don't throw tantrums.  But I really hate to lose.  So, you can only imagine what I feel like when I'm having 'one of those nights' while playing video poker.   Gambling isn't exactly the type of thing one does if they hate to lose.  Even if you're playing video poker or blackjack, games that are near 100%, you're still going to lose more than 50% of the time over short sessions.  Not a bad record if you're the Marlins, but I prefer to win, well, closer to 100% of the time.

            When I'm on the sports field, I have a significant amount of control in the outcome.  If I'm playing tennis, well, it is just about all on me.  If I'm playing softball, I can do my best to get on base when I'm at bat and make all the plays that come to me.  I can't help my right fielder catch the ball, however.  In this regard, gambling is more of a team sport than a single Player sport.  I'm an expert at just about any game in the casino that I will sit down to play.  So, I can make sure that I'll play each hand the way I should to maximize my overall payback.

            Unfortunately, luck still plays a significant portion of casino gambling (kind of like my right fielder catching the flyball?).  I can't control which hands I'm dealt.  In the long run, I know I will get my fair share of each type of hand.  In a given night, the difference between winning and losing is about getting your fair share of key hands.  You're not going to make money off of 4-Card Straights, so you don't usually keep track of how many you got. 

            When we look at the final paying hands of video poker, it should be no surprise that most of the payback comes from the bottom 3 hands.  Jacks or better gives us about 21-22% of our payback.  Two Pair gives us 26%, and Three of a Kind gives us another 20-21%.  This is almost 70% of a total of 99.5% payback.  Straights give us over 4%, Flushes over 6% and and Full Houses around 10%.  That brings us to 90%.   Four of a Kinds give us about 6%, Straight Flushes a mere 0.5% and Royal Flushes the remaining 2%. 

            The more common a hand is, the more likely no matter how weird your session is going that at the end of it, you're going to have very close to the number of those hand that you are supposed to.   So, if you play 3000 hands and the average shows that you should have about 650 High Pairs, you're not going to find out that you only had 500 of them.  Maybe you have 630 on a bad night and 670 on a good night, but you'll get very close to the 21-22% payback you are supposed to.

            On the other end of the spectrum is the Royal Flush.  If you play 3000 hands, you're well below the roughly 40,000 hands it takes to play to catch a Royal.  If you play a session and miss the Royal, you're inherently playing at 97.5%.  If you hit one then, well, you're assuredly playing well over 100%.   As a result, there really isn't a lot to discuss where the Royal is concerned.  It is literally hit or miss.  Straight Flushes simply don't add enough to the mix and are also so rare that you can't really look to them for a good or bad night.

            The critical hand is the Four of a Kinds.  Earlier I said that they make up 6% of the payback.  That is on a jacks or better game.  Move to Bonus or Double Bonus or Double Double Bonus and these number goes way up.   You win or lose in these games based on two key factors.  Do you get your fair share of Quads and which Quads do you get (when playing the bonus games)?   If you play 3000 hands, you can 'expect' to hit about 7 Four of a Kinds.  It would not be uncommon to play this many hands and get only 2 or 3.  If you have one of these nights, you're not likely to walk out a winner.  Quite frankly, you may not walk out with any of your bankroll left.  Fortunately, it is just as common to get 10 or 11 of them.  In these cases, you are very likely to walk out a winner.  If you're playing Double Double, you'll also want to hit some of the bonus Quads and/or the 'double' bonus quad with one of the kickers. 

            Playing the right strategy is, of course, a critical component of getting your fair share of Four of a Kinds.  But, the right strategy does only so much to make the 5th card in Quad 3's also be a 2, 4 or Ace.  Sometimes it just takes luck to have that good night.  Sometimes my right fielder actually catches the ball.  All I can do is hope.

Nutritional Labels for Casino Games?

            Today's column topic comes from my Freshman college roomate.  He posted a question to one of my old columns on my blog (gambatria.blogspot.com).  He wanted to know if I thought if the casinos would ever have to disclose all the key statistics about each game - a sort of 'nutritional label' for each game.  My response was that I didn't think so for 3 reasons.  The latter 2 were more political than mathematical.  This column is about that first reason.  With the exception of slot machines, all that information about each game is already fully known.

            While admittedly, if the average person were to walk up to a game that he has never seen before, he isn't going to know what the payback or win frequency is.   I'm an expert and I couldn't necessarily tell you these key stats about a game I've never seen before.  I might be able to take a good guess about it, depending on whether we are talking about a complete game or a sidebet.  There isn't a lot of variation in table game paybacks.  There are probably very few that are below 97% and, of course, none above 100%.  Sidebets can have a much larger range, as some are as low as 75% and others go up to the mid 90's or even a smidge higher.   If I were to walk up to a video poker machine that has a foreign paytable, but is based on one of the better known games, I can probably peg the payback to within .25% by doing some quick math in my head.

            There is little doubt that putting the key statistics on each machine would make this information far more readily available than the way it is currently done.  But, I wouldn't equate this to a can of soup without a nutritional label.   The list of possible ingredients and the exact quantities in the soup is nearly endless.  Throw in the fact that there are hundreds of thousands of food products (or more?) and it is completely impossible to make a choice based on nutritional content without these labels.  When you walk into a particular casino, you have perhaps a dozen or so choices of which table game to play.  Yes, each casino may have its variation of rules.  One may offer a 6-deck shoe for blackjack and the other may have a single-deck game.  One may hit on soft 17 and the other may stop on all 17s.  But, if you spend time reading a book or two on gambling, you'll quickly learn and likely remember the paybacks of most of these rule variations.

            For many games, there is almost no variations available - especially for the base game.  Want to play Three Card Poker?  It has a 97.98% payback for Ante/Play.  While there are some variations of Pair Plus, the overwhelming number of them have the same paytable, paying 92.72%.   These numbers are not known because Shuffle Entertainment published them, they are known because any mathematician/programmer can calculate these numbers using a variety of techniques.  In the case of Ante/Play, there are a total of 6 cards dealt to the Player and the Dealer (3 each).  There are 22,100 possible Player hands and 18,424 possible Dealer hands for each of the Player hands.  Thanks to the speed of today's computers, a program can run through ALL of these hands (numbering well into the Trillions), determine the right strategy for each Player hand and tell us absolutely everything we would ever want to know about the game - the payback, the win fequency, the probability of winning given any Player hand, how often the Player folds, how often the Dealer doesn't qualify, etc... 

            Unlike food, casino games are, well, gambling.  Part of gambling is rewarding those people who are more prepared and more knowledgeable about gambling.   The strategy for Three Card Poker doesn't take a PhD to learn.  It takes about 20 seconds (or less).  Play a Q-6-4 or better.    You could read this just about anywhere on the internet.  If you want to know the details about the strategy (how and why), you can read a booklet on the game (I suggest my very own Expert Strategy for Three Card Poker, but that's just me!)  Armed with this strategy you are very likely to do better than someone who has no idea what to do over the short run and almost assuredly so over the long run. 

            For years, people have asked me if I'm banned from casinos because of my in-depth knowledge of table games or if I'm 'hated' by the casinos for arming people with the strategies for how to play the games.  I'd like to think that I've had at least some influence on how people play.  But, I don't think the casinos care one bit.  Even with the best strategies, all casino games (except a few video poker variants) have house advantages.  The casinos are totally fine with a few people playing near the theoretical payback as results are all relative.  A few people who are winning in the short run or who are doing better than the rest can keep the rest of the Players in the game.  After all, if the other guy can win, why can't I?  Of course, this is far more true IF you know the right strategy. 

            I've often surmised that if I were to stand near a Three Card Poker table, handing out my booklet for free that only 20-25% of the Players would actually use the strategy.  Half of these people would probably give it up within the hour when the results don't match the theory - ignoring the time factor that is required for this to happen.  What this really translates to is that I don't think it would matter one bit if the casinos were to put a little sign on each table that had the payback and win frequency of the game.  Most Players would probably ignore them.  After all, how many people really read those nutritional labels on food anyhow?  And that's about what actually goes INTO your body!