Strategize

            Every casino game that is more than pure luck has some strategy associated with it.  This goes beyond the basic strategy that simply says you're better off not playing at all.  For many games, the strategy can be summed up with a simple sentence or two.  For Three Card Poker, it is Play Q-6-4 or better.  Four Card Poker has a two sentence strategy that tells you when to fold and when to Raise.  Let It Ride's strategy takes a few sentences telling you when to pull down the 1 and 2 wagers.

            As strategy gets more complex, it is helpful to try and put it into as easy as a format as possible to help a mere mortal to utilize it.  It is relatively easy to program a computer to play a game perfectly.   Very few humans can take every game to this level.  Also, expending that much energy on memorizing a very complex strategy can pretty much sap the fun right out of the game.  Blackjack utilizes a relatively simple matrix that crosses the Player's hand with the Dealer's upcard. 

            Creating a strategy for video poker is quite a challenge.  As said earlier, telling a computer which one of the 32 ways to play a hand is relatively easy.  But, there are 2,598,960 unique 5-card deals from a standard deck.  Coming up with a way to group these together in a way that a Player can use is a whole different story.  I believe it was my father, Lenny Frome, who was the first person who accomplished this.  He grouped hands together in a way that Players could easily understand and hopefully memorize. 

            A video poker strategy table consists of only two columns.  The first contains the hand rank as it was categorized by my father.  The second contains the expected value of the hand.  Ironically, this second column isn't even needed to play video poker properly.  It is there just for reference.  So, that means the video poker strategy table consists of a single column - usually with about 30-40 rows/entries in it.  To play video poker the correct way, you have to memorize the order of these entries.  This is not nearly as daunting as it seems.  About 10-15 of these entries are more than a little obvious.  So, you're left with about 25 hand types that you need to learn.

            Let's start at the top of the strategy table which contain the most obvious hands:

·       Royal Flush

·       Straight Flush

·       Four of a Kind

·       4- Card Royal

·       Full House

·       Flush

·       Three of a Kind

·       Straight

            We'd be having a great night at video poker if these were the only hands we were dealt.  These are all big winners, all with expected values of 4.00 or better.  In fact, only one of these hands is not a sure winner - the 4-Card Royal.  This is also the only hand that might overlap with any of the others, creating the only strategy decision in the bunch.  What do you do if you are dealt a Straight (or a Flush) that is also a 4-card Royal?  Well, now you know the answer.  You have to throw away the sure winner to go for the big winner.  The good news is that if you have a 4-Card Royal, you have a very good chance of still winding up a winner.  There are 47 possible draws, 1 of which will result in the Royal.  Another will give you a Straight Flush.  6 or 7 more (depending on whether you threw away a Straight or Flush) will result in a Flush.  5 or 6 will result in a Straight and a host more will give you at least a High Pair which will seem like small consolation.

            While this decision might be agonizing, mathematically, it is very clearly the proper play.  The expected value of the 4-Card Royal is 18.66.  The expected value of the Flush is 6 and the Straight is 4.  Of course, don't expect to see this hand every hour.  A 4-Card Royal will show up once in about 2700 hands and only about a third of these will be a Straight or a Flush.   One other key point to note.  Do NOT throw away a Straight Flush to go for the Royal.  That Straight Flush has an expected value of 50 which far exceeds the 18+ of the 4-Card Royal.

            Next week, I'll move down the strategy table to the hands that require a bit more thought.

Table your Hunches

            Last week, I described how all casino game strategy is based on expected values.   You hit or stick in blackjack not because you hope the next card is of a certain value, but because there are certain probabilities as to what the next card will be and how it will affect your hand and your chances of winning or losing.   If you're dealt two face cards, you don't give much thought to strategy.  Hopefully, you're not one of those Players who even thinks about splitting 10's! 

            But, if you are dealt a 16 and the Dealer has a 7, you start giving thought to the strategy.  With a 16, you have 5 cards that will help you and 8 that will bust you.  The odds don't look to good and this is why a lot of people stick on this hand, albeit incorrectly.  You can stay put, but with a 16, the only way you can win is if the Dealer busts, which will happen only 26% of the time.  So, your choices are a 61% chance of busting right away or sticking and having a 74% chance of losing that way.  Of course, by hitting you also have an opportunity improve your hand.  All of the 5 possibilities improve your hand.  If you pick up an Ace, you'll be most likely to push.  Pick up a 5 and you'll win more than 92% of the time.  Don't get me wrong, it is not a strong hand and the decision to hit is not an overwhelming one, but it is still the right move.  In the simplest form, if you face this situation enough times - which you will if you play for a few hundred hours, you'll find that you do better by hitting than by sticking.

            In blackjack, you don't have to memorize all of the math behind the game.  You don't have to figure out how many cards will bust you or bust the Dealer.  To learn to play blackjack, many Players use a simple strategy table.  It is a simple little chart that shows every possible Player hand and each possible dealer upcard.  It then shows what to do - hit, stick, double, split, surrender, etc..  Guys like me have already done all the number crunching for you.

            Video poker is no different than blackjack except the decision making process is far more complex.  In blackjack, the result is essentially binary - you win or you lose (okay, you can tie also, so it is not really binary).  In video poker, you can have 1 of many results - ranging from a Royal Flush down to a High Pair or you can lose.  Since each of the different winning hands pays a different amount, the specific result must be taken into account.  If someone invented a game of video poker in which all hands above a certain rank paid a fixed amount, then we'd be able to lump all the hands into win or lose.  But, we need to know the probability of each final outcome with a different payout in order to appropriately determine the value of getting that hand.  Surely, it is more valuable to wind up with a Straight Flush than just a Straight.

            Video poker is also more complex than blackjack in that there is more than just a handful of different possibilities for each hand.  The Player can hold all 5 cards or discard all 5 cards or anything in between for 32 different possible plays.  Yes, most of these possibilities will be quickly discarded, but they still must be considered from a mathematical perspective.  They are only discarded because the human mind can quickly recognize possible draws that would clearly not be the best strategy. 

            Despite the extra complexity of video poker, the similarities are still stronger than the differences.  In the end the decision still comes down to the expected value.  Like in blackjack, you don't have sit there trying to figure out how many cards you need to complete a Straight or the like.  Again, guys like me have already done the job.  We have looked at every possible deal, every possible draw for every possible deal and summed up all of the final hands.  Using this distribution, each possible draw is assigned an expected value.  Whichever draw has the highest expected value is deemed the right play.  The last step in the process is too try and categorize the way each hand is played into a format that a human can use to play the hands.  We call this a strategy table.

            Unlike blackjack where the strategy is a matrix that crosses Player hands with Dealer hands and tells you what to do, a video poker strategy chart lists all the possible playable hands in order in a simple table.  The table usually contains the expected value of each hand too, but this is just for information.  To use the strategy table, you basically work from the top and find the first hand that your dealt hand can make and that is the way to play the hand.  So, if you are dealt a hand that is a 4-Card Straight and a Low Pair, you start at the top of the table and work downward.  If a 4-Card Straight appears first, you play that.  If a Low Pair appears first, you play the hand that way.  If you can't find any hand that matches the hand you were dealt, then you fall to the bottom of the table and find a RAZGU which means throw all five cards.

            Next week, we'll begin breaking down a strategy table for full-pay jacks or better.  You'll be on your way to becoming an Expert Player.

The Advantage of Expert Play

            This morning, I had a discussion with a friend of mine about a game he is developing.  I explained that playing 'perfect' strategy would be nearly impossible due to some subtle complexities of the way the game is played.  As a result of this, the game would not likely play anywhere near its 'theoretical' payback.  Many games have this 'problem'.  Blackjack pays 99.5%, but very few players play anywhere near this.  Ultimate Texas Hold'em has a payback well into the 99% range too, but stats from the casinos make it clear that very few Players, if any, can manage this high of a payback.

            My friend stated that he thought that he would be able to play the game close to the theoretical because he is an accomplished Poker Player.   I asked him if he was an accomplished video poker Player and he said that he wasn't.  I told him that any table game against a Dealer was really nothing more than playing video poker and had no resemblance to poker even if the game resembles poker.   Poker is about reading Players, understanding their betting patterns and their tells.  Video Poker is about one thing - math.   There is no one to bluff.  All that matters is what is the probability of all final hands given what I choose to discard.   Let's take a look at a simple example:

5♠        5♦        6♣       7♥        8♦

            In theory, there are 32 ways to play this hand, but I think we can quickly rule out 29 of them.  I don't think anyone is seriously going to consider holding only the off-suit 6-8 or holding all 5 cards (which would result in an immediate loss).    There are really on 3 possibilities, 2 of which are identical.  The Player can either hold the Pair of 5's or the 4-Card Straight (hence, the 2 identical possibilities as it doesn't matter which 5 the Player keeps.)

            If the Player keeps the 4-Card Straight, 8 cards will result in a Straight and the rest will result in a loss.  So, if we add up the total payout, we'd have 8 Straights at 4 units each for a total of 32 units.  There are 47 possible draws.  We divide the 32 by 47 to get 0.68.  This is called the Expected Value (or EV) of this hand using this possible discard strategy.

            Calculating the Expected Value of holding the Pair is a bit more complex, but easy enough to calculate using a computer.  There are 16,215 possible draws if the Player holds 2 cards.  We look at these possible draws and look at the final hands.  The Player can wind up with a Four of a Kind, Full House, Three of a Kind or Two Pair.  We add up the total payout of all of these winning hands and divide by 16,215.  The result is an EV of 0.82. 

            This Expected Value is greater than that of the 4-Card Straight, so the proper play is to hold the Low Pair.  When Playing video poker (and virtually every other casino game), the proper play is to follow the one with the highest EV.  You don't go with a 'hunch' that a 5 is coming up or that you just feel a 4 or a 9 is going to fill out that Straight.  There is a distinct probability of each of these events occurring and we use those probabilities to our advantage.  This is what allows a Player go achieve the theoretical playback of a game. 

            It is an 'advantage' because most Players don't play this way.  Because of this, the casinos can off the games with a relatively high payback, knowing that they can rely on human error to pad their profits.  For the Players who play according to the math, they have the advantage of being able to play to the theoretical payback over the long run.

            Mastering video poker takes some significant effort.  The strategy is a complex one and learning whether to hold the Low Pair or the 4-Card Straight is merely one example of where a strategy where you play by what you think is right may in fact be quite wrong.  The good news is that thanks to guys like me, the toughest party of learning the strategy (creating it) has already be done for you.  The next step is learning that strategy and putting it to practical use.  We'll save more of that for next week.

Video Poker Primer

            It was just over 10 years ago that I started writing for Gaming Today.  I have to be honest, that really blows me away.  That means I've written roughly 500 columns when I take into account off weeks and the fact that for the first 6 or 9 months, my column was bi-weekly.  I remember when I wrote my first few columns, I would wax poetic about how my father (Lenny Frome) had written nearly 1000 columns for a variety of different publications.  I remember when I hit column number 100, I remarked how far behind I was.  Now, my total count is probably about 600-700 columns and I can almost see myself someday surpassing my dad's total.  That said, I definitely don't plan on taking steroids or PEDs to get me there.

            Part of what is so amazing about having written 500+ articles is that I have somehow managed to come up with that many things to write about.  I'm not really sure that there are 500 unique subjects to write about.  I have to remember that if I borrow a subject from 2005 that there is a strong likelihood that if someone reads it today, they didn't read that article from 8 years ago.  So, in that spirit, I'm going to start back at the beginning today and discuss some basics about video poker.

            Video poker is truly a unique game in the casino.   Far too often it is lumped together with Slots, but there is little in common except for the technology.  I don't think of a video blackjack machine as a slot machine and the same is true for video poker.   As the world starts turning more to online gambling, the separation will no longer be about the technology.  Instead it should be about the essence of the game.  Video Poker is a game that is based more on skill than almost any other game in the casino.  This doesn't mean that luck doesn't play a part, especially in the short run.  But, if I were to challenge a random Player to a slot competition, there would be no way to gain an advantage.  If I were to challenge a random Player to a video poker competition, I'd like to believe that I would have a distinct advantage.  The longer the competition runs, the more strategy and skill will rule the day and the less that luck will impact the results.

            How is video poker a game of skill?  Because the Player must make a decision that will clearly impact his results.  This decision is frequently NOT of the 'no-brainer' variety.  Technically, in the game of Casino War, the Player must make a decision to - whether or not to go to War when the Player and Dealer tie.  But, the proper decision is the same all the time - to go to War.  So, while technically, there is 'strategy', I doubt very many people get this one wrong.  In Three Card Poker, there is one strategy decision - to Play or Fold.  The decision is also relatively simple.  If the Player has Q-6-4 or better, he should Play.  As simple as this sounds, many Players don't follow this rule (and I don't mean that they go with Q-6 or Q or better), and as a result, they give up a larger portion of their bankroll to the casino than they need to.

            Video Poker strategy is far more complex than this.  First of all, the decision is not one of Fold or Play, but rather which cards to Discard.  There are 32 ways that a Player can make each of these decisions, ranging from keeping them all to discarding them all.  Granted many of these possibilities will fall into the brainless category.  If you are dealt Three of a Kind and two off-suit kickers, which cards to discard is pretty obvious.  If you are dealt a Straight, then you don't have to discard at all.  Oh wait, what if it is also a 4-card Straight Flush or a 4-Card Royal, then what is the proper play?

            If you are dealt the following:

4♦        4♠        5♠        6♠        7♣

the decisions get a bit more complex.  You might keep the Pair of 4's, or the 4-Card Straight or maybe the 3-Card Straight Flush.  This is 3 of the 32 ways the hand can be played.  The other 29 are quickly discarded, so there isn't a need to go through 32 possible decisions for each hand.  Obviously, you're not going to keep the off-suit 4-7 in this case.

            Unlike table poker (which involves even a higher level of skill), the strategy in video poker is based strictly on math.  You don't play hunches and you're not trying to beat another Player.  You don't have to worry that you might pull your Straight and he might come up with a Flush.  All that matters is the likelihood (aka probability) of each final hand and how much that hand pays.  But, I'll leave that for next week.  For now, I'll be happy if I've convinced you just a little bit that video poker is not slots.

            

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.

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!

            

Advantage: Dealer

            I don't think this will shock any of you.  Every table game has a house advantage.  Numerous mechanisms are used to build this house advantage.  By now, most Players are probably used to most of these methods, that they barely notice them.  If the game of Three Card Poker were played such that the Player made a wager, got three cards and then simply went head-to-head against the Dealer's 3 cards, the game would be a 100% payback.  Any game in which the Player and Dealer get the same number of cards and no decisions after the initial wager is made is simply one big push.

            In the game of blackjack, the Player must act first.  If he busts, he loses.  It won't matter if the Dealer busts also.  This is an advantage for the house.  The Player's ability to double down, split and decide when to hit/stick are advantages for the Player.  I've often be quite amazed that the game of blackjack was developed centuries ago without the use of computers (obviously) and somehow managed to deliver a payback right where you would want it! 

            In the game of Three Card Poker, the Player and Dealer receive the same number of cards, so that's an even game.  The Player, however, gets to decide when to Play/Fold so this is an advantage to him.  He can take his really weak hands and walk away from them without making another wager.  He can wait for his stronger hands and Play.  In the background to this process is the fact that because the Dealer always gets 3 cards, the Player knows what the 'average' hand for the Dealer is.  In fact, he can know the frequency of every possible hand.  This is what allows him to create the proper strategy for Playing vs. Folding.  If the game ended here, the Player would have a significant advantage.  To offset this and get back to a house advantage, the Dealer must qualify with a Queen High Hand.  As a result of this, the Dealer essentially surrenders 30% of his weakest hands and cuts the payout to the Player in half.  For a small portion of these hands, a bad Player might actually benefit - by Playing a hand below Q-6-4 and going against the right strategy.  Despite these occasional wins, the casinos will more than gladly make up for this with all the Jack High hands that the Player will lose.

            Ultimate Texas Hold'em adds a twist to the idea of Dealer qualifying.  In UTH, if the Dealer doesn't qualify, the Ante wager pushes, but the Play wager stays in Play.  If we were to use this rule in Three Card Poker, it wouldn't make a difference to the overall payback because a Player should fold every hand that would result in loss where the Dealer does not qualify.  However, in UTH, Players sometimes make a 4x wager or a 2x wager with something less than a Pair.  If the hand doesn't develop (usually you're shooting for a Straight or a Flush), the Player may be left with a very poor hand.  If we used the TCP qualifying rule, the Play wager might push and the Ante wager would pay even money.  In UTH qualifying, the Ante pushes and the Play wager is in play.  The Player could be left with a Queen High hand.  If the Dealer has an Ace High hand, the Ante will push and the Play wager will lose.  This subtle difference in how qualifying is handled gives the casino just a smidge more edge.  In the case of UTH, this is the difference between the game having no house edge and having just the right amount of house edge.

            Moving on, we find ourselves at Four Card Poker.  Four Card Poker has no Dealer qualifying.  Every hand is in play.  All wagers are in play (assuming the Player doesn't fold).   So, where does the house advantage come from?  The Dealer gets an extra card.  Despite the name of the game, the Player gets five cards to make his best 4-card hand.  The Dealer gets six cards to make his best 4-card hand.  This little 'advantage' is enough to get rid of qualifying and to allow the Player to make a 3x Play wager if he so chooses.  If the Dealer were to get the same number of cards as the Player, then each would win the same percent of hands.  Even to allow an optional 1x Player wager would require the adding of some sort of qualifying.  To allow a 3x Play wager, the qualifying might not even be enough.  Instead the Dealer gets an extra card, meaning that he will win a larger percentage of the hands. 

            I'm sure that if I were to look at all the games on the casino floor, I'd see a variety of other different methods for creating a house advantage.  While each has a math component and provide different amounts of house advantage, the real impact of the methods is more psychological than mathematical.  How do you feel about the Dealer having a stronger hand, on average, by being dealt more cards?  If you beat the Dealer, you might win more than you would if you play him in a game where you are each dealt the same number of cards.  There is no real correct answer.  There is simply a variety of proven methods for doing this - and probably even more that haven't been thought of yet.

House Money Breaks the Mold

            As most of you know, I wear two hats in the gaming analysis world.  There are some that might see my two roles as being opposed to each other.  Quite frankly, at first, so did I.  Over the years, however, I realize that they are more complementary than anything else.  On one hand, I analyze games already created and write about them, with the goal being to educate the Player to become the best possible Player he can be.  On the other, I help invent games.  Some may think I do this using my knowledge of how Players act to create games designed to trip them up.  This simply is not the case.  Even when working with inventors, I do my best to steer the game in a direction that offers the highest paybacks possible.

            Let me be clear.  Games are created with a house edge.  If you consider that to be 'rigged', then there isn't much more to discuss.  No casino is going to purposefully put a game on the floor that has a Player edge.  The one and only exception, to the best of my knowledge, is video poker, where there still remains some full-pay machines that pay over 100%.  However, as most of these are at too low of a denomination to really do harm to the casino, they are content to let the very few profit at the expense of the overwhelming majority. 

            In the last several years, I have the pleasure of helping to develop Mississippi Stud and Ultimate Texas Hold'em.  These two games boast paybacks in the mid to high 98% range and up.  Part of the reason they are able to do this is because they require intricate strategy in order to achieve these theoretical paybacks.  This is also one of the reasons why video poker can offer such high paybacks.  To achieve these paybacks require that a Player play using a robust strategy that most Players do not bother to learn.  Slot machines in contrast offer absolutely no strategy.  As a result, the casinos cannot rely on human error for any part of their profits and they must offer lower paybacks.

            The same is true of sidebets for table games.  For the most part, it has pained me when I see the paybacks on sidebets.  It is not uncommon for them to be the mid 80% to low 90% range.  Some, go even lower into the high 70's.  Some sidebets, especially Progressives, offer huge payouts for the Player and so Players are willing to trade this low payback for the remote chance of the life-changing payout.  Like slot machines, casinos must offer these lower paybacks because the sidebets offer no strategy and they cannot rely on any human error to drive profits.  The problem with attempting to offer sidebets with strategy is that the strategy almost assuredly works against the basic strategy of the underlying game.  This is a 'no-no' because the combined payback will now be lower than the two separate paybacks AND it can require the Player to learn some new hybrid strategy that may be more trouble than it is worth.

            Less than a year ago, one sidebet broke this model completely.  I've written about it before, and I have to admit that it is the only sidebet that actually gets me excited.  On the one hand, it is definitely a sidebet.  On the other, it is almost an entirely new game within a game.  Yet, if a Player chooses not to play it, it does not impact the base game.  Quite frankly, even if he does choose to play it, it doesn't affect the base game.  But, it does require learning a strategy for the sidebet.  The game is called House Money , and it is a sidebet to blackjack.

            The game is really quite simple.  If you make the House Money sidebet, you will get paid if the first two cards you are dealt for blackjack are a Suited AK, a 2-Card Straight Flush, a Pair or a Straight.  This works out to be about 21.5% of the time.  The most common payouts are 9,4,3,1 respectively (although there are multiple paytables).   Now, the fun begins.  After you are paid for your sidebet, you have the option to take all of your winnings from your sidebet (which includes the original sidebet wager) and you can add it to your base blackjack wager.  This is AFTER you have seen your two cards and AFTER you have seen the Dealer's upcard.   So, if you're dealt a 10-J suited, you will win 4 to 1 for your sidebet.  Assuming you wagered $5, you will now have the right to take the entire $25 (the $20 you won plus the $5 sidebet wager) and add it to your base blackjack wager. 

            In the case of the 10-J you would ALWAYS want to do this.  The Dealer will check for blackjack prior to you making this additional wager, so you are not risking your winnings if the Dealer has blackjack.  Imagine have a $5 wager on the base game and $5 on the sidebet when dealt this hand.  Dealer turns a 7 up and then flips over a 10.  Your $5 sidebet becomes $25, which turns your base wager into a $30 wager.   When you win this, you just won $50 for being dealt a suited 10-J and winning the blackjack hand.

            One strange fact about House Money is that the payback of the sidebet actually goes UP with more decks.  This is because some of the winning hand are more frequent with more decks.  With 6 or 8 decks, House Money pays 97+% and it makes absolutely NO IMPACT to the base game of blackjack.   That said, it is imperative that you choose to let your winnings ride (i.e. cap your wager) at the right times AND that you play proper blackjack strategy.  If you are dealt a 5-6 against a 7 and choose not to cap your wager OR cap your wager but then 'chicken out' and not Double Down (which requires doubling the ENTIRE wager), then you will not achieve the 97+% payback.

            Below is a matrix that shows the proper strategy for House Money for 6 and 8 deck shoes when the Dealer hits a soft 17.  There are some minor modifications if you are playing with less shoes or if the Dealer sticks on all 17s.  As for basic blackjack strategy, you can find that almost anywhere on the internet or in a book on blackjack.

Hand	Dealer Upcard
	2	3	4	5	6	7	8	9	10	A
A-2	Y	Y	Y	Y	Y	Y	Y	N	N	N
2-3	N	N	N	N	Y	N	N	N	N	N
3-4	N	N	N	N	Y	N	N	N	N	N
4-5	Y	Y	Y	Y	Y	Y	Y	N	N	N
5-6	Y	Y	Y	Y	Y	Y	Y	Y	Y	Y
6-7	N	N	N	N	N	N	N	N	N	N
7-8	N	N	N	N	N	N	N	N	N	N
8-9	N	N	N	N	N	N	N	N	N	N
9-10	Y	Y	Y	Y	Y	Y	Y	Y	Y	Y
10-J/J-Q/Q-K	Y	Y	Y	Y	Y	Y	Y	Y	Y	Y
K-A	Y	Y	Y	Y	Y	Y	Y	Y	Y	Y
2-2	N	N	Y	Y	Y	Y	N	N	N	N
3-3	N	N	Y	Y	Y	N	N	N	N	N
4-4	N	Y	Y	Y	Y	Y	N	N	N	N
5-5	Y	Y	Y	Y	Y	Y	Y	Y	Y	Y
6-6	N	N	Y	Y	Y	N	N	N	N	N
7-7	N	N	Y	Y	Y	N	N	N	N	N
8-8	Y	Y	Y	Y	Y	Y	N	N	N	N
9-9	Y	Y	Y	Y	Y	Y	Y	N	N	N
10-10/JJ/QQ/KK	Y	Y	Y	Y	Y	Y	Y	Y	Y	Y
A-A	Y	Y	Y	Y	Y	Y	Y	Y	Y	Y

Y - Cap the wager                   N - Take the winnings

            House Money can now be found in Las Vegas at the following casinos - The Cannery, Fiesta Las Vegas, Green Valley Ranch, Jerry's Nugget, Monte Carlo, Palace Station, The Palazzo, Santa Fe Las Vegas, Sunset Station, Texas Station and The Venetian.