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!

            

Psychological Warfare - How they 'rig' slot machines

            A few years ago, I wrote a column about a story I read in The Economist magazine.  It described a study done testing the impact of near misses on a slot machine on the human brain.  What the researchers found out was that near misses generated almost an identical reaction in the brain as an actual win.  So, if bar-bar-plum (a loser) can make the Player feel almost as good as bar-bar-bar (as winner), all the manufacturers have to do is figure out how make near misses show up a lot and Players will feel like their winning almost all the time.  Fortunately, the regulations and the technology do not make this much of a challenge.  Slot machines can legally be programmed to generate a disproportionate number of near misses relative to what might be considered random.   So, while they might throw in some fruit salad once in a while as an ugly loser, most of your losses will appear to be 'oh so close' to winners.

            Now, a new study was released this week that says the bells and whistles used on slot machines makes the Player feel like he is winning even when he isn't.  The days of coins dropping out of the slot are virtually gone, so the casinos added sound effects to the machine.  When you used to hit a cherry and get 2 coins back and heard klink-klink, this was simply not the same as hearing 20 or 100 coins going klink-klink-klink.  But, in the digital age, no one says the sound effects has to mimic the actual win.  So, the casinos can have a simple 2-coin win sound a lot like a 10-coin win.   To prove the theory, the researchers had slot Players play with sound and without sound.  Those with sound had a stronger impression that they were winning, even when they weren't.

            While this latter concept can be used for video poker, it holds a little less water because in most varieties of video poker there is no such thing as winning but really losing.  While many hands in video poker result in a push - which may FEEL like winning because your original wager is returned (i.e. Jacks or Better), there is generally no hand that returns only a portion of your original wager.  With the new generation of slot machines it is not uncommon to wager dozens of coins.  Frequently, a 'win' will result in getting only a fraction of your wager back.  Did you really win?  If you wager 20 coins and get back 5, is this a win or a loss.  Admittedly, I am the first to argue that once you wager the money it is lost and any money you get back is a 'victory'.  This seems much more applicable to table games where you play 30-40 hands/hour rather than a slot or video poker machine where you can play hundreds of hands per hour and repeatedly wagering 20 and returning 5 can quickly wipe out your bankroll.

            So, what is a Player to do when faced with all of this psychological warfare used by the casinos?  Ironically, you have to use your own type of science against them.  The science of math.  Yes, with the exceptions of some varieties of video poker, the math says that in the long run you will lose.  I've written many times that you need to look at casino games as a form of entertainment.  The question is do you want your night of entertainment to cost $20-$40 or to cost $100-$200?  I'm guessing that you'll get a lot more value for your money if you spend less money.  Most of the games in the casino are built to allow the Player to win about a third of the time over a 3 hour session.  This assumes that you learn to play each game correctly and try to pick the right games/paytables to play. 

            While I strongly advocate for playing video poker, if you wind up playing a jacks or better that pays 6-5 (Full House/Flush), you'll be playing a game that has a payback below 96% and your chances of winning will decrease considerably.   In similar fashion, playing a full-pay game has limited value if you don't learn the right strategy.  Casinos rely on these two factors for games like video poker.  Slots have no strategy and inherently have lower paybacks, so they need to come up with ways to essentially fool the Player into thinking he is doing better than he actually is.  Video Poker doesn't need to create artificial near misses.  A deck of cards and a dealt hand do an amazing job of creating these in its natural random fashion. 

            To combat the near misses and the bells and whistles of the casino requires doing a little bit of homework to learn which games to play and to learn the right strategy for those games.    It requires some discipline to stick to those strategies and to seek out the right games.  Math can be your rock to the casino's 'psychological warfare' scissors.

An Error of Commission?

            A couple of weeks ago I discussed methods used by game developers to create a house advantage.  I realized that I left off two common one.  They are somewhat related as the second one was created in attempt to get rid of the first.  The first method is called taking a commission, which I've generally thought of as a misnomer, because it only applies to winning bets.  In the games of Pai Gow Poker and Baccarat, certain wagers pay a 5% commission when they win.  Another way of looking at this is that the Player is paid 19 to 20 for a winning wager, which I think is more accurate.  Commissions, to me, are paid on a wager, not on a winning wager.  If you pay a commission to a real estate agent, you don't pay it if you get a good deal or only on your profit, you pay it when your house sells - on the gross sales price.

            If you wager $20 and you lose, you lose $20.  If the wager pushes, you get your full $20 back.  If you win, you get $39 - your $20 plus the $19 you win.  So, in reality, you're simply making a wager that pays a little less than even money.  In Pai Gow Poker, this applies to the base wager.  A mechanism such as this must be used because the only other advantage that the House has is that it wins hands that are copies.  But, with a 2-card hand and a 5-card hand, ties are not that common.  While this provides some advantage to the house, it simply isn't enough.  So, they pay 19 to 20 for winning hands.  At first glance, this might seem to create a 2.5% house advantage because the Player and Dealer win nearly the same number of hands.   However, since it is paid only only wins and about 42% of all hands finish as pushes, we find that it really only generates a little under a 1.5% house edge.  When combined with the house edge generated by the house winning copies and the overall house edge is about 2.73%.  This is offset somewhat if the Player chooses to act as the banker which provide an edge for the Player.  But, I'll save that for another day.

            In Baccarat, the Player has the option to wager on either the Player or the Banker hand.  In reality, it is more like Hand 1 and Hand 2 because no hand really belongs to the Player if you can wager on the other hand.  Based on the drawing rules used in Baccarat, the Banker hand has a small advantage.  Because the Player can wager on this hand, this translates to an advantage to the Player.  To offset this, the House again takes a commission on winning wagers on the Banker Hand.   Again, winning wagers on the Banker Hand pay 19 to 20.  The net impact is that the Banker Hand wager has a 1.06% house edge, which is actually LOWER than the Player Hand Wager without a commission.

            The problem with paying commissions is not that it costs the Player money.  Every casino game costs the Player money.  The real question is not what mechanism is used to generate the house edge, but how much of a house edge it generates.  In the case of these two games, it generates a relatively normal sized edge.  Pai Gow's edge is a little on the high side and Baccarat's is on the lower side.  But, nothing incredibly unusual about either.  The issue is that the commission is slow and messy.  Players don't always wager in multiples of $20.  In these cases, the casino might use some method to accrue the commission and then take it when the amount adds up to a round amount.  Calculating a 19 to 20 payback is also not a simple thing for the Dealer.  Sure, a $100 wager pays $95 which is easy enough, but still messier than paying $100.  But, what about when the Player wagers $75?

            These issues led to a desire to do away with the commissions in these games.  In both cases, a similar mechanism was used.   In the case of Pai Gow, a hand that is normally a sure loser for the House is turned into a Push.  In one common version of 'commission free' Pai Gow, if the Dealer has a Queen High Pai Gow hand, then the hand is automatically a Push.  This creates a house advantage nearly identical to the commission.   Now all wins can pay even money and the game is cleaner and simpler.   Only in the occasional situation where the Dealer has this hand is the normal flow interrupted at all, and the impact is relatively minimal to game speed.

            In Baccarat, one of the common mechanisms is to take a sure winner for the Banker hand and turn it into a Push.  The most common hand is a Banker 3-card 7 which wins.  The impact, like in Pai Gow is a virtually identical payback but with the messy commission removed.  Now all wagers can pay even money and the only impact is that special Banker Hand and even when that happens it simply becomes a push.

            In order to be an Expert Player, a Player needs to understand that all casino games are built with a House edge.  The edge comes from a variety of mechanisms.  The specific mechanism is not important to the end financial result.  It can impact the feel of the game and a Player may prefer one mechanism vs. another.  However, that House edge will be there no matter what.  If you play a no-commission version of Baccarat or Pai Gow, mathematically you're playing a nearly identical version of the game.  If you like the simplicity of the no-commission version, play that.  If you get annoyed and pushing hands you should win, then maybe these versions aren't for you.  At the end of the night, you'll probably be a nearly similar financial situation.

            

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.

The Nature of the Game

            My elder son has finished up his year in college and came home the other day.  As we do our best to keep him entertained while in Vegas, we went to the Laugh Factory at the Tropicana the other night.  Invariably, when comedians are in Las Vegas, they will tell jokes about the dry heat and about losing money while gambling.  I think I've been very honest about the odds of long-term winning while gambling.  With the rare exception of some tough to find video poker games and/or the ability to count in blackjack, you're simply not going to win in the long term.  But, this doesn't mean that you have to 'lose your shirt' either. 

            A few weeks ago, I showed how playing blackjack for an hour, a $5 Player should expect to lose only a little over $1/hour.  This, of course, assumes playing properly.  If you are too timid to double down on soft hands, or don't like splitting 2's looking into a 7, then, well, all bets are off as to what your payback will really be.  The comedian was hopefully joking when he talked about struggling to add up his cards while playing blackjack.  If you're really struggling with this, maybe you should try Casino War or Three Card Poker.

            In that same column where I talked about the average you can expect to lose while playing blackjack, I also spoke of the average you can expect to lose while playing full-pay jacks or better video poker.  As the two games have similar paybacks, the only real difference is the average amount you wager in an hour of each game.  Much to many Player's surprise, a max-coin quarter video poker actually wagers more in an hour than a $5 blackjack Player.  That said, however, the game of video poker is far more volatile and while the average loss rate by only be a couple of bucks an hour (depending on speed of play), actual results will wind up all over the place.  Blackjack is a much less volatile game and we will find that our actual results will really tend to be very close to the theoretical amount.

            To help illustrate this point, I ran 100,000 multi-hour sessions of blackjack, each consisting of 100 hands.  I then tabulated the amount won or lost, rounding to the nearest dollar.   First of all, the Player had a winning session nearly 46% of the time.  He lost 49% of the time, with the remainder being breaking even.  Around 32% of the time, the Player will wind up within $20 of his starting point, with only a slight slant towards the losing side.    He will wind up within $40 of his original bankroll more than 55% of the time.   He will wind up losing $100 or more only 5% of the time.  To be clear, this is NOT the same as saying that if he starts with $100, he will go 'bust' only 5% of the time.  The simulation I ran does NOT take into account a Player who may have at some point been down more than $100 and then came back to lose less than $100.  This will not be a huge number, but it will add to the total.

            I'm not downplaying the impact of losing $100.  This is not a small amount and could be considered to be a high cost for 2+ hours of entertainment.  At the same time, we are only talking about a 1 in 20 chance.  At the same time, the Player has a 4.4% chance of WINNING $100 or more.   That's why it is called gambling.

            But, the overall point is that the notion that everytime you gamble you're going to lose your shirt is simply not accurate.  If we assume that 'paying' up to $25 is a fair price for the 2-3 hours of entertainment value, then we find that the Player will meet this goal 62% of the time.  In fact of this 62%, he will actually wind up winning money nearly 75% of the time. 

            As stated earlier, this all assumes playing properly.  This tends to be what trips up Players far more often that the basic nature of the game.  Blackjack has a payback of about 99.5% when played properly.  Played improperly, the payback could drop dramatically,  If you drop it to 98%, which is still a respectable payback for most table games, this may not seem like a lot.  However, turned around, it means the casino advantage increases fourfold.  If I were to simulate such a strategy, we would find that the numbers are not so generous to the Player, and the likelihood of losing one's shirt will go up considerably.

            Thus, while the nature of the game it still one where the Player will lose in the long run, the Player can still greatly control (within reason), just how much will be lost by learning to play using the right strategy.