Thursday, April 28, 2011

The Case For War

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

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

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

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

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

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

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

Wednesday, April 27, 2011

Bankroll Considerations

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

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

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

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

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

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

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

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

Wednesday, April 20, 2011

What To Do When You Win Early

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

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

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

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

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

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


Tuesday, April 12, 2011

Who Isn't Crazy 4 Poker?

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

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

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

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

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

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

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

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

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

Tuesday, April 5, 2011

The Storm After the Calm

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

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

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

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

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

            The basic strategy is as follows:
  • Play 3x if you have a Pair of 10’s or Better
  • Play 1x if you have a Pair of 3’s through 9’s
  • Fold if you have a Pair of 2’s or less

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

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