Casino Math


The key to understanding the mathematics of craps is to understand the dice combinations, or probabilities. In my strategies, we only want to play the bets that have the best probabilities of winning. These are the pass line with odds, come bets with odds, occasional place bets on the 6 and 8, don’t pass laying the odds, and don’t come either with or without laying the odds.

If you play the above mentioned bets, the house percentage in craps is the lowest of any casino game. Taking single odds on pass line and come bets reduces the house percentage to 0.8%… double odds reduces it to 0.6%… triple odds reduces it further to 0.5%… and 10 times up to 100 times odds makes the game almost dead even.

At seminars, I am always asked why place bets are not as good as come bets. The answer lies in the dice combinations. A place bet can be used to illustrate this point. A bet placed directly on the number 5, as an example (aka place bet), can only win on a total of four dice combinations: 1-4, 4-1, 2-3, 3-2. That’s it! When a 7 is rolled, which has a total of 6 dice combinations, the bet loses. That’s 6 to 4, or 3 to 2 against you based on the dice combinations alone.

Now let’s look at a come bet. When the come bet sits in the come area, it wins on a seven or 11 for a total of eight dice combinations and loses on a 2, 3 or 12 for a total of 4 dice combinations. That’s 6 to 4, or 2 to 1 in your favor for the immediate win versus an immediate loss. If that come bet should go to the 5, as an example, it now has another 4 dice combinations to win. So, the come bet that started in the come area and went to the 5 had 12 dice combinations to win, versus only 5 combinations for the place bet on the 5. That’s a huge advantage. This analysis can be applied to every place bet.

Adding the fact that you can take odds on all come bets, the casino advantage on place bets on the 4 or 10 is 6.7%; on place bets on the 5 or 9, it’s 4%; and place bets on the 6 and 8, it’s 1.5%. A come bet, no matter what number it goes to is only 0.8% with single odds, the exact same odds as the pass line with single odds.

To win in craps, you must minimize the casino’s advantage and use money management to capitalize on all streaks, do or don’t. That’s what the Benson Strategies are all about.


Blackjack is the only casino game where the player’s advantage or disadvantage changes with each card played. The game itself favors the house by 4%, mainly because if you break and the dealer breaks, guess who gets the money? The house, of course!

This house advantage can be reduced to 1.5% by playing basic strategy. This in itself makes it a good game to play. With proper basic play and proper money management you could expect to show a positive return over time.

Furthermore, tracking of the cards played, combined with basic strategy, can change the advantage to the player by 1%. The player’s advantage increases as more high cards are left in the unplayed deck (or shoe). High cards favor the player because they give the player a better chance to get a “pat” hand and also they increase the dealer’s chance of breaking. The dealer has to hit on 16 or less. With high cards remaining, this creates a higher chance of a dealer break.

Most common methods for tracking are simple hi-lo counts (good on single deck games) and card clumping methods (good on shoe games). A 1% advantage means that expertly played blackjack is the only casino game that offers the player an expected positive mathematical return.


Baccarat is known as a negative expectation game (the same as craps, roulette, and other). This means that the odds always favor the house. By always, I mean that there is no known method of play that will place the odds in favor of the player mathematically. This can only be done with perfect blackjack card counting (which is why of course they don’t let you win a lot).

The way we win at baccarat is to follow the trend. A trend will develop in any random or near random series of events. Remember, you will not have sufficient lay to establish real probability numbers, since these depend on lots of play to reach statistical significance. You could be skewed in one direction: 50% more players than bankers for instance (which would be very nice, by the way).

The casino sees real statistical significance since they have so much action going on all the time. They cannot lose from gaming itself. They can only lose from not getting enough players or from typical business profit/loss scenarios. But they do not LOSE on the gaming itself. It is not possible. But it is very possible for the casino to lose to individual players. The casino makes up for these losses because they have enough players to make the mathematics work for them in the long run.

This last point is very important. Because unless you play 24 hours a day, you will never be playing by the same mathematical statistics as the casino. Our departure rules and money management eliminate this immediately. The casino will only beat the Baccarat player by his or her lack of discipline and/or poor play.바카라


Roulette has a 5.26% advantage over the player. The reason for this is that there are actually 38 numbers on the wheel: 1-36 and 0 and 00. The payoffs, however, are based on the 36 numbers only, not the 0 and 00. The single number pays 35-1. So, simply stated, the 0 and 00 are the casino’s edge.

Over a long period of time, the casino will have a definite mathematical advantage.

Casino’s Math


  • Needs lots of playing action to achieve true odds.
  • All statistics are based on an infinite number of rolls.
  • Hates deviations in bet sizes.
  • Does not like structured play, especially in departure rules and money management.
  • Once the volume of play is achieved the mathematical edge is guaranteed.
  • The casino will offer any enticement to achieve this guaranteed mathematical edge.


The Leonard Benson Company – Your partner in winning!