Notes

Casino Math

Craps

Understanding the probabilities and dice combinations is key to understanding craps mathematics. In my strategies, we only want to play the bets that have the best probabilities of winning. These are the pass lines with odds, the come bets, the occasional place bets, the 6 and 8 don't pass placing the odds and can't be placed with or without the odds.

The house percentage in craps falls to 0.8% if you make the above-mentioned wagers. The house percentage drops to 0.8 %... double chances. This reduces to 0.6 three odds. This reduces to 0.5 , and then to 0.5 . It can also be reduced to 0.5 triple and ten times to 100 times the odds.

I'm often asked at seminars why place bets don't perform as well as come bets. The answer lies within the dice combinations. A place bet can be used to illustrate this point. You can only win a direct bet on the number 5, which is also known as a place betting, on four different dice combinations: 1-4-4-1, 2-3, 3-2 and 2-2. That's it! The bet is declared lost when a 7 is rolled. virtual reality gives you a total of 6 combinations. This is 6 to 4 or 3 to 2 against, depending on the combination of dice.

Let's take a look at a "come bet". If the come bet is placed in the come area, it will win on a seven or 11, for a total eight dice combinations, and lose on a 2, 3, 12 or 12 for total of 4 dice combinations. The odds of winning an immediate win are 6 to 4 or 2 to 1. This means that if the come bet is placed on the 5, it has an additional 4 combinations of dice to win. The come wager that started in a come area and moved to the 5 had 12 options to win. This was compared to 5 options for the place bet. That's a huge advantage. This analysis is valid for all types of bets.

You can also take odds on all of your come bets. Place bets for the 4 or 10 are 6.7% and 4% respectively; place bets for the 5 or 9 are 4% and place bets for the 6 or 8 are 1.5%. A come wager, regardless of the number, is 0.8% with single chances and the exact opposite odds to the pass line.

To win in craps you must limit the casino's advantage. Also, money management will allow you to take advantage of all streaks. The Benson Strategies help you do just that.

Blackjack

Blackjack is the only casino game in which the advantage or disadvantage of a player changes with every card that is played. The game itself favors 4% the house, because if the dealer breaks, guess who takes the money. The house of course!

Playing basic strategy can help reduce the house advantage by as much as 1.5% This is enough to make it a worthwhile game. It is possible to expect a positive return with good basic play and smart money management.

In addition, basic strategy combined with tracking of cards played can increase the player's advantage 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. This increases the chance of a dealer breaking if there are still high cards.

Most common methods for tracking are simple hi-lo counts (good on single deck games) and card clumping methods (good on shoe games). The 1% advantage is the highest expected mathematical return for expertly played blackjack.

Baccarat

Baccarat can be described as a game of negative expectation (just like craps or roulette). games to play means that the odds always favor the house. This means that mathematically, there is no way to place the odds in the favor of the player. This is possible only with perfect blackjack card counting (which, of course, doesn't let them let you win much).

You can win at baccarat by following the trends. A trend can form in any random or nearly random series of events. It is important to remember that you won't have enough data to make statistically significant probabilities. These numbers are dependent on a lot more play. There is a possibility that you could have bias in one direction. Bankers might have 50% more players than banksters, for example. This would be very good.


Because there is so much activity, the casino has real statistical significance. They cannot lose because of gaming. They can only lose from not getting enough players or from typical business profit/loss scenarios. However, they can't lose on the gaming. This is impossible. However, it is possible for the casino lose to players. They make up these losses by having enough players to make the math work in the end.

This last point is very important. It is important because you won't be playing 24 hours a days if you don't play by the same mathematical statistics of the casino. This is eliminated immediately by our money management and departure rules. The casino will only beat the Baccarat player by his or her lack of discipline and/or poor play.

Roulette

Roulette has a 5.26% advantage over the player. This is because the wheel has 38 numbers: 1-36, 0, and 00. However, the payoffs depend on only the 36 numbers and not 0 and 00. A single number pays 35-1. Simply put, the casino's edge is between 0 and 0.

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.
Abweichungen in bet sizes by Hates
Does not like structured play, especially in departure rules and money management.
Once you reach a certain volume of play, the mathematical edge is yours.
Any enticement is offered by the casino to help you achieve this guaranteed mathematical edge.




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