Notes

Casino Math

Craps

Understanding the probabilities and dice combinations is key to understanding craps mathematics. We only want to make the most likely bets. 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.

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.

I am often asked by seminar attendees why place bets perform better than come bets. The answer lies with the combinations of dice. 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. This 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 now take a look at the come bet. The come bet that is in the come zone wins on a seven, 11 or 12 for a total 8 dice combinations. It loses on 2, 3, or 12, for a total 4 dice combinations. You win 6 to 4, or 2:1 in your favor for the instant win, and you lose 1. This means that if the come bet is placed on the 5, it has an additional 4 combinations of dice 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. This is a big advantage. This analysis is applicable to any place you bet.

When you consider that all come bets can be placed, the casino advantage is 6.7% for place wagers on the 4-10; 4% for place wagers on 5-9; 1.5% place bets upon the 6-8 and 8. 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.

You must reduce the advantage of the casino and manage your money to maximize any streaks. The Benson Strategies help you do just that.

Blackjack

Blackjack is one of the few casino games where the advantage or disadvantage of the player changes with each card. Because you lose and the dealer wins, the game favors house by 4%. Of course, it's the house.

By playing basic strategy, you can reduce your house advantage down to 1.5% 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.


The player's advantage can be increased by as much as 1% through the combination of basic strategy and tracking the cards. As more high cards remain in an unplayed deck or shoe, the advantage of the player increases. High cards favor the player, as they give them a greater chance of getting a "pat", and increase the dealer’s chance at breaking. The dealer cannot hit on more than 16 cards. The dealer will break more often if there is a high number of cards.

Simple hi-lo counts are good for single deck games, and card clumping is good for shoe games. These are the most common methods of tracking. The 1% advantage is the highest expected mathematical return for expertly played blackjack.

Baccarat

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 happen with perfect blackjack counting (which is also why they don't allow you to win a lot).

You can win at baccarat by following the trends. Any random or close to random sequence of events can create a trend. There won't be enough play to calculate statistical significance. It is possible to be biased in one direction. For instance, 50% more bankers could play than players. (Which would be great, by the way).

The casino sees real statistical significance since they have so much action going on all the time. Gaming is the only way they can lose. They cannot lose by not having enough players or typical business profit/loss situations. However, they don't lose the gaming itself. fun games to play online is impossible. It is possible, however, for the casino to lose individual players. They make up these losses by having enough players to make the math work in the end.

This last point should be 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. free games to play of discipline or poor play will make the casino beat you as a Baccarat gambler.

Roulette

Roulette has an advantage of 5.26% over the player. This is because there are 38 numbers on the wheel, including 0 through 00. Payoffs are calculated based only on 36 numbers, and not the zero or 00. The 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

You need to play lots to have any chance of winning.
Statistics can only be derived from an infinite number of rolls.
Abweichungen in bet sizes by Hates
Structured play is not something that he likes, especially with regard to departure rules and money management.
Once you reach a certain volume of play, the mathematical edge is yours.
To achieve this mathematical edge, the casino will make every effort to entice you.




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