Notes

Casino Math

Craps

The key to understanding the mathematics of craps is to understand the dice combinations, or probabilities. We only want to make the most likely bets. These include the pass-line with odds, come wagers with odds, occasional bets on 6 and 8 and don't pass laying any odds.

If you play the above mentioned bets, the house percentage in craps is the lowest of any casino game. If you only take single odds on pass line or come bets, the house percentage is 0.8 %... double odds. That reduces to 1.5 third odds. That reduces further to 1 and then down to 0.5 %.... A 10x to 100-fold increase in odds results in the game being almost dead even.

At seminars, I am often asked why place and come bets aren't as profitable as they used to be. The answer lies with the combinations of dice. play the game can be illustrated with a place bet. Placing a bet directly on the number 5 (also known as place bet) can only win on four combinations of dice: 1-4, 4-1 and 2-3. That's it! The bet is declared lost when a 7 is rolled. This gives you a total of 6 combinations. This means that you lose 6 to 4 dice combinations or 3 to 2.

Let's now take a look at the come bet. The come bet wins on a seven- or eleven-dice combination and loses on a 2, 3, or 12 for a total total of four dice combinations. This is 6 to 4, or 2:1 in your favor for an immediate win and a loss. For example, if that come bet went to the 5, it now has 4 different dice combinations to win. The come bet that began in the come area and ended at the 5 had 12 combinations of dice to win, while the place bet on 5 had only 5 combinations. That is a significant advantage. This analysis is valid for all types of bets.


Add to that the fact you can place all kinds of come bets and get 6.7% casino advantage; 4% for the 5 or 9; 1.5% for the 6 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. That's what the Benson Strategies are all about.

Blackjack

Blackjack is the only online casino game where the benefit or disadvantage of each card can change. The game itself favors 4% the house, because if the dealer breaks, guess who takes the money. The house of course!

By playing basic strategy, you can reduce your house advantage down to 1.5% This makes it an enjoyable game. You can expect a positive return on your investment if you practice good money management and basic play.

In addition, basic strategy combined with tracking of cards played can increase the player's advantage by 1%. As long as there are no high cards in the deck or shoe, the player has an advantage. High cards favor the players because they increase their chances of getting a "pat," or a hand that is a good deal. They also give the dealer a higher chance of breaking. The dealer must hit 16 or less cards. A dealer break is more likely if there are high cards left.

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

Baccarat is known as a negative expectation game (the same as craps, roulette, and other). most played games means that the house is always in the lead. The odds are always in favor of the house mathematically. This can only be done with perfect blackjack card counting (which is why of course they don't let you win a lot).

To win at Baccarat, you must follow the trend. A trend will develop in any random or near 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.

Casinos have a lot of activity and statistical significance. Gaming is the only way they can lose. They will only lose if they don't get enough players, or in typical business profit/loss scenarios. However, they don't lose the gaming itself. It's impossible. However, it is possible for the casino lose to 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 crucial. Because you can't play 24 hours per day and you won't be using the same mathematical statistics as the casinos. Our departure rules and money management eliminate this immediately. Bad play and lack of discipline are the only things that can beat a Baccarat dealer.

Roulette

Roulette has a 5.26% edge over the game. This is because there are 38 numbers on the wheel, including 0 through 00. However, the payouts are based only upon the 36 numbers, not the 0, and 00. The single number pays out 35-1. Simply put, the casino's edge is between 0 and 0.

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

The Casino's Math

You need to play lots to have any chance of winning.
All statistics are based upon an infinite number roll.
Abweichungen in bet sizes by Hates
Does not like structured play, especially in money management and departure rules.
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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