Notes

Casino Math

Craps

Understanding the probabilities or dice combinations is the key to understanding the mathematics behind craps. In my strategies, I only want to choose the bets that offer the greatest chance of winning. These include the pass line with odds and come bets with chances.

If you play the above mentioned bets, the house percentage in craps is the lowest of any casino game. 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.

At most played games , I am always asked why place bets are not as good as come bets. The answer lies in the combination of dice. This point can be illustrated by a place bet. If computer place a bet directly upon the number 5, (aka place wager), you can only win on any of these four dice combinations: 4-1, 2-3 and 3-2. That's it! The bet is declared lost when a 7 is rolled. This gives you a total of 6 combinations. Based on the individual dice combinations, that's 6-4 or 3-4 against.

Let's examine a 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. The odds of winning an immediate win are 6 to 4 or 2 to 1. The come bet that goes to the 5 has four more winning combinations. The come bet which started in the come zone and went to the five had 12 different combinations to win, as opposed to just 5 for the bet on the place. This is a significant advantage. This analysis can be used for any 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 at craps you need to minimize the casino's advantage. You also need to manage money so that you can capitalize on any streaks. This is what the Benson Strategies do.


Blackjack

Blackjack is the only casino game in which the advantage or disadvantage of a player changes with every card that is played. Because source lose and the dealer wins, the game favors house by 4%. The house, naturally!

Basic strategy can reduce the house advantage to 1.5%. This alone makes it an attractive game. If technology play well and manage your money properly, you can expect to see a positive return over the long-term.

play games of basic strategy and card tracking can help to improve the advantage for the player by 1%. As long as there are no high cards in the deck or shoe, the player has an advantage. 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 can only hit on 16 or fewer cards. With high cards remaining, this creates a higher chance of a dealer break.

The most common methods for tracking are simple high-lo counts (good for single-deck games) and card clustering methods (good to track shoe games). Expertly playing 1 player games offers a 1% probability of receiving a positive mathematical return.

Baccarat

Baccarat has a negative expectation, which is the same as roulette, craps and other games. This means that the house is always in the lead. By always, play free games mean that there is no known method of play that will place the odds in favor of the player mathematically. This is possible only with perfect blackjack card counting (which, of course, doesn't let them let you win much).

To win at Baccarat, you must follow the trend. Trends will emerge in any combination of random or almost random events. There won't be enough play to calculate statistical significance. One possibility is that there are 50% more bankers than players, which would be very interesting.

Casinos have a lot of activity and statistical significance. Gaming is the only way they can lose. They cannot lose by not having enough players or typical business profit/loss situations. But visit this page do not LOSE on the gaming itself. It's impossible. However, the casino can lose to specific players. Because they have enough players, the casino can make up the losses.

This last point is crucial. Because unless you play 24 hours a day, you will never be playing by the same mathematical statistics as the casino. video games 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

The advantage that roulette has over the player is 5.26% This is because the wheel has 38 numbers: 1-36, 0, and 00. The payoffs, however, are based on the 36 numbers only, not the 0 and 00. The single number pays out 35-1. The casino's edge can be summarized as 0 and 0, which is essentially a single number.

Over a long time, the casino can enjoy a distinct mathematical advantage.

Casino Math

For true odds to be achieved, there must be a lot of playing.
All statistics are based upon an infinite number roll.
Variations in bet sizes are known as Hates deviations.
Structured play is not his favorite, especially when it comes to money management and departure rules.
Once you have reached the required volume, the mathematical edge will be yours.
The casino will offer any enticement to achieve this guaranteed mathematical edge.




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