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 and come bets with chances.

The house percentage in craps falls to 0.8% if you make the above-mentioned wagers. 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. It all comes down to the dice combinations. You can illustrate this point with a place betting. 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 loses if a 7, which is the sum of six dice combinations, is rolled. 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. It's 6-4, or 2 to 1 in favor of you for the immediate win over an immediate loss. The come bet that goes to the 5 has four more winning combinations. 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. This is a significant advantage. This analysis can also be applied to all places bets.

You can also place odds on all come wagers. The casino advantage for place bets of the 4 and 10 is 6.7%, while the 4% on the 5 and 9 is 4% and the 1.5% on the 6 or 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.

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

Blackjack is the only casino game in which the advantage or disadvantage of a player changes with every card that is played. Because the game favors the house by 4 percent, you can break the dealer and get the money. Of course, the house!

Basic strategy can reduce the house advantage to 1.5%. This makes it an enjoyable game. It is possible to expect a positive return with good basic play and smart money management.

The player's advantage can be increased by as much as 1% through the combination of basic strategy and tracking the cards. As the deck (or shoe) is unplayed, more high cards are added to the player's 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 cannot hit on more than 16 cards. High cards mean a greater chance of a dealer fracas.

Simple hi-lo counts, which are useful for single deck game play, and card clumping techniques (which are great for shoe games), are the most commonly used methods for tracking. 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). This means the house always wins. I don't mean there is a mathematical method that can place the odds in the favour of the player. This can only be done with perfect blackjack card counting (which is why of course they don't let you win a lot).

Follow the trend to win at baccarat. Trends will emerge in any combination of random or almost random events. You won't have enough lay to determine statistical significance, as these numbers depend on a lot of play. 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. They can't lose by gaming. They only have to lose when they do not get enough players or are subject to typical business loss/profit scenarios. However, they can't lose on the gaming. website is impossible. However, it is possible that the casino may lose to certain 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. 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. 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.

best free to play games has a 5.26% advantage on the player. 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. A single number pays 35-1. The casino's edge can be summarized as 0 and 0, which is essentially a single number.

Over a long duration, the casino will have a clear mathematical advantage.

Casino Math

To achieve real odds, you need to play a lot.
All statistics are dependent on an infinite amount of rolls.
Variations in bet sizes are known as Hates deviations.
Structured play is not something that he likes, especially with regard to departure rules and money management.
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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