Notes

Casino Math

Craps

Understanding the probabilities, or the combinations of dice is crucial to understanding the math of craps. In my strategies, I only want to choose the bets that offer the greatest chance of winning. These are the pass line and odds, come bets and odds, occasionally place bets and the 6-8, don't pass the odds laying them, and don’t come with or without the 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.

I am often asked by seminar attendees why place bets perform better than come bets. The answer lies in the combination of dice. To illustrate, a place wager can be used. 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! games to play is lost if a 7 is rolled. There are 6 possible combinations. Based on the individual dice combinations, that's 6-4 or 3-4 against.

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. You win 6 to 4, or 2:1 in your favor for the instant win, and you lose 1. The come bet that goes to the 5 has four more winning combinations. games to play come bet that started at the come and ended at the 5, had 12 possible winning combinations, compared to only 5 for the place wager on the 5. That's a huge advantage. This analysis can be applied to every place bet.

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 is 0.8% with one odds. It has the exact same odds and odds as a 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. The Benson Strategies help you do just that.

Blackjack

Blackjack is the only online casino game where the benefit or disadvantage of each card can change. Because you lose and the dealer wins, the game favors house by 4%. Of course, the house!


Basic strategy can reduce the house advantage to 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%. 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 on 16 cards or less. This increases the chance of a dealer breaking if there are still high 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. best play games of 1% means that blackjack, when played correctly, is the only casino game that can provide a positive mathematical return.

Baccarat

Baccarat can be described as a game of negative expectation (just like craps or roulette). This means that the house is always in the lead. I don't mean there is a mathematical method that can place the odds in the favour of the player. This can only be achieved with perfect blackjack cards counting (which is why they don’t let you lose a lot).

The way we win at baccarat is to 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. 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).

Since there is so much happening at the casino, they are statistically significant. Gaming is the only way they can lose. They are only able to lose players and typical business profit/loss. However, they can't lose on the gaming. This is impossible. However, it is possible for the casino lose to players. These losses are compensated by the casino because they have enough players who can make the math work for them long-term.

This last point is crucial. You cannot play 24/7 and still be able to use the same mathematical statistics that 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 of the 38 numbers that are on the wheel: 1-36, zero and 00. Payoffs are calculated based only on 36 numbers, and not the zero or 00. The single number pays 35-1. The casino's edge is the 0 or 00.

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

Casino Math

It takes a lot of play to win true odds
Statistics are calculated using an infinite number rolls.
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 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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