Notes

Casino Math

Craps

To understand the math behind craps, you need to be able to recognize the probability of winning. We only want to make the most likely bets. 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.

The house percentage in craps has the lowest rate of any casino game if you place the above-mentioned bets. 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 seminars, I am always asked why place bets are not as good as come bets. It all comes down to the dice combinations. To illustrate, a place wager can be used. A bet placed directly on the number 5, as an example (aka place bet), can only win on a total of four dice combinations: 1-4, 4-1, 2-3, 3-2. That's it! The bet loses if a 7, which is the sum of six dice combinations, is rolled. This means that you lose 6 to 4 dice combinations or 3 to 2.

Now let's look at a come bet. When the come wager is in the coming area, it wins with a seven or eleven for a total number of eight dice combinations. It loses with a 2, 3 and 12 for a total loss of four dice combinations. The odds of winning an immediate win are 6 to 4 or 2 to 1. If that come bet should go to the 5, as an example, it now has another 4 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 applicable to any place you bet.

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.

To win at craps, you have to reduce the casino's advantage. Money management is key. That's the Benson Strategies.

Blackjack

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

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

In addition, basic strategy combined with tracking of cards played can increase the player's advantage by 1%. The advantage of the player increases if there are more high cards left in their unplayed hand (or deck). 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 must hit on 16 cards or less. A dealer break is more likely if there are high cards left.

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 is a game with negative expectations, just like roulette and craps. This means the house always wins. It means that the odds of the house always favor the player mathematically. This can only be done with perfect blackjack card counting (which is why of course they don't let you win a lot).

The way we win at baccarat is to follow the trend. A trend will develop in any random or near random series of events. There won't be enough play to calculate statistical significance. There is a possibility that you could have bias in one direction. virtual reality might have 50% more players than banksters, for example. This would be very good.

The casino sees real statistical significance since they have so much action going on all the time. They can't lose in gaming. They can only lose from not getting enough players or from typical business profit/loss scenarios. But they do NOT lose on the gaming. This is impossible. However, it is possible that the casino may lose to certain players. They make up these losses by having enough players to make the math work in the end.

online is crucial. internet is because unless you play 24 hour a day, your mathematical statistics will not be the same as those at the casino. This is immediately eliminated by our departure rules and money management. Bad play and lack of discipline are the only things that can beat a Baccarat dealer.

Roulette

Roulette has a 5.26% advantage on the player. This is because the wheel has 38 numbers: 1-36, 0, and 00. However, the payouts are based only upon the 36 numbers, not the 0, and 00. click for more pays 35-1. The casino's edge lies between the numbers 0 and 00.

Over fun games to play , the casino will have a clear mathematical advantage.

The Casino's Math

To achieve real odds, you need to play a lot.
All statistics are based upon an infinite number roll.
The Hates deviations of bet sizes
Structured play is not for him, particularly in the area of money management and departure rules.
The mathematical edge is assured once the volume of play has been reached.
Casinos will provide any incentive to get this guaranteed mathematical edge.





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