Notes

Casino Math


Craps

Understanding the probabilities or dice combinations is the key to understanding the mathematics behind craps. laptop 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.

The house percentage in craps has the lowest rate of any casino game if you place the above-mentioned bets. To reduce the house percentage, you can take only one odds on the pass line and come bets. This will reduce it to the 0.8 %... single odds. To reduce it further to the 0.6 %... tri odds. To make it almost as good as dead even, you can reduce it to the 0.5 %... triple odds.

At seminars, I am always asked why place bets are not as good as come bets. best play games lies in 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. Based on the individual dice combinations, that's 6-4 or 3-4 against.

Now let's look at 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. This is 6 to 4, or 2:1 in your favor for an immediate win and a loss. If that come bet should go to the 5, as an example, it now has another 4 dice combinations to win. 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.

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. No matter the number, a come bet is just 0.8% with single odds. This is the exact same odds that the pass line with one 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. 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 you lose and the dealer wins, the game favors house by 4%. The house of course!

This house advantage can be reduced to 1.5% by playing basic strategy. This is enough to make it a worthwhile game. If you play well and manage your money properly, you can expect to see a positive return over the long-term.

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 are a favor to the player as they increase the chance of getting a "pat hand" and the dealer's chances of breaking. The dealer must hit on 16 cards or less. With high cards remaining, this creates a higher chance of a dealer break.

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. A 1% advantage means that expertly played blackjack is the only casino game that offers the player an expected positive mathematical return.

Baccarat

Baccarat has a negative expectation, which is the same as roulette, craps and other games. This means that the odds always favor the house. I don't mean there is a mathematical method that can place the odds in the favour of the player. This is only possible with perfect blackjack count (which is the reason they don't let players win a lot).

Follow the trend to win at baccarat. games to play at home will emerge in any combination of random or almost random events. There won't be enough play to calculate statistical significance. 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.

Because there is so much activity, the casino has real 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 don't lose the gaming itself. It is not possible. But it is very possible for the casino to lose to individual 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. 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.

play free has a 5.26% advantage over the player. This is because the wheel has 38 numbers: 1-36, 0, and 00. However, the payoffs are only based on the 36 numbers and not the 0 or 00. The single number pays 35-1. So, simply stated, the 0 and 00 are the casino's edge.

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

Casino Math

It takes a lot of play to win true odds
Statistics can only be derived from an infinite number 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 the volume is reached, the mathematical edge can be guaranteed.
To achieve this mathematical edge, the casino will make every effort to entice you.




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