Notes

Casino Math

Craps

To understand the math behind craps, you need to be able to recognize the probability of winning. In my strategies we want to only play bets with the highest 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.

The house percentage of craps is the lowest casino game. 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.

I am often asked by seminar attendees why place bets perform better than come bets. The answer lies within the dice combinations. This point can be illustrated by a place bet. 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! The bet loses if a 7, which is the sum of six dice combinations, is rolled. That's 6 to 4, or 3 to 2 against you based on the dice combinations alone.

Let's now take a look at the 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. The odds of winning an immediate win are 6 to 4 or 2 to 1. For example, if that come bet went to the 5, it now has 4 different dice combinations to win. The 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. This is a big advantage. This analysis can be applied to every place bet.

When you consider that all come bets can be placed, the casino advantage is 6.7% for place wagers on the 4-10; 4% for place wagers on 5-9; 1.5% place bets upon the 6-8 and 8. A come bet, regardless of what number it is, is only 0.8% and has single odds. most played games are available for the pass line, which has single odds.

To win in craps you must limit the casino's advantage. Also, money management will allow you to take advantage of all streaks. 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. The game itself favors 4% the house, because if the dealer breaks, guess who takes the money. Of course, the house!

By playing basic strategy, you can reduce your house advantage down to 1.5% This alone makes it a great game. It is possible to expect a positive return with good basic play and smart money management.


Furthermore, tracking of the cards played, combined with basic strategy, can change the advantage to the player by 1%. The player's advantage increases as more high cards are left in the unplayed deck (or shoe). 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 can only hit on 16 or fewer cards. High cards mean a greater chance of a dealer fracas.

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

Baccarat

Baccarat can be described as a game of negative expectation (just like craps or roulette). This means that the house always has the advantage. I don't mean there is a mathematical method that can place the odds in the favour of the player. This is possible only with perfect blackjack card counting (which, of course, doesn't let them let you win much).

The way we win at baccarat is to follow the trend. Any random or close to random sequence of events can create a trend. You won't have enough lay to determine statistical significance, as these numbers depend on a lot of play. You could be skewed in one direction: 50% more players than bankers for instance (which would be very nice, by the way).

The casino is a statistical powerhouse because they have so many games going on at once. Gaming is the only way they can lose. They are only able to lose players and typical business profit/loss. They do not lose on gaming. It is not possible. However, it is possible for the casino lose to players. Because they have enough players, the casino can make up the losses.

This last point matters. Because unless you play 24 hours a day, you will never be playing by the same mathematical statistics as the casino. free to play pc games is immediately eliminated by our departure rules and money management. The lack of discipline or poor play will make the casino beat you as a Baccarat gambler.

Roulette

Roulette has a 5.26% advantage over the player. This is because there are 38 numbers on the wheel, including 0 through 00. The payoffs, however, are based on the 36 numbers only, not the 0 and 00. The single number pays 35-1. The casino's edge is the 0 or 00.

The casino will enjoy a mathematical advantage over a long time.

The Casino's Math

For true odds to be achieved, there must be a lot of playing.
Statistics can only be derived from an infinite number of rolls.
Abweichungen in bet sizes by Hates
Structured play is not something that he likes, especially with regard to departure rules and money management.
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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