Notes

Casino Math

Craps

The key to understanding the mathematics of craps is to understand the dice combinations, or probabilities. In my strategies, we only want to play the bets that have the best probabilities of winning. 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 falls to 0.8% if you make the above-mentioned wagers. 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 often asked why place and come bets aren't as profitable as they used to be. The answer lies within the dice combinations. This point can be illustrated by a place bet. For example, a place bet on the number 5 can only win on one of four possible dice combinations: 1-4 to 4-1, 2-3 to 3-2, and 2-3 to 3-2. That's it! play online loses when a 7 (which has 6 different combinations) is rolled. Based on the individual dice combinations, that's 6-4 or 3-4 against.

Let's examine a come bet. When the come bet sits in the come area, it wins on a seven or 11 for a total of eight dice combinations and loses on a 2, 3 or 12 for a total of 4 dice combinations. It's 6-4, or 2 to 1 in favor of you for the immediate win over an immediate loss. If that come bet should go to the 5, as an example, it now has another 4 dice combinations to win. click for more info 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. That's a huge advantage. This analysis can also be applied to all places bets.

Adding the fact that you can take odds on all come bets, the casino advantage on place bets on the 4 or 10 is 6.7%; on place bets on the 5 or 9, it's 4%; and place bets on the 6 and 8, it's 1.5%. A come bet, regardless of what number it is, is only 0.8% and has single odds. The exact same odds 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 why the Benson Strategies exist.

Blackjack

Blackjack is the only casino game where the player's advantage or disadvantage changes with each card played. The house is favored by 4% because the dealer will break if you make a mistake. Guess who wins the money! Of course, it's the house.

This house advantage can be reduced to 1.5% by playing basic strategy. This alone makes it a great game. With proper basic play and proper money management you could expect to show a positive return over time.

Additionally, simple strategy can also be combined with card tracking to increase the player's advantage of 1%. As more high cards remain in an unplayed deck or shoe, the advantage of the player increases. 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 has to hit on 16 or less. With high cards remaining, this creates a higher chance of a dealer break.


The most common methods for tracking are simple high-lo counts (good for single-deck games) and card clustering methods (good to track shoe games). An advantage of 1% means that blackjack, when played correctly, is the only casino game that can provide a positive mathematical return.

Baccarat

Baccarat is a game with negative expectations, just like roulette and craps. This means that the house has always the upper hand. This means that mathematically, there is no way to place the odds in the favor of the player. play online is only possible with perfect blackjack count (which is the reason they don't let players win a lot).

To win at Baccarat, you must follow the trend. A trend will develop in any random or near random series of events. It is important to remember that you won't have enough data to make statistically significant probabilities. These numbers are dependent on a lot more play. 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.

Since there is so much happening at the casino, they are statistically significant. Gaming is the only way they can lose. They will only lose if they don't get enough players, or in typical business profit/loss scenarios. But they do NOT lose on the gaming. This is impossible. 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 very important. Because you can't play 24 hours per day and you won't be using the same mathematical statistics as the casinos. This is quickly eliminated with our money management rules and departure rules. A bad play and/or lack of discipline will not win the Baccarat player.

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 payoffs are only based on the 36 numbers and not the 0 or 00. The single number pays out 35-1. The casino's edge can be summarized as 0 and 0, which is essentially a single number.

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

Casino's Math

For true odds to be achieved, there must be a lot of playing.
All statistics are based on an infinite number of rolls.
There are always deviations in the bet sizes of 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.
Any enticement is offered by the casino to help you achieve this guaranteed mathematical edge.




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