Notes

Casino Math

Craps

Understanding the probabilities or dice combinations is the key to understanding the mathematics behind craps. In my strategies, I only want to choose the bets that offer the greatest chance of winning. These are the pass lines with odds, the come bets, the occasional place bets, the 6 and 8 don't pass placing the odds and can't be placed 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. 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.

At click for more info , I am always asked why place bets are not as good as come bets. The answer lies with the combinations of dice. This can be illustrated with a place bet. If you place a bet directly upon the number 5, (aka place wager), you can only win on any of these four dice combinations: 4-1, 2-3 and 3-2. That's it! The bet is declared lost when a 7 is rolled. This gives you a total of 6 combinations. Based on just the dice combinations, it's 6-4 or 3-4 against you.

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. It's 6-4, or 2 to 1 in favor of you for the immediate win over an immediate loss. It now has 4 more dice combinations to win if the come bet goes to the 5. 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. That is a significant advantage. This analysis is applicable to any place you 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 wager, regardless of the number, is 0.8% with single chances and the exact opposite odds to the pass line.

To win in craps, you must minimize the casino's advantage and use money management to capitalize on all streaks, do or don't. That's why the Benson Strategies exist.

single player games is the only casino game where the player's advantage or disadvantage changes with each card played. Because visit the website favors the house by 4 percent, you can break the dealer and get the money. Of course, the house!

Basic strategy can reduce the house advantage to 1.5%. This alone makes it an attractive game. You can expect a positive return on your investment if you practice good money management and basic play.

The basic strategy of basic strategy and card tracking can help to improve the advantage for the player by 1%. As trends as there are no high cards in the deck or shoe, the player has an advantage. High cards favor the player, as they give them a greater chance of getting a "pat", and increase the dealer’s chance at breaking. The dealer must hit 16 or less cards. With high cards remaining, this creates a higher chance of a dealer break.

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. 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 known as a negative expectation game (the same as craps, roulette, and other). This means that the house is always in the lead. The odds are always in favor of the house mathematically. This can only be achieved with perfect blackjack cards counting (which is why they don’t let you lose a lot).

Following the trend is how we win at Baccarat. A trend will develop in any random or near random series of events. Because statistical significance depends on many plays, there won't be enough lay to create real probability numbers. You could be skewed in one direction: 50% more players than bankers for instance (which would be very nice, by the way).

Since there is so much happening at the casino, they are statistically significant. They can't lose by gaming. They can only lose from not getting enough players or from typical business profit/loss scenarios. They do not lose on gaming. It is impossible. However, it is possible that the casino may lose to certain 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. This is because unless you play 24 hour a day, your mathematical statistics will not be the same as those at the casino. Our money management and departure rules eliminate this instantly. The only thing that will beat a Baccarat player is his or her inability to be disciplined and/or poor play.

Roulette

Roulette has a 5.26% advantage on the player. This is due to the fact that there are 38 numbers on roulette: 1-36, 0 and 00. The payoffs, however, are based on the 36 numbers only, not the 0 and 00. The single number pays out 35-1. The casino's edge is the 0 or 00.

Over a long time, the casino can enjoy a distinct mathematical advantage.

Casino's Math

For true odds to be achieved, there must be a lot of playing.
Statistics are calculated using an infinite number rolls.
There are always deviations in the bet sizes of Hates.
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.
virtual reality will offer any enticement to achieve this guaranteed mathematical edge.




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