Notes

Casino Math

Craps

The key to understanding the mathematics of craps is to understand the dice combinations, or probabilities. My strategies only allow me to place bets with the highest probability 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 craps house percentage is the lowest among all casino games. 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.

I am often asked by seminar attendees why place bets perform better than come bets. The answer lies with the combinations of dice. You can illustrate this point with a place betting. Placing a bet directly on the number 5 (also known as place bet) can only win on four combinations of dice: 1-4, 4-1 and 2-3. 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 now look at a come wager. When the come wager is in the coming area, it wins with a seven or eleven for a total number of eight dice combinations. best games to play loses with a 2, 3 and 12 for a total loss of four dice combinations. You win 6 to 4, or 2:1 in your favor for the instant win, and you lose 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 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 huge 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. 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 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.

Blackjack

Blackjack is the only online casino game where the benefit or disadvantage of each card can change. Because the game favors the house by 4 percent, you can break the dealer and get the money. Of course, the house!

Playing basic strategy can help reduce the house advantage by as much as 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.

Additionally, simple strategy can also be combined with card tracking to increase the player's advantage of 1%. The advantage of the player increases if there are more high cards left in their unplayed hand (or deck). play video are better for the player than the dealer because they increase the chances of the dealer breaking and give the player a better chance of getting "pat" hands. The dealer can only hit on 16 or fewer cards. The dealer will break more often if there is a high number of cards.


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. If video games is played well, it offers a 1% mathematical advantage.

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. By always, I mean that there is no known method of play that will place the odds in favor of the player mathematically. This can only be achieved with perfect blackjack cards counting (which is why they don’t let you lose a lot).

To win at Baccarat, you must follow the trend. Trends will emerge in any combination of random or almost random events. Remember, you will not have sufficient lay to establish real probability numbers, since these depend on lots of play to reach statistical significance. It is possible to be biased in one direction. For instance, 50% more bankers could play than players. (Which would be great, by the way).

Since there is so much happening at the casino, they are statistically significant. They can't lose in gaming. 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 itself. It 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 matters. Because unless you play 24 hours a day, you will never be playing by the same mathematical statistics as the casino. This is quickly eliminated with our money management rules and departure rules. The lack of discipline or poor play will make the casino beat you as a Baccarat gambler.

Roulette

The advantage that roulette has over the player is 5.26% This is due to the fact that there are 38 numbers on roulette: 1-36, 0 and 00. However, the payouts are based only upon the 36 numbers, not the 0, and 00. The single number pays out 35-1. The casino's edge lies between the numbers 0 and 00.

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

Casino's Math

Needs lots of playing action to achieve true odds.
All statistics are based on an infinite number of rolls.
Variations in bet sizes are known as Hates deviations.
Structured play is not for him, particularly in the area of money management and departure rules.
Once you reach a certain volume of play, the mathematical edge is yours.
The casino will offer any enticement to achieve this guaranteed mathematical edge.




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