Casino Math

Craps

Understanding the probabilities, or the combinations of dice is crucial to understanding the math of craps. My strategies only allow me to place bets with the highest probability 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 in craps falls to 0.8% if you make the above-mentioned wagers. Taking single odds on pass line and come bets reduces the house percentage to 0.8%... double odds reduces it to 0.6%... triple odds reduces it further to 0.5%... and 10 times up to 100 times odds makes the game almost dead even.

At seminars, I am always asked why place bets are not as good as come bets. The answer lies with the combinations of dice. This point can be illustrated by a place bet. 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! When a 7 is rolled, which has a total of 6 dice combinations, the bet loses. This is 6 to 4 or 3 to 2 against, depending on the combination of dice.

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. That's 6 to 4, or 2 to 1 in your favor for the immediate win versus an immediate loss. This means that if the come bet is placed on the 5, it has an additional 4 combinations of dice to win. The come bet that began in the come area and ended at the 5 had 12 combinations of dice to win, while the place bet on 5 had only 5 combinations. This is a big advantage. This analysis can be used for any place bet.

You can also take odds on all of your come bets. Place bets for the 4 or 10 are 6.7% and 4% respectively; place bets for the 5 or 9 are 4% and place bets for the 6 or 8 are 1.5%. 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. The Benson Strategies help you do just that.

Blackjack

Blackjack is one of the few casino games where the advantage or disadvantage of the player changes with each card. 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 in itself makes it a good game to play. It is possible to expect a positive return with good basic play and smart money management.

The player's advantage can be increased by as much as 1% through the combination of basic strategy and tracking the cards.  play the game  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 must hit 16 or less cards. This increases the chance of a dealer breaking if there are still high cards.

Most common methods for tracking are simple hi-lo counts (good on single deck games) and card clumping methods (good on shoe games). Expertly playing blackjack offers a 1% probability of receiving a 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. By always, I mean that there is no known method of play that will place the odds in favor of the player mathematically. This is possible only with perfect blackjack card counting (which, of course, doesn't let them let you win much).

You can win at baccarat by following the trends. Trends will emerge in any combination of random or almost random events. You won't have enough lay to determine statistical significance, as these numbers depend on a lot of play. 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 by gaming. They can only lose from not getting enough players or from typical  business  profit/loss scenarios. But they do NOT lose on the gaming. This is impossible. However, it is possible that the casino may lose to certain players. They make up these losses by having enough players to make the math work in the end.

This last point is crucial. You cannot play 24/7 and still be able to use the same mathematical statistics that the casino. This is immediately eliminated by our departure rules and money management. The only thing that will beat a Baccarat player is his or her inability to be disciplined and/or poor play.

Roulette

The advantage that roulette has over the player is 5.26% This is because the wheel has 38 numbers: 1-36, 0, and 00. Payoffs are calculated based only on 36 numbers, and not the zero or 00. 35-1 is the single number. Simply put, the casino's edge is between 0 and 0.

Over a long duration, the casino will have a clear mathematical advantage.

Casino's Math

To achieve real odds, you need to play a lot.
Statistics are calculated using an infinite number rolls.
There are always deviations in the bet sizes of Hates.
Does not like structured play, especially in money management and departure rules.
Once the volume is reached, the mathematical edge can be guaranteed.
Casinos will provide any incentive to get this guaranteed mathematical edge.