Notes

Casino Math

Craps

To understand the math behind craps, you need to be able to recognize the probability of winning. My strategies only allow me to place bets with the highest probability of winning. These include the pass line with odds and come bets with chances.

If you play the above mentioned bets, the house percentage in craps is the lowest of any casino game. 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 frequently asked why come bets do not perform as well in seminars. The answer lies with the combinations of dice. A place bet can be used to illustrate this point. 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! The bet is lost if a 7 is rolled. There are 6 possible combinations. This means that you lose 6 to 4 dice combinations or 3 to 2.

Let's take a look at a "come bet". When the come wager is in the coming area, it wins with a seven or eleven for a total number of eight dice combinations. It loses with a 2, 3 and 12 for a total loss of four 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. 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. That is a significant 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. A come wager, regardless of the number, is 0.8% with single chances and the exact opposite odds to the pass line.

You must reduce the advantage of the casino and manage your money to maximize any streaks. This is what the Benson Strategies do.

Blackjack

Blackjack is the only casino game in which the advantage or disadvantage of a player changes with every card that is played. The house is favored by 4% because the dealer will break if you make a mistake. Guess who wins the money! The house, of course!

By playing basic strategy, you can reduce your house advantage down to 1.5% This makes it an enjoyable game. 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. As games online (or shoe) is unplayed, more high cards are added to the player's advantage. 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 has to hit on 16 or less. High cards mean a greater chance of a dealer fracas.

The most popular methods of tracking are simple hi-lo count (good for single deck games) or card clumping (good for shoe games). The 1% advantage is the highest expected mathematical return for expertly played blackjack.

Baccarat

Baccarat has a negative expectation, which is the same as roulette, craps and other games. This means that the house always has the advantage. The odds are always in favor of the house mathematically. This can only happen with perfect blackjack counting (which is also why they don't allow you to win a lot).

Following the trend is how we win at Baccarat. Trends can develop in any random, or very near random sequence of events. Because statistical significance depends on many plays, there won't be enough lay to create real probability numbers. One possibility is that there are 50% more bankers than players, which would be very interesting.

The casino sees real statistical significance since they have so much action going on all the time. They cannot lose from gaming itself. They are only able to lose players and typical business profit/loss. However, they don't lose the gaming itself. It is impossible. It is possible, however, for the casino to lose individual players. The casino compensates for these losses as they have enough people to make the mathematics work long term.

This is an important point. Because unless free play online 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 casino will only beat the Baccarat player by his or her lack of discipline and/or poor play.


Roulette

Roulette has a 5.26% advantage on the player. This is because there are 38 numbers on the wheel, including 0 through 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.

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

Casino's Math

Needs lots of playing action to achieve true odds.
All statistics are based on an infinite number of rolls.
Hates deviations in bet sizes.
Does not like structured play, especially in departure rules and money management.
Once the volume is reached, the mathematical edge can be guaranteed.
Casinos will provide any incentive to get this guaranteed mathematical edge.




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