Notes

Casino Math

Craps

To understand the math behind craps, you need to be able to recognize the probability of winning. In my strategies, we only want to play the bets that have the best probabilities 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. 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.

I am frequently asked why come bets do not perform as well in seminars. The answer lies in the dice combinations. To illustrate, a place wager can be used. 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! 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 take a look at the 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. It now has 4 more dice combinations to win if the come bet goes to the 5. 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 significant advantage. This analysis can be used for any place bet.

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, no matter what number it goes to is only 0.8% with single odds, the exact same odds as the pass line with single odds.

To win at craps you need to minimize the casino's advantage. You also need to manage money so that you can capitalize on any streaks. That's what the Benson Strategies are all about.

Blackjack

Blackjack is the only game where the player's advantage and disadvantage change with every card played. Because the game favors the house by 4 percent, you can break the dealer and get the money. Of course, it's the house.

games to play on pc can reduce this house advantage to 1.5% by using basic strategy. This is enough to make it a worthwhile game. It is possible to expect a positive return with good basic play and smart money management.

The basic strategy of basic strategy and card tracking can help to improve the advantage for the player by 1%. The player's advantage 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 has to hit on 16 or less. High cards mean a greater chance of a dealer fracas.

Most common methods for tracking are simple hi-lo counts (good on single deck games) and card clumping methods (good on shoe games). best play games means that expertly played blackjack is the only casino game that offers the player an expected positive mathematical return.

Baccarat

Baccarat has a negative expectation, which is the same as roulette, craps and other games. This means the house always wins. This means that mathematically, there is no way to place the odds in the favor of the player. This can only be done with perfect blackjack card counting (which is why of course they don't let you win a lot).

You can win at baccarat by following the trends. A trend can form in any random or nearly 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. Your results could be skewed one way: Bankers may have 50% more players than you (which would be wonderful, by the side).


The casino sees real statistical significance since they have so much action going on all the time. Gaming is the only way they can lose. They cannot lose by not having enough players or typical business profit/loss situations. However, they can't lose on the gaming. It is not possible. But it is very possible for the casino to lose to individual 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. Our departure rules and money management eliminate this immediately. The casino will only beat the Baccarat player by his or her lack of discipline and/or poor play.

games to play on pc that roulette has over the player is 5.26% The reason for this is that there are actually 38 numbers on the wheel: 1-36 and 0 and 00. Payoffs are calculated based only on 36 numbers, and not the zero or 00. 35-1 is the single number. The casino's edge is the 0 or 00.

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

Casino's Math

It takes a lot of play to win true odds
All statistics are dependent on an infinite amount of rolls.
The Hates deviations of bet sizes
Does not like structured play, especially in money management and departure rules.
Once play video is reached, the mathematical edge can be guaranteed.
This guaranteed mathematical edge can be achieved by any casino offer.




Here's my website: http://www.aren.org/