Notes

Casino Math

Craps

Understanding the probabilities or dice combinations is the key to understanding the mathematics behind craps. In my strategies we want to only play bets with the highest chance of winning. These are the pass line with odds, come bets with odds, occasional place bets on the 6 and 8, don't pass laying the odds, and don't come either with or without laying the odds.

The house percentage in craps falls to 0.8% if you make the above-mentioned wagers. 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 seminars, I am always asked why place bets are not as good as come bets. The answer lies in the combination of dice. To illustrate, a place wager can be used. 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 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. It loses with a 2, 3 and 12 for a total loss of four dice combinations. This is 6 to 4, or 2:1 in your favor for an immediate win and a loss. For example, if that come bet went to the 5, it now has 4 different dice combinations to win. The come bet which started in the come zone and went to the five had 12 different combinations to win, as opposed to just 5 for the bet on the place. That is a significant advantage. This analysis can be applied to every place 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. free games to play now 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 in craps you must limit the casino's advantage. Also, money management will allow you to take advantage of all streaks. The Benson Strategies help you do just that.

games online is the only online casino game where the benefit or disadvantage of each card can change. The house is favored by 4% because the dealer will break if you make a mistake. Guess who wins the money! Of course, it's the house.

You can reduce this house advantage to 1.5% by using basic strategy. This makes it an enjoyable game. You can expect a positive return on your investment if you practice good money management and basic play.


Furthermore, tracking of the cards played, combined with basic strategy, can change the advantage to the player by 1%. As the deck (or shoe) is unplayed, more high cards are added to the player's advantage. technology 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 must hit 16 or less cards. This increases the chance of a dealer breaking if there are still high cards.

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 is a game with negative expectations, just like roulette and craps. This means that the house always has the advantage. I don't mean there is a mathematical method that can place the odds in the favour of the player. This is only possible with perfect blackjack count (which is the reason they don't let players 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. There won't be enough play to calculate statistical significance. Your results could be skewed one way: Bankers may have 50% more players than you (which would be wonderful, by the side).

Because there is so much activity, the casino has real statistical significance. They can't lose by gaming. They are only able to lose players and typical business profit/loss. They do not lose on gaming. This 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 should be very important. It is important because you won't be playing 24 hours a days if you don't play by the same mathematical statistics of the casino. Our departure rules and money management eliminate this immediately. A bad play and/or lack of discipline will not win the Baccarat player.

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. trends , however, are based on the 36 numbers only, not the 0 and 00. A single number pays 35-1. The casino's edge is the 0 or 00.

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

Casino's Math

To achieve real odds, you need to play a lot.
All statistics are based upon an infinite number roll.
The Hates deviations of bet sizes
Does not like structured play, especially in money management and departure rules.
Once you reach a certain volume of play, the mathematical edge is yours.
Any enticement is offered by the casino to help you achieve this guaranteed mathematical edge.




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