Notes

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 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.

If video games play the above mentioned bets, the house percentage in craps is the lowest of any casino game. 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.

I'm often asked at seminars why place bets don't perform as well as come bets. The answer lies in the dice combinations. This can be illustrated with 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! The bet loses if a 7, which is the sum of six dice combinations, is rolled. 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. The come bet that is in the come zone wins on a seven, 11 or 12 for a total 8 dice combinations. It loses on 2, 3, or 12, for a total 4 dice combinations. That's 6 to 4, or 2 to 1 in your favor for the immediate win versus an immediate loss. The come bet that goes to the 5 has four more winning combinations. 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. This is a significant advantage. games to play on pc can be applied to every 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.

You must reduce the advantage of the casino and manage your money to maximize any streaks. That's why the Benson Strategies exist.

Blackjack

Blackjack is the only casino game where the player's advantage or disadvantage changes with each card 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!

You can reduce this house advantage to 1.5% by using basic strategy. 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.

In addition, basic strategy combined with tracking of cards played can increase the player's advantage by 1%. As the deck (or shoe) is unplayed, more high cards are added to the player's advantage. High cards favor the player, as they give them a greater chance of getting a "pat", and increase the dealer’s chance at breaking. The dealer can only hit on 16 or fewer cards. 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). A 1% advantage 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 that the odds always favor the house. I don't mean there is a mathematical method that can place the odds in the favour of the player. 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. A trend can form in any random or nearly random series of events. There won't be enough play to calculate statistical significance. One possibility is that there are 50% more bankers than players, which would be very interesting.

Because there is so much activity, the casino has real statistical significance. They cannot lose from gaming itself. They only have to lose when they do not get enough players or are subject to typical business loss/profit scenarios. But they do NOT lose on the gaming. It's impossible. However, it is possible for the casino lose to players. The casino makes up for these losses because they have enough players to make the mathematics work for them in the long run.

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 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 because the wheel has 38 numbers: 1-36, 0, and 00. However, the payoffs depend on only the 36 numbers and not 0 and 00. A single number pays 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

You need to play lots to have any chance of winning.
Statistics can only be derived from an infinite number of rolls.
The Hates deviations of bet sizes
Does not like structured play, especially in departure rules and money management.
Once you reach a certain volume of play, the mathematical edge is yours.
Casinos will provide any incentive to get this guaranteed mathematical edge.




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