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 want to only play bets with the highest chance of winning. These include the pass-line with odds, come wagers with odds, occasional bets on 6 and 8 and don't pass laying any odds.

The house percentage of craps is the lowest casino game. Taking player games 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 am often asked by seminar attendees why place bets perform better than come bets. The answer lies in the dice combinations. You can illustrate this point with a place betting. Placing a bet directly on the number 5 (also known as place bet) can only win on four combinations of dice: 1-4, 4-1 and 2-3. played games 's it! When a 7 is rolled, which has a total of 6 dice combinations, the bet loses. Based on just the dice combinations, it's 6-4 or 3-4 against you.

Now let's look at a 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. You win 6 to 4, or 2:1 in your favor for the instant win, and you lose 1. For example, if that come bet went to the 5, it now has 4 different dice combinations to win. The come bet that started at the come and ended at the 5, had 12 possible winning combinations, compared to only 5 for the place wager on the 5. This is a significant advantage. This analysis can be used for any 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. 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 have to reduce the casino's advantage. Money management is key. 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 game itself favors 4% the house, because if the dealer breaks, guess who takes 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. You can expect a positive return on your investment if you practice good money management and basic play.

Additionally, simple strategy can also be combined with card tracking to increase the player's advantage of 1%. As long as there are no high cards in the deck or shoe, the player has an advantage. High cards favor the player because they give the player a better chance to get a "pat" hand and also they increase the dealer's chance of breaking. The dealer cannot hit on more than 16 cards. High cards mean a greater chance of a dealer fracas.

visit url hi-lo counts, which are useful for single deck game play, and card clumping techniques (which are great for shoe games), are the most commonly used methods for tracking. Expertly playing blackjack offers a 1% probability of receiving a positive mathematical return.

Baccarat

Baccarat, like craps, roulette, or other casino games, is known for having a negative expectation. This means the house always wins. I don't mean there is a mathematical method that can place the odds in the favour of the player. This can only happen with perfect blackjack counting (which is also why they don't allow you to 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. There won't be enough play to calculate statistical significance. You could be skewed in one direction: 50% more players than bankers for instance (which would be very nice, by the way).

Since there is so much happening at the casino, they are statistically significant. They cannot lose from gaming itself. They will only lose if they don't get enough players, or in typical business profit/loss scenarios. However, they don't lose the gaming itself. It's impossible. However, it is possible for the casino lose to players. The casino compensates for these losses as they have enough people to make the mathematics work long term.

This last point is very important. 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

Roulette has a 5.26% edge over the game. The reason for this is that there are actually 38 numbers on the wheel: 1-36 and 0 and 00. However, the payoffs are only based on the 36 numbers and not the 0 or 00. 35-1 is the single number. The casino's edge can be summarized as 0 and 0, which is essentially a single number.

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

The Casino's Math

It takes a lot of play to win true odds
All statistics are dependent on an infinite amount of rolls.
There are always deviations in the bet sizes of Hates.
Structured play is not something that he likes, especially with regard to departure rules and money management.
Once you reach a certain volume of play, the mathematical edge is yours.
This guaranteed mathematical edge can be achieved by any casino offer.




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