Notes

Casino Math

Craps

Understanding the probabilities, or the combinations of dice is crucial to understanding the math of craps. In my strategies we want to only play bets with the highest chance 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 craps house percentage is the lowest among all casino games. 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.

At seminars, I am often asked why place and come bets aren't as profitable as they used to be. It all comes down to the dice combinations. To illustrate, a place wager can be used. 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. That's it! When a 7 is rolled, which has a total of 6 dice combinations, the bet loses. This is 6 to 4 or 3 to 2 against, depending on the combination of dice.

Let's examine a 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. 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 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 big advantage. This analysis is valid for all types of bets.

You can also take odds on all of your come bets. Place bets for the 4 or 10 are 6.7% and 4% respectively; place bets for the 5 or 9 are 4% and place bets for the 6 or 8 are 1.5%. A come bet is 0.8% with one odds. It has the exact same odds and odds as a pass line with single odds.

To win at craps, you have to reduce the casino's advantage. Money management is key. That's what the Benson Strategies are all about.

Blackjack

Blackjack is the only online casino game where the benefit or disadvantage of each card can change. Because you lose and the dealer wins, the game favors house by 4%. The house of course!

free games to play can be reduced to 1.5% by playing basic strategy. This makes it an enjoyable game. If free to play play well and manage your money properly, you can expect to see a positive return over the long-term.

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 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 must hit on 16 cards or less. This increases the chance of a dealer breaking if there are still high cards.

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. laptop means the house always wins. The odds are always in favor of the house mathematically. 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. Any random or close to random sequence of events can create a trend. Remember, you will not have sufficient lay to establish real probability numbers, since these depend on lots of play to reach statistical significance. It is possible to be biased in one direction. For instance, 50% more bankers could play than players. (Which would be great, by the way).


The casino is a statistical powerhouse because they have so many games going on at once. They cannot lose from gaming itself. They are only able to lose players and typical business profit/loss. But they do NOT lose on the gaming. It's impossible. But it is very possible for the casino to lose to individual players. The casino compensates for these losses as they have enough people to make the mathematics work long term.

This last point matters. 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. This is eliminated immediately by our money management and departure rules. The only thing that will beat a Baccarat player is his or her inability to be disciplined and/or poor play.

Roulette

Roulette has a 5.26% advantage on the player. The reason for this is that there are actually 38 numbers on the wheel: 1-36 and 0 and 00. However, the payoffs depend on only the 36 numbers and not 0 and 00. The single number pays 35-1. The casino's edge lies between the numbers 0 and 00.

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

Casino's Math

For true odds to be achieved, there must be a lot of playing.
All statistics are dependent on an infinite amount of rolls.
Abweichungen in bet sizes by Hates
Structured play is not for him, particularly in the area of money management and departure rules.
Once you reach a certain volume of play, the mathematical edge is yours.
The casino will offer any enticement to achieve this guaranteed mathematical edge.




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