Notes

Casino Math

Craps

Understanding the probabilities, or the combinations of dice is crucial to understanding the math of craps. In my strategies, I only want to choose the bets that offer the greatest chance of winning. best free to play games 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. Take single odds on come and pass lines reduces the house percent to 0.8 %... double and further reduces it to 0.06 Triple odds. Further, it drops to 0.0.5 quad odds which reduces it further to 0.0.5 %.... The game is almost even if you take 10 to 100 odds.

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. This point can be illustrated by 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. 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 bet sits in the come area, it wins on a seven or 11 for a total of eight dice combinations and loses on a 2, 3 or 12 for a total of 4 dice combinations. This is 6 to 4, or 2:1 in your favor for an immediate win and a loss. The come bet that goes to the 5 has four more winning combinations. So, the come bet that started in the come area and went to the 5 had 12 dice combinations to win, versus only 5 combinations for the place bet on the 5. That's a huge advantage. This analysis is applicable to any place you 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 wager, regardless of the number, is 0.8% with single chances and the exact opposite odds to the pass line.

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. This is what the Benson Strategies do.

Blackjack

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

Playing basic strategy can help reduce the house advantage by as much as 1.5% This alone makes it an attractive game. With proper basic play and proper money management you could expect to show a positive return over time.

Additionally, simple strategy can also be combined with card tracking to increase the player's advantage of 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 can only hit on 16 or fewer 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). Expertly playing blackjack offers a 1% probability of receiving a positive mathematical return.

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 can only be done with perfect blackjack card counting (which is why of course they don't let you win a lot).

The way we win at baccarat is to follow the trend. A trend can form in any random or nearly random series of events. You won't have enough lay to determine statistical significance, as these numbers depend on a lot of play. Your results could be skewed one way: Bankers may have 50% more play ers than you (which would be wonderful, by the side).


Casinos have a lot of activity and statistical significance. They can't lose by gaming. They can only lose from not getting enough players or from typical business profit/loss scenarios. However, they don't lose the gaming itself. 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 matters. This is because unless you play 24 hour a day, your mathematical statistics will not be the same as those at 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 an advantage of 5.26% over the player. This is due to the fact that there are 38 numbers on roulette: 1-36, 0 and 00. Payoffs are calculated based only on 36 numbers, and not the zero or 00. A single number pays 35-1. The casino's edge is the 0 or 00.

The casino will enjoy a mathematical advantage over a long time.

Casino's Math

To achieve real odds, you need to play a lot.
All statistics are based on an infinite number of rolls.
Abweichungen in bet sizes by Hates
Structured play is not his favorite, especially when it comes to money management and departure rules.
Once the volume of play is achieved the mathematical edge is guaranteed.
Any enticement is offered by the casino to help you achieve this guaranteed mathematical edge.




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