Notes

Casino Math

Craps

Understanding the probabilities and dice combinations is key to understanding craps mathematics. In my strategies, I only want to choose the bets that offer the greatest 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. 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.

I am frequently asked why come bets do not perform as well in seminars. The answer lies with the combinations of dice. A place bet can be used to illustrate this point. 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. Based on just the dice combinations, it's 6-4 or 3-4 against you.

Let's take a look at a "come bet". free to play come bet wins on a seven- or eleven-dice combination and loses on a 2, 3, or 12 for a total total of four 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 that began in the come area and ended at the 5 had 12 combinations of dice to win, while the place bet on 5 had only 5 combinations. This is a big advantage. This analysis is applicable to any place you bet.

When you consider that all come bets can be placed, the casino advantage is 6.7% for place wagers on the 4-10; 4% for place wagers on 5-9; 1.5% place bets upon the 6-8 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 in craps, you must minimize the casino's advantage and use money management to capitalize on all streaks, do or don't. 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. 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!

Playing basic strategy can help reduce the house advantage by as much as 1.5% This alone makes it a great game. It is possible to expect a positive return with good basic play and smart money management.

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 are a favor to the player as they increase the chance of getting a "pat hand" and the dealer's chances 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). If blackjack is played well, it offers a 1% mathematical advantage.

Baccarat

Baccarat is known as a negative expectation game (the same as craps, roulette, and other). This means that the house is always in the lead. most played games 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).

Follow the trend to win at baccarat. A trend will develop in any random or near random series of events. There won't be enough play to calculate 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 sees real statistical significance since they have so much action going on all the time. They cannot lose from gaming itself. They can only lose from not getting enough players or from typical business profit/loss scenarios. They do not lose on gaming. It's impossible. But it is very possible for the casino to lose to individual players. best free to play games compensates for these losses as they have enough people to make the mathematics work long term.

This last point is crucial. 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 immediately eliminated by our departure rules and money management. Bad play and lack of discipline are the only things that can beat a Baccarat dealer.

Roulette

Roulette has an advantage of 5.26% over the player. This is because the wheel has 38 numbers: 1-36, 0, and 00. However, the payouts are based only upon the 36 numbers, not the 0, and 00. 35-1 is the single number. The casino's edge lies between the numbers 0 and 00.

Over a long duration, the casino will have a clear mathematical advantage.

Casino Math


For true odds to be achieved, there must be a lot of playing.
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 the volume of play is achieved the mathematical edge is guaranteed.
To achieve this mathematical edge, the casino will make every effort to entice you.




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