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 include the pass line with odds and come bets with chances.

The house percentage in craps falls to 0.8% if you make the above-mentioned wagers. Take fun player games 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 often asked by seminar attendees why place bets perform better than come bets. The answer lies in the dice combinations. To illustrate, a place wager can be used. 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 is lost if a 7 is rolled. There are 6 possible combinations. Based on the individual dice combinations, that's 6-4 or 3-4 against.

Let's take a look at a "come bet". When the come wager is in the coming area, it wins with a seven or eleven for a total number of eight dice combinations. It loses with a 2, 3 and 12 for a total loss of four dice combinations. This is 6 to 4, or 2:1 in your favor for an immediate win and a loss. If that come bet should go to the 5, as an example, it now has another 4 dice combinations to win. 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. This is a huge advantage. This analysis is applicable to any place you bet.

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, regardless of what number it is, is only 0.8% and has single odds. The exact same odds are available for the pass line, which has single odds.

To win in craps you must limit the casino's advantage. Also, money management will allow you to take advantage of all streaks. This is what the Benson Strategies do.

Blackjack

Blackjack is the only game where the player's advantage and disadvantage change with every card played. Because the game favors the house by 4 percent, you can break the dealer and get the money. Of course, the house!

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.

Furthermore, tracking of the cards played, combined with basic strategy, can change the advantage to the player by 1%. As more high cards remain in an unplayed deck or shoe, the advantage of the player increases. 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 must hit 16 or less cards. This increases the chance of a dealer breaking if there are still high cards.

The most common methods for tracking are simple high-lo counts (good for single-deck games) and card clustering methods (good to track shoe games). If blackjack is played well, it offers a 1% mathematical advantage.

Baccarat

Baccarat is a game with negative expectations, just like roulette and craps. This means that the house is always in the lead. By always, I mean that there is no known method of play that will place the odds in favor of the player mathematically. This is possible only with perfect blackjack card counting (which, of course, doesn't let them let you win much).

The way we win at baccarat is to follow the trend. Trends will emerge in any combination of random or almost random events. Because statistical significance depends on many plays, there won't be enough lay to create real probability numbers. One possibility is that there are 50% more bankers than players, which would be very interesting.

The casino is a statistical powerhouse because they have so many games going on at once. can i play a game cannot lose from gaming itself. They will only lose if they don't get enough players, or in typical business profit/loss scenarios. But they do NOT lose on the gaming. This is 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 should be very important. Because you can't play 24 hours per day and you won't be using the same mathematical statistics as the casinos. 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 of the 38 numbers that are on the wheel: 1-36, zero and 00. However, the payouts are based only upon the 36 numbers, not the 0, and 00. A single number pays 35-1. The casino's edge is the 0 or 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 based on an infinite number of rolls.

Hates deviations in bet sizes.
Structured play is not for him, particularly in the area of money management and departure rules.
The mathematical edge is assured once the volume of play has been reached.
Casinos will provide any incentive to get this guaranteed mathematical edge.




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