Notes

Casino Math

Craps

Understanding the probabilities, or the combinations of dice is crucial to understanding the math of craps. In my strategies, we only want to play the bets that have the best probabilities of winning. mobile games include the pass line with odds and come bets with chances.

The house percentage of craps is the lowest casino game. 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 always asked why place bets are not as good as come bets. The answer lies in the combination of dice. A place bet can be used to illustrate this point. If you place a bet directly upon the number 5, (aka place wager), you can only win on any of these four dice combinations: 4-1, 2-3 and 3-2. That's it! The bet loses when a 7 (which has 6 different combinations) is rolled. Based on the individual dice combinations, that's 6-4 or 3-4 against.

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. 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 wager that started in a come area and moved to the 5 had 12 options to win. This was compared to 5 options for the place bet. This is a big advantage. This analysis can be applied to every place 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 is 0.8% with one odds. It has the exact same odds and odds as a pass line with 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. That's the Benson Strategies.

Blackjack


Blackjack is one of the few casino games where the advantage or disadvantage of the player changes with each card. The game itself favors the house by 4%, mainly because if you break and the dealer breaks, guess who gets 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%. 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. High cards mean a greater chance of a dealer fracas.

Simple hi-lo counts are good for single deck games, and card clumping is good for shoe games. These are the most common methods of tracking. The 1% advantage is the highest expected mathematical return for expertly played blackjack.

Baccarat

Baccarat has a negative expectation, which is the same as roulette, craps and other games. This means that the house always has the advantage. The odds are always in favor of the house mathematically. This is only possible with perfect blackjack count (which is the reason they don't let players win a lot).

You can win at baccarat by following the trends. A trend will develop in any random or near 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).

Casinos have a lot of activity and statistical significance. They cannot lose because of gaming. They will only lose if they don't get enough players, or in typical business profit/loss scenarios. They do not lose on gaming. It's impossible. It is possible, however, for the casino to lose 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 is 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 quickly eliminated with our money management rules and departure rules. The casino will only beat the Baccarat player by his or her lack of discipline and/or poor play.

mobile games has a 5.26% edge over the game. This is because there are 38 numbers on the wheel, including 0 through 00. However, the payoffs depend on only the 36 numbers and not 0 and 00. The single number pays out 35-1. The casino's edge is the 0 or 00.

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

Casino Math

You need to play lots to have any chance of winning.
Statistics can only be derived from an infinite number of rolls.
Variations in bet sizes are known as Hates deviations.
Structured play is not his favorite, especially when it comes to money management and departure rules.
Once you reach a certain volume of play, the mathematical edge is yours.
Casinos will provide any incentive to get this guaranteed mathematical edge.




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