Notes

Casino Math

Craps

To understand the math behind craps, you need to be able to recognize the probability of winning. In my strategies, I only want to choose the bets that offer the greatest chance of winning. These are the pass lines with odds, the come bets, the occasional place bets, the 6 and 8 don't pass placing the odds and can't be placed with or without the odds.

The house percentage in craps has the lowest rate of any casino game if you place the above-mentioned bets. 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 in the dice combinations. You can illustrate this point with a place betting. 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! The bet loses if a 7, which is the sum of six dice combinations, is rolled. This is 6 to 4 or 3 to 2 against, depending on the combination of dice.

Let's now take a look at the come bet. If the come bet is placed in the come area, it will win on a seven or 11, for a total eight dice combinations, and lose on a 2, 3, 12 or 12 for total of 4 dice combinations. The odds of winning an immediate win are 6 to 4 or 2 to 1. If that come bet should go to the 5, as an example, it now has another 4 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.

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 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. That's what the Benson Strategies are all about.

Blackjack


Blackjack is the only casino game in which the advantage or disadvantage of a player changes with every card that is played. The house is favored by 4% because the dealer will break if you make a mistake. Guess who wins the money! Of course, it's the house.

This house advantage can be reduced to 1.5% by playing basic strategy. This alone makes it a great game. If you 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%. The advantage of the player increases if there are more high cards left in their unplayed hand (or deck). High cards are better for the player than the dealer because they increase the chances of the dealer breaking and give the player a better chance of getting "pat" hands. The dealer has to hit on 16 or less. High cards mean a greater chance of a dealer fracas.

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 has a negative expectation, which is the same as roulette, craps and other games. This means that the odds always favor the house. It means that the odds of the house always favor the player 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. Trends can develop in any random, or very near random sequence of 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.

played games have a lot of activity and statistical significance. Gaming is the only way they can lose. They cannot lose by not having enough players or typical business profit/loss situations. But they do NOT lose on the gaming. This is impossible. It is possible, however, for the casino to lose individual players. They make up these losses by having enough players to make the math work in the end.

This last point should be very important. Because unless you play 24 hours a day, you will never be playing by the same mathematical statistics as 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 a 5.26% advantage on 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. The single number pays 35-1. The casino's edge is the 0 or 00.

Over computer of time, the casino will have a definite mathematical advantage.

The Casino's Math

For true odds to be achieved, there must be a lot of playing.
All statistics are based on an infinite number of rolls.
Abweichungen in bet sizes by Hates
Does not like structured play, especially in departure rules and money management.
The mathematical edge is assured once the volume of play has been reached.
This guaranteed mathematical edge can be achieved by any casino offer.




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