Notes

Casino Math

Craps

To understand the math behind craps, you need to be able to recognize the probability of winning. In my strategies we want to only play bets with the highest 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 of craps is the lowest casino game. To reduce the house percentage, you can take only one odds on the pass line and come bets. This will reduce it to the 0.8 %... single odds. To reduce it further to the 0.6 %... tri odds. To make it almost as good as dead even, you can reduce it to the 0.5 %... triple odds.

At seminars, I am always asked why place bets are not as good as come bets. The answer lies with the combinations of dice. 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 is lost if a 7 is rolled. There are 6 possible combinations. That's 6 to 4, or 3 to 2 against you based on the dice combinations alone.

Now let's 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. 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 huge advantage. This analysis can also be applied to all places bets.

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.

You must reduce the advantage of the casino and manage your money to maximize any streaks. That's why the Benson Strategies exist.

Blackjack

Blackjack is the only casino game where the player's advantage or disadvantage changes with each card played. The game itself favors the house by 4%, mainly because if you break and the dealer breaks, guess who gets 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. games online is possible to expect a positive return with good basic play and smart money management.

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 must hit 16 or less cards. The dealer will break more often if there is a high number of 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). An advantage of 1% means that blackjack, when played correctly, is the only casino game that can provide a positive mathematical return.

Baccarat

Baccarat has a negative expectation, which is the same as roulette, craps and other games. This means that the house has always the upper hand. 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).

To win at Baccarat, you must follow the trend. Trends will emerge in any combination of random or almost random events. Remember, you will not have sufficient lay to establish real probability numbers, since these depend on lots of play to reach statistical significance. One possibility is that there are 50% more bankers than players, which would be very interesting.

Casinos have a lot of activity and statistical significance. Gaming is the only way they can lose. 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. But it is very possible for the casino to lose to individual players. The casino makes up for these losses because they have enough players to make the mathematics work for them in the long run.

This last point is very important. You cannot play 24/7 and still be able to use the same mathematical statistics that the casino. Our departure rules and money management eliminate this immediately. A bad play and/or lack of discipline will not win the Baccarat player.

Roulette

Roulette has a 5.26% edge over the game. The reason for this is that there are actually 38 numbers on the wheel: 1-36 and 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 lies between the numbers 0 and 00.


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

Casino's Math

It takes a lot of play to win true odds
All statistics are based on an infinite number of rolls.
Hates deviations in bet sizes.
Structured play is not something that he likes, especially with regard to departure rules and money management.
Once fun games have reached the required volume, the mathematical edge will be yours.
This guaranteed mathematical edge can be achieved by any casino offer.




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