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. These are the pass line and odds, come bets and odds, occasionally place bets and the 6-8, don't pass the odds laying them, and don’t come with or without the odds.

If you play the above mentioned bets, the house percentage in craps is the lowest of any casino game. If you only take single odds on pass line or come bets, the house percentage is 0.8 %... double odds. That reduces to 1.5 third odds. That reduces further to 1 and then down to 0.5 %.... A 10x to 100-fold increase in odds results in the game being almost dead even.

I'm often asked at seminars why place bets don't perform as well as come bets. It all comes down to the dice combinations. You can illustrate this point with a place betting. 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. http://www.turquoisemorningpressbookstore.com/paremmat-voittomahdollisuudet-online-kolikkopeleissa/ 's it! The bet is lost if a 7 is rolled. There are 6 possible combinations. Based on just the dice combinations, it's 6-4 or 3-4 against you.

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. That's 6 to 4, or 2 to 1 in your favor for the immediate win versus an immediate loss. If that come bet should go to the 5, as an example, it now has another 4 dice combinations to win. The come bet which started in the come zone and went to the five had 12 different combinations to win, as opposed to just 5 for the bet on the place. That is a significant advantage. This analysis can be used for any place 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, 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 what the Benson Strategies are all about.

Blackjack

Blackjack is the only game where the player's advantage and disadvantage change with every card played. Because you lose and the dealer wins, the game favors house by 4%. The house, of course!

By playing basic strategy, you can reduce your house advantage down to 1.5% This alone makes it an attractive game. It is possible to expect a positive return with good basic play and smart money management.

The basic strategy of basic strategy and card tracking can help to improve the advantage for the player by 1%. As long as there are no high cards in the deck or shoe, the player has an advantage. High cards favor the players because they increase their chances of getting a "pat," or a hand that is a good deal. They also give the dealer a higher chance of breaking. The dealer has to hit on 16 or less. 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). A 1% advantage means that expertly played blackjack is the only casino game that offers the player an expected positive mathematical return.

Baccarat

Baccarat has a negative expectation, which is the same as roulette, craps and other games. This means that the house is always in the lead. This means that mathematically, there is no way to place the odds in the favor of the player. This can only be achieved with perfect blackjack cards counting (which is why they don’t let you lose a lot).

The way we win at baccarat is to follow the trend. A trend can form in any random or nearly random series of events. Because statistical significance depends on many plays, there won't be enough lay to create real probability numbers. Your results could be skewed one way: Bankers may have 50% more players than you (which would be wonderful, by the side).

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. This is impossible. But it is very possible for the casino to lose to individual players. Because they have enough players, the casino can make up the losses.

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

Roulette

The advantage that roulette has over the player is 5.26% This is because there are 38 numbers on the wheel, including 0 through 00. However, the payoffs are only based on the 36 numbers and not the 0 or 00. A single number pays 35-1. The casino's edge is the 0 or 00.

Over a long time, the casino can enjoy a distinct mathematical advantage.

Casino's Math

To achieve real odds, you need to play a lot.

All statistics are dependent on an infinite amount of rolls.

Abweichungen in bet sizes by Hates

Does not like structured play, especially in money management and departure rules.

The mathematical edge is assured once the volume of play has been reached.

To achieve free play , the casino will make every effort to entice you.