Notes

Casino Math

Craps

Understanding the probabilities or dice combinations is the key to understanding the mathematics behind craps. In my strategies, we only want to play the bets that have the best probabilities 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. Taking single odds on pass line and come bets reduces the house percentage to 0.8%... double odds reduces it to 0.6%... triple odds reduces it further to 0.5%... and 10 times up to 100 times odds makes the game almost dead even.

I'm often asked at seminars why place bets don't perform as well as come bets. The answer lies in the dice combinations. This can be illustrated with a place bet. 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! When a 7 is rolled, which has a total of 6 dice combinations, the bet loses. This means that you lose 6 to 4 dice combinations or 3 to 2.

Let's take a look at a "come bet". When the come bet sits in the come area, it wins on a seven or 11 for a total of eight dice combinations and loses on a 2, 3 or 12 for a total of 4 dice combinations. This is 6 to 4, or 2:1 in your favor for an immediate win and a loss. It now has 4 more dice combinations to win if the come bet goes to the 5. 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 big advantage. This analysis can be applied to every place bet.

apps 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, no matter what number it goes to is only 0.8% with single odds, the exact same odds as the pass line with single odds.

To win at craps, you have to reduce the casino's advantage. Money management is key. The Benson Strategies help you do just that.

Blackjack


Blackjack is the only online casino game where the benefit or disadvantage of each card can change. Because you lose and the dealer wins, the game favors house by 4%. The house, naturally!

Basic strategy can reduce the house advantage to 1.5%. This in itself makes it a good game to play. You can expect a positive return on your investment if you practice good money management and basic play.

The basic strategy of basic strategy and card tracking can help to improve the advantage for 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 because they give the player a better chance to get a "pat" hand and also they increase the dealer's 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.

go to the website hi-lo counts, which are useful for single deck game play, and card clumping techniques (which are great for shoe games), are the most commonly used methods for tracking. Expertly playing blackjack offers a 1% probability of receiving a positive mathematical return.

Baccarat

Baccarat is known as a negative expectation game (the same as craps, roulette, and other). This means the house always wins. The odds are always in favor of the house mathematically. This can only be done with perfect blackjack card counting (which is why of course they don't let you win 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. 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. They can't lose by gaming. 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. 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 is crucial. This is because unless you play 24 hour a day, your mathematical statistics will not be the same as those at the casino. 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.

Roulette

Roulette has a 5.26% advantage over the player. This is because there are 38 numbers on the wheel, including 0 through 00. Payoffs are calculated based only on 36 numbers, and not the zero or 00. A single number pays 35-1. So, simply stated, the 0 and 00 are the casino's edge.

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

Casino's Math

To achieve real odds, you need to play a lot.
Statistics are calculated using an infinite number rolls.
There are always deviations in the bet sizes of Hates.
Does not like structured play, especially in departure rules and money management.
Once fun player games is reached, the mathematical edge can be guaranteed.
To achieve this mathematical edge, the casino will make every effort to entice you.




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