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. 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. 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.

At seminars, I am often asked why place and come bets aren't as profitable as they used to be. The answer lies in 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. That's it! The bet is lost if a 7 is rolled. There are 6 possible combinations. This means that you lose 6 to 4 dice combinations or 3 to 2.

Let's examine 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. You win 6 to 4, or 2:1 in your favor for the instant win, and you lose 1. It now has 4 more dice combinations to win if the come bet goes to the 5. 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 used for any place bet.

You can also place odds on all come wagers. The casino advantage for place bets of the 4 and 10 is 6.7%, while the 4% on the 5 and 9 is 4% and the 1.5% on the 6 or 8. A come wager, regardless of the number, is 0.8% with single chances and the exact opposite odds to the pass line.

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

fun player games is one of the few casino games where the advantage or disadvantage of the player changes with each card. The house is favored by 4% because the dealer will break if you make a mistake. Guess who wins the money! The house, naturally!

You can reduce this house advantage to 1.5% by using basic strategy. This alone makes it an attractive game. It 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 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 must hit on 16 cards or less. The dealer will break more often if there is a high number of cards.

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 can be described as a game of negative expectation (just like craps or roulette). This means that the house always has the advantage. I don't mean there is a mathematical method that can place the odds in the favour of the player. click here 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. Any random or close to random sequence of events can create a trend. There won't be enough play to calculate statistical significance. Your results could be skewed one way: Bankers may have 50% more players than you (which would be wonderful, by the side).

Because there is so much activity, the casino has real statistical significance. They can't lose in gaming. They will only lose if they don't get enough players, or in typical business profit/loss scenarios. However, they can't lose on the gaming. This is impossible. However, it is possible for the casino lose to 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. Because unless you play 24 hours a day, you will never be playing by the same mathematical statistics as the casino. This is eliminated immediately by our money management and departure rules. 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 due to the fact that there are 38 numbers on roulette: 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. Simply put, the casino's edge is between 0 and 0.

Over a long duration, the casino will have a clear mathematical advantage.

The Casino's Math

Needs lots of playing action to achieve true odds.
All statistics are based upon an infinite number roll.
There are always deviations in the bet sizes of Hates.
Does not like structured play, especially in money management and departure rules.
Once the volume 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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