Casino Math
Craps
The key to understanding the mathematics of craps is to understand the dice combinations, or probabilities. My strategies only allow me to place bets with the highest probability of winning. These include the pass-line with odds, come wagers with odds, occasional bets on 6 and 8 and don't pass laying any odds.
If you play the above mentioned bets, the house percentage in craps is the lowest of any casino game. 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 often asked by seminar attendees why place bets perform better than come bets. The answer lies with the combinations of dice. A place bet can be used to illustrate this point. You can only win a direct bet on the number 5, which is also known as a place betting, on four different dice combinations: 1-4-4-1, 2-3, 3-2 and 2-2. That's it! The bet loses if a 7, which is the sum of six dice combinations, is rolled. Based on just the dice combinations, it's 6-4 or 3-4 against you.
Now let's look at 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. It's 6-4, or 2 to 1 in favor of you for the immediate win over 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 that started at the come and ended at the 5, had 12 possible winning combinations, compared to only 5 for the place wager on the 5. That is a significant advantage. This analysis can be applied to every 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, 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 need to minimize the casino's advantage. You also need to manage money so that you can capitalize on any streaks. This is what the Benson Strategies do.
Blackjack
Blackjack is the only casino game in which the advantage or disadvantage of a player changes with every card that is played. The game itself favors 4% the house, because if the dealer breaks, guess who takes the money. Of course, it's the house.
Basic strategy can reduce the house advantage to 1.5%. This is enough to make it a worthwhile game. If you play well and manage your money properly, you can expect to see a positive return over the long-term.
The player's advantage can be increased by as much as 1% through the combination of basic strategy and tracking the cards. As the deck (or shoe) is unplayed, more high cards are added to the player's 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 must hit 16 or less cards. This increases the chance of a dealer breaking if there are still high cards.
Most common methods for tracking are simple hi-lo counts (good on single deck games) and card clumping methods (good on shoe games). The 1% advantage is the highest expected mathematical return for expertly played blackjack.
Baccarat
Baccarat is known as a negative expectation game (the same as craps, roulette, and other). 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. This is possible only with perfect blackjack card counting (which, of course, doesn't let them let you win much).
Following the trend is how we win at Baccarat. Trends will emerge in any combination of random or almost random events. played games is important to remember that you won't have enough data to make statistically significant probabilities. These numbers are dependent on a lot more play. blog could be skewed one way: Bankers may have 50% more players than you (which would be wonderful, by the side).
The casino sees real statistical significance since they have so much action going on all the time. They can't lose in gaming. They are only able to lose players and typical business profit/loss. However, they don't lose the gaming itself. It is not possible. However, it is possible for the casino lose to players. They make up these losses by having enough players to make the math work in the end.
This last point is very important. It is important because you won't be playing 24 hours a days if you don't play by the same mathematical statistics of 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 over the player. The reason for this is that there are actually 38 numbers on the wheel: 1-36 and 0 and 00. Payoffs are calculated based only on 36 numbers, and not the zero or 00. The single number pays out 35-1. The casino's edge can be summarized as 0 and 0, which is essentially a single number.
Over a long time, the casino can enjoy a distinct mathematical advantage.
Casino Math
You need to play lots to have any chance of winning.
All statistics are dependent on an infinite amount of rolls.
Variations in bet sizes are known as Hates deviations.
Structured play is not his favorite, especially when it comes to money management and departure rules.
The mathematical edge is assured once the volume of play has been reached.
The casino will offer any enticement to achieve this guaranteed mathematical edge.