Casino Odds

The basics of casino odds are probably easier than you think. The math behind a mega-jackpot on a $1 million dollar slot machine is tough, but figuring out how hard it is to throw a seven on a standard set of dice is pretty easy.

The game of craps is played with a single set of six-sided dice with dots on each side from one to six. Casinos use dice that are guaranteed to be accurate to 1/20,000 of one inch. When you roll both dice there are 36 possible outcomes. If you roll a single die the chance of it coming up a six are one in six, expressed as 1/6. If you roll both dice, the chance of both coming up a six are 1/6 x 1/6 = 1/36.

If you want to know about rolling that seven, it can be rolled six ways: 1-6 or 6-1, 2-5 or 5-2, and 3-4 or 4-3 (6/36). If you make a one-roll bet on seven, you have six ways to win and 30 ways to lose. The bet pays 4 to 1. The math looks like this: 36 bets of $1 ($36) and you win six times for $24 plus your $6 in bets back ($30) - which gives us 30/36 for a return of 83 percent. The house keeps almost 17%. Yikes!

When you place a bet on 12 (both dice coming up on a six as shown above), you will hit the bet once in every 36 rolls on average. However, that crazy 12 might come up this roll and the very next roll also, or it might not come up for 200 straight rolls. Every roll is independent of the last. Just because you haven't seen a 12 roll for half an hour doesn't make it more likely to come up on the next roll. The odds of the next roll coming up twelve are still 1 chance in 36. Consider taking a look at the usual craps bets and their payoffs before hitting the tables!

The difference between craps and blackjack is that as cards are removed from the deck, the odds change! A standard blackjack deck uses 52 cards of four suits numbered from one (ace) through King. The odds of getting a blackjack on the first hand off the top of the deck are about 4.8 percent or 20.8 to 1.

However, if during the first hand all four aces are used, you will have zero chance of getting a blackjack on subsequent hands. At this point the house has a huge edge over you the rest of the deck with no aces available.

The math for this is pretty easy. There are two parts to the problem. If your first card is an ace (4 chances in 52 or 4/52), you need a ten-value card as your second (16 chances in 51 or 16/51). You need to multiply these together because the two events are independent of each other. 4/52 x 16/51 = 64/2652

If your first card is a ten-value card (16 chances in 52 or 16/52), you need an ace as your second card (4 chances in 51 or 4/51). You need to multiply these together because the two events, again, are independent of each other and you need them both to occur. 16/52 x 4/51 = 64/2652.

Now that you know both ways of making a blackjack, you can add the two probabilities together: 64/2652 + 64/2652 = 128/2652 This gives you a 4.8 percent chance of making a blackjack off the top of the deck. What are the odds? Take 100 percent and divide by 4.8 or 100/4.8 and you get 20.8

If you play roulette in the United States you will most likely find that the wheels have number "1" through "36" plus a "0" and a "00." When you bet a single number and win, the casino will pay you 35-1 for your bet. A $1 bet returns a total of $36, $35 plus your original $1 wager.

The house edge comes from the fact that there are 38 pockets for the ball to fall in. Instead of being paid 37-1, you get 35-1. On average, with a non-biased wheel, the casino will keep 2 of every 38 bets: 2/38 = 0.0526 Thus the house roulette edge on a single or straight-up bet is 5.26 percent.