Probability: The chances of some event happening. Ways to represent probability are:

1. As a decimal between 0 and 1. A zero represents no possibility and a 1 represents a total certainty. For example the probability of rolling a six on a fair die would be 0.1666667.
2. As a fraction between 0 and 1. Again, on a zero to one scale. For example the probability of rolling a six on a fair die would be 1/6.
3. As a percentage. The percentage is on a 0 to 100 scale, so is equal to 100 times the decimal or fraction probability. For example the probability of rolling a six on a fair die would be 16.6777%.

True Odds: Often just called "odds." Another way to represent probability measured as the number of ways against an event happening to the event happing. To convert a decimal probability of x to true odds take the inverse of the probability and subtract one. If the decimal probability of an event happening is x then the odds against it are (1/x)-1 to 1. For example the odds against rolling a six on one die are 5 to 1. If the fractional probability of an event happening is x/y then the odds against it are y-x to x.

Payoff Odds: What a bet will pay if it wins. Payoff odds are usually on a "to" basis, in which event the player keeps his original wager if it wins. For example a column bet in roulette pays 2 to 1 odds. If a $10 column bet wins the player will win $20 and keep his original $10. If it loses the player will lose his $10 bet. Sometimes payoff odds are on a "for" basis, often in craps. In this case the player does NOT get to keep his original wager if he wins. For example the any seven bet in craps pays 5 for 1 odds. If the player bets $10 he will get back a total of $50, including his original wager. The "to" basis is much more common and is preferred by myself.

Expected Value: The mathematical gain (positive) or loss (negative) the PLAYER can expect per one unit initial bet made. For example the expected value of a red or black bet in standard American roulette is –0.052632. In other words for every dollar the player bets he can expect to lose 5.26 cents.

Calculating the Expected Value: The expected value can be calculated by taking the sum over all possible outcomes of the product of the payoff odds and the probability. For example the "full pay" field bet in craps pays 3-1 on a 12, 2-1 on a 2, 1-1 on a 3, 4, 9, 10, or 11, and loses on all other numbers. The following table shows the probability of all outcomes, the payoff odds, and the contribution to the return. The total return in the lower right cell shows an expected return of –1/36, or about 2.78%. So for every dollar the player bets on the field he can expect to lose 2.78 cents on average.

House Edge: The mathematical gain (positive) or loss (negative) the CASINO can expect per one unit initial bet made. For example the house edge of a red or black bet in standard American roulette is +0.052632. In other words for every dollar the player bets the casino can expect to profit 5.26 cents. Also referred to as the House Advantage. It is the opposite of the expected value. The house edge does NOT ignore ties and is NOT relative to the total wager (including doubles, raises, etc.).

Calculating the House Edge: First calculate the expected value and then multiply by –1. Also, if you know the payoff odds are x to 1 and the true odds are y to 1 then the house edge is (y-x)/(y+1).