Probability - The measure of how likely or how often something is going to happen. Probability is always a number between 1 and 0. A 1 would indicate something is always going to happen and a 0 would mean something is never going to happen. Most gambling situations have a probability somewhere in between the two. (And if you add the probability of something not happening with the probability of something happening, your total will always be 1.) A probability is a fraction unless it's a certainty.
Odds - Odds is a way of stating a probability as a relationship between something happening and something not happening. For example, the probability of rolling a 6 when rolling a die is 1/6. The odds would be considered 5 to 1. (The first number is the number of times it won't happen, and the second number is the number of times it will happen.) To calculate the odds, take the number on top of the fraction, subtract the number on top, and put the difference first and the number on top of the fraction second. So for 1/6, 6-1=5, or 5 to 1.
The thing to remember about odds in a casino game situation is that the casino doesn't pay you according to the true odds, and this is what gives them the advantage, and this is what makes them profitable. Roulette's a perfect example. The odds of the ball landing on any individual number are 37 to 1. But betting on any individual number only pays 35 to 1. The difference in the true odds and the odds that the casino pays out to the player is the house edge.
House edge - The house edge is the mathematical advantage on any given bet that the casino has over the player. It's normally in percentage format. (For example, the house edge in roulette is 5.46%)
Expectation - The amount of money you'll win or lose by making a certain decision in a gambling game. It's calculated using the house edge and the amount of the wager. For example, if you bet $100 at roulette, the house edge is 5.46%, or $5.46. So long term, you can expect to lose $5.46 on every $100 wager.
Understanding these concepts in detail will do a few things for you. They'll give you a better understanding and enjoyment of the games you're playing. They'll improve your chances of winning. And they'll give you an understanding of why the casinos are so profitable. (A better understanding of this than about 90% of the people playing in the casino have, in fact.)
See also: How to Calculate Probability?
