House advantage is a
gambling term to describe how much the
probabilities are tilted towards the
casino. Casinos
make money because their games are, in general,
not fair. That is, their games have a bias towards the casino. The house advantage is a measure of how large that bias is. For games where you play against other players, casinos take a fixed percentage of the money bet (the
house take).
The house advantage is expressed as a percentage of money bet that the casino expects to get on each hand. For example, if you bet $20 on a game where the house take is 3%, the casino expects to make 60 cents ($20 * 0.03) on that game. Of course, this is the expectation. You may win $2,000 or you may lose $20. However, if you played that game 1000 times with a $20 bet, you would lose close to $600 (0.60 * 1000).
In some games, such as Let It Ride and Three Card Poker, the amount bet varies depending on the player's decisions during the game. The house advantage is measured against the amount the player must bet to play the game. For example, in Let It Ride, the player can pull back all but the last bet. Thus, the house advantage is calculated as a percentage of that bet. In Three Card Poker, you can choose to play or fold (and lose the ante), so the house advantage is based purely on the ante.
To compute the house advantage, consider all possible outcomes. For each outcome, multiple the chance that outcome occurs by the winnings (or loss) if it happens, presuming you bet $1. Add up the numbers, negate it, and you'll get the house advantage.
Roulette is the simplest standard casino game to compute the house advantage (presume 0 and 00 slots and standard USA rules). If you bet a single number, the probability of you winning is 1 / 38 (1 winning number, 38 total numbers). If you win, you win $35 on a $1 bet. If you lose, which happens with probability 37 / 38, you lose your $1 bet. Thus, the house advantage is (1/38) * 35 + (37/38) * -1 = -0.0526. Thus, the house advantage is 5.26%.
It is important to be aware of the house advantage, as it estimates the rate at which you lose money. Since gambling is entertainment, why spend more than you need to spend? For example, the five numbers bet in Roulette pays 6 to 1. The probability of winning is 5 / 38 and the probability of losing is 33 / 38. Thus, the house advantage is (5/38) * 6 + (33 / 38) * -1 = 0.0789, or 7.89%. You may chose to bet this to increase your excitement, but you should do so with the knowledge that it is a worse bet.
House advantage is difficult to determine for slot machines, especially video slots, as you do not know the probability distribution of the outcomes. However, for table games, it is possible, although the arithmetic can get very messy. Resorting to Monte Carlo simulation is often the easiest way to get the house advantage, although that yields only an estimate.
If you are interesting in house advantages for many games, Wizard of Odds is a great resource, at http://www.wizardofodds.com/.