In gambling, one’s advantage (or disadvantage) refers to the percent of each bet a gambler (or the houseThe house is a colloquial term for the casino. The "house edge" is the casino's edge. "The house always wins" refers to the idea that...) can expect to win (or lose) on average, over the long run. Like expected valueExpected value or EV is the average return one can expect to get from a repeated decision, such as from a gamble, if it is..., this can be calculated by summing the product of each outcome’s value by its probability across all outcomes, but to get the advantage instead of the expected value, the value of each outcome needs to first be divided by the amount risked (if that amount risked is different for each possible outcome; if it’s the same, then the EV can just be divided by the amount risked).
This technical conception of advantage or disadvantage makes it easier to compare expected value across different gambles, since it normalizes EV by the amount risked. For example, consider the example used in the expected value definition. The gambler will win $1 for each toss landing on heads and lose $1.50 for each toss landing on tails. Each of those coin flips could be conceptualized as putting $1.50 at risk (since that’s the maximum amount that could be lost with each flip) with a 50% chance of gaining $1.00 ($1/$1.5 = a 66.7% gain on that outcome) and a 50% chance of losing $1.50 (-$1.50/$1.50 = a 100% loss on that outcome). The dollar amount is replaced in each part of the EV equation by the percentage gained or lost to calculate the players advantage or disadvantage: 0.5*(+1/1.5)+0.5*(-1.5/1.5) = (1/3) – (1/2) = -1/6 or -16.7%. This corresponds to a disadvantage of -16.7% (of the amount put at risk). In other words, over the long run, the coin-flip gambler can expect to lose 16.7% of whatever they put at risk. Note this is the same as dividing the -$0.25 expected value of the gamble by the $1.50 put at risk in the original example.
Edge is synonymous with advantage. Often we refer to the house edge, which refers to the casino’s advantage, since casino games are offered with the intention of providing an edge to the house (i.e., the casino).
Vig is short for vigorish and is a common term used to describe the casino’s built-in advantage, either because the casino subtracts the money as a percentage or fixed amount of the initial bet, as in sports betting or poker, or because the structure of a game of chance gives the casino a precisely calculable advantage. Vig is synonymous with house edge or house advantage, except that it is limited to these more narrow domains where the edge is built into the game rather than a matter of post-hoc assessment based on the casino’s average performance.