Probability of Losing = 0.99 (99 numbers out of 100)Įxpected Value (spin wheel) = ($95 x. Probability of Winning = 0.01 (1 number out of 100) Let’s try another example … a spinning wheel with 100 numbers and a $95 payoff on a $1 bet. Here the expectation is that on average the bettor will lose $.05 on every one-dollar bet. Let’s try another example, but this time let’s lower the payoff on the coin toss to $.90 for each $1 bet.Įxpected Value (coin toss) = ($.90 x. In other words, EV is the anticipated outcome of the average of many samples. This is because expected value is subject to the Law of Large Numbers - the more samples (coin tosses in our example), the closer the average will come to the expected value. However, something here doesn’t make sense as a single coin-toss is never going to return $0 as the EV analysis predicts the payoff is always going to be minus $1 or plus $1 as the bettor is always going to win or lose his bet of $1. Based on this, there’s nothing to gain or lose on this bet. This means that the bettor should expect to win $0 on every coin-toss bet, which he will on average if he plays long enough. Using the EV formula, we get an expected value $0:Įxpected Value (coin toss) = ($1 x 50%) - ($1 x 50%) = $.50 - $.50 = $0 Probability of Losing = 50% (one out of two possible coin faces) Probability of Winning = 50% (one out of two possible coin faces) Let’s try it with a coin toss, a $1 bet, and a one-for-one (1:1) payoff: Investors use a similar technique to evaluate their investments. The difference between the two is the expected value.ĮV = (Payoff x Probability of Winning) - (Bet x Probability of Losing)Ī positive and negative EV tells the gambler that the bet is good or bad. This risk-reward evaluation is quantified by expected value (EV), which weighs the bet by the probability-of-losing and the payoff by the probability-of-winning. Whenever someone makes a wager, he is evaluating the risk of losing against the reward of winning. This section describes some of the mathematical and statistical ideas that are part of the game.

Blackjack probability table