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The variance is the probability-weighted sum of squared distances from the expected value. The squaring gives "disproportionate" weights to large distances, e. : when you double your bet size, your profit/loss in both the win or loose scenario doubles. The probabilities to win or loose stay unchanged. Nor would players enjoy wagering $1 in the machine that says “change” with its 0% house edge and zero variance. Both of these zero variance games sound pretty dumb. Brown always bets a dollar on the number 13 at roulette. To help cure mr. Brown of playing roulette, kind friend always bets brown $20 at even money that brown will be behind at the end of 36 plays. The objective of this exercise is to flnd out how the cure is working. If you bet exactly $200$ you will have an expected value of $10-\frac {200}{37}$. That is as i said, the ev will be the same for any sequence of bets. The thing that changes is the variance. Many small bets have small variance, a few large ones have large variance. High odds bets, like one number, have high variance. Suppose you're playing a roulette and you decide to bet on black everytime. When doing so, the probability that you win is 0. If you decide to play 100 rounds, and let x be the number of rounds won. What is the distribution of x? what is the mean and variance of x? Example – american roulette the game of american roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or blackVariance of playing roulette, red hot sevens slots
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