A roulette wheel contains 38 pocketsthe numbers 1 through...

A roulette wheel contains 38 pocketsthe numbers 1 through $36,0,$ and $00 .$ The wheel is spun and the "winning" pocket is recorded, with any one pocket just as likely as any other. Suppose you bet $\$ 5$ on the number 18 . The payoff on this type of bet is usually $\$ 35$ for a $\$ 1$ bet. What is your expected gain?

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Key Concepts

Betting Odds and Payoff Structures

Betting odds and payoff structures describe the relationship between the stake placed on a bet and the potential winnings if the bet is successful. Understanding these odds helps in determining the risk versus reward of a particular bet by specifying how much can be won relative to the amount wagered.

Probability

Probability is the measure of the likelihood of an event occurring and is crucial in determining outcomes in games of chance. It allows us to assign a numerical value to the likelihood of each outcome, which is then used to calculate the expected value of bets or investments.

Expected Value

Expected value is a fundamental concept in probability and statistics that represents the long-run average outcome of a random event if the process is repeated many times. In betting and gambling scenarios, calculating the expected value helps determine whether a bet is favorable or unfavorable by accounting for all possible outcomes weighted by their probabilities.

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