Expected Value The expected value is the longterm average of an experiment.
Example 1: In a Roulette game, bet $1.00 on 0 and 00. Either win $17 if 0 or 00 comes up, or lose $1.00 if any other number comes up. However, to determine the Expected Value, the longterm outlook of the bet, the probability of each outcome must be considered.
$17(2/38) + $1(36/38) = $34  $36
=  $2
=  $0.052 ~  5 cents every bet. That’s why the house wins. They are there for the longterm, so with every bet, they will make 5 cents. Rule: to find expected value, multiply value of each outcome by its probability and add the results. Decision Theory: What is the better bet, $1 on a single number or $1 in the lottery? Expected Value of Roulette bet = $35(1/38) + ($1)(37/38) = 35/38 – 37/38 = $2/38 =  .052 ~ 5 cents. (same as EX 1) Expected value of lottery 53/6 with $6,000,000 jackpot = $6,000,000(1/22,957,480) + ($1)(22,957,479/22,957,480) = ( 6,000,000 – 22,957,479)/22,957,480 = $16,957,479/22,957,480 = $.7386 ~  74 cents. the roulette bet is – 5 cents, while the lottery is – 74 cents.
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