Expected Value Section 3.5   The expected value is the long-term 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 long-term outlook of the bet, the probability of each outcome must be considered.         \$17(2/38) + -\$1(36/38) = \$34 - \$36                                                 18           =   - \$2  =  - \$0.052 ~ - 5 cents every bet.                18 That’s why the house wins.  They are there for the long-term, 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.   Back to Statistics Main Page Back to the Survey of Math Ideas Home Page e-mail Questions and Suggestions