Suppose that a casino lets you bet on the outcome of flipping
a balanced coin -- heads you win, tails you lose. If it costs one
dollar to play, but the payoff odds are only one to two, then
what would be the house edge for this unfair game ?
| Let p | = | P( win ) = 1 / 2 | |
| Let B | = | size of your bet | |
| Let W | = | amount you stand to win = ( 1 / 2 ) * B |
| E | = | expectation = ( W * p ) + ( - B ) * ( 1 - p ) | |
| = | ( 1 / 2 ) B ( 1 / 2 ) - B * ( 1 / 2 ) | ||
| = | B * [ ( 1 / 4 ) - ( 1 / 2 ) ] | ||
| = | - B / 4 | ||
| H | = | house edge = | E | / B = 1 / 4 = 25 % | |