Question 1149812
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399/400 chance of losing the $4 bet; 1/400 chance of making the $4 bet and winning $500, a gain of $496.  The expected payback is<br>
{{{(399/400)*(-4)+(1/400)*(+496) = (-1596+496)/400 = -1100/400 = -11/4 = -2.75}}}<br>
The expected payback is -$2.75.<br>
Although it doesn't use the formal mathematical definition of expected value, you can determine the expected value with a simpler calculation.<br>
You win one game in 400;
it costs $4 for each play, for a total of $1600 for the 400 games;
you win $500 once.<br>
Your payback for the 400 games is -$1600 + $500 = -$1100; the expected payback (per game) is -$1100/400 = -$2.75.<br>