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A gambling problem

Go to solution Solved by gavinksong,


A gambler has $5,000 and is playing a game of chance with a win probability of .95. Every time he wins, he raises his stake to 1/4, of his bankroll. The gambler doesn't reduce his stake when he loses

If he keeps at it, what are his expected winnings?

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6 hours ago, bonanova said:
  1. What is his initial bet (stake)?
  2. Did you mean to say "Every time he wins, he raises his stake by 1/4 of his bankroll"?

His initial bet is $1250.  Every time he wins, he calculates his total and takes 1/4 of it to bet.  So initially he has 5000, 5000 x .25 = 1250.  If he were to win, he would earn double his bet so he would have $6250.  Recalculating he would bet $1562.50.  If he loses his bet he would maintain that amount in his next bet.  He keeps at it until he is unable to make his desired bet.

Edited by BMAD
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