A short introduction Cookie policy

Solution to: Faites Vos Jeux

Let the original bet be equal to b. The probability that you lose a round is 18/37. The probability that you lose n consecutive rounds (which means that you must quit with a loss) is (18/37)n. Therefore, the probability that you win once is 1-(18/37)n. If you lose n consecutive rounds, your total bet (and loss) equals (2n-1) × b. If you win once, your profit equals b. So, the expected value for your profit is (18/37)n × ( -(2n-1) × b ) + ( 1-(18/37)n ) × b = ( 1-(38/37)n ) × b.

Note that this expected value is negative for all values of n greater than 0. You cannot expect a profit, but a loss!



back to the puzzle

Copyright © 1996-2016. RJE-productions. All rights reserved. No part of this website may be published, in any form or by any means, without the prior permission of the authors.
This website uses cookies. By further use of this website, or by clicking on 'Continue', you give permission for the use of cookies. If you want more information, look at our cookie policy.Continue