Assume I flip a fair coin n times until it comes up Heads. Now I take two large boxes, in one of which I place $3^n (3 to the power of n dollars) and in the other I place $3^(n+1) (3 to the power of n+1 dollars). I then give you the two closed seemingly identical boxes and allow you to open one box and count the money. At this point you can either take the money in the box you chose or take the unknown amount of money in the other box. Is there a strategy which you may employ in order to maximize your expected gain?(adsbygoogle = window.adsbygoogle || []).push({});

For example, if you open a box and see $3 you should always switch because there will definitely be $9 in the other box. However, if you open a box and see $9, switching might get you $3 or might get you $27.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Box Clever

Loading...

Similar Threads - Clever | Date |
---|---|

News Porsche - not just clever engineers | Jan 8, 2009 |

Clever little ideas | Apr 19, 2007 |

Im not too clever, but faster than light? | Sep 3, 2006 |

Do you have to be clever ? | May 10, 2006 |

Impressive military cleverness | Dec 16, 2005 |

**Physics Forums - The Fusion of Science and Community**