I have a puzzle which asks the following question:

You have the choice to pick between two games. Assume the coins are fair.

Game 1: You toss a coin once. Heads you win \$10 and tails you lose \$10.

Game 2: You toss a coin 10 times. Heads you win \$1 and tails you lose \$1.

Which game do you prefer?

My initial thoughts were that I would prefer the second game, as I would be wiped out a lot slower.

How would you approach this question?

  • 1
    $\begingroup$ Calculate the expected value of each game. If one is higher, you should prefer that game. If they are the same, calculate the variance of each game, and you should prefer the game with lower variance. (A "surer thing" is better than a big gamble.) $\endgroup$ – kccu Aug 23 at 20:27
  • $\begingroup$ As the expected value of each game is $0$ you are not given any reason to prefer one to the other, or to prefer either to doing nothing. There is no mathematical answer unless we are given some way to prefer one. $\endgroup$ – Ross Millikan Aug 23 at 20:36
  • $\begingroup$ If you want to play for longer and draw it out, play Game 2. If you want to end it quick, play Game 1. $\endgroup$ – automaticallyGenerated Aug 23 at 20:37

Which you prefer depends on your personality. If you are risk-averse, you should prefer the second game. If you are a gambler, you may prefer the first, with high risk and high reward. Even if you are generally risk-averse, there are circumstances under which you would prefer the second game. Look at the first paragraph of How to Gamble If You Must


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