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Interesting Brainteaser

Posted By: Igor
Date: Monday, 7 March 2016, at 11:08 p.m.

In Response To: Interesting Brainteaser (AP)

We can also solve this using game theory. A player's strategy is the threshold p, 0A player using strategy p will have an expected payoff of

(1+p)/2 x (1-p) + 1/2 x p = 1/2(1+p-p^2).

The maximum payoff is 5/8 and it's attained at p=1/2. However, the goal of the game is not to get as large a number as possible, but to get a number larger than your opponent's as often as possible.

The equilibrium strategy is the one where the expected payoff is the same as the threshold for rerolling. So solving

p = 1/2(1+p-p^2)

we get p = (\sqrt{5}-1)/2

which is the same as 1/(golden ratio).

This is the idea, I don't have time to prove the details.

Messages In This Thread

• Interesting Brainteaser
  AP -- Monday, 7 March 2016, at 2:15 p.m.
  • Interesting Brainteaser
    Bob Koca -- Monday, 7 March 2016, at 5:46 p.m.
    • Interesting Brainteaser
      AP -- Monday, 7 March 2016, at 9:21 p.m.
      • Interesting Brainteaser
        Bob Koca -- Monday, 7 March 2016, at 9:53 p.m.
  • Interesting Brainteaser
    Igor -- Monday, 7 March 2016, at 11:08 p.m.