Spin spinner with n numbers twice (win if you hit same number twice), or flip n coins (win if all heads)?

This is a tough one, so make sure you justify your reasoning with mathematics

December 18, 2013Uncategorized

Spin spinner with n numbers twice (win if you hit same number twice), or flip n coins (win if all heads)?

This is a tough one, so make sure you justify your reasoning with mathematics

Michael Paul GoldenbergIn the roulette wheel bet, do you have to pick the number in advance of the first spin? I assume so. In that case, this is really “cute” in that assuming that n must be greater than 1, things vary for the first four values of n. Starting with that fourth value (n = 5), it will always be better to pick the coin flipping option. For n = 2, the chances are equal, as is the case for n = 4. For n = 3, the roulette wheel is the better choice. Thereafter, 1/n^2 will always be greater than 1/(2^n).

Michael Paul GoldenbergIn the roulette wheel bet, do you have to pick the number in advance of the first spin? I assume so. In that case, this is really “cute” in that assuming that n must be greater than 1, things vary for the first four values of n. Starting with that fourth value (n = 5), it will always be better to pick the coin flipping option. For n = 2, the chances are equal, as is the case for n = 4. For n = 3, the roulette wheel is the better choice. Thereafter, 1/n^2 will always be greater than 1/(2^n).

Dan Anderson (@dandersod)Cool one. Depends on the n. Is (1/n)^2 > (1/2)^n? Here’s some python code to hack away at some small sample sizes: https://dl.dropboxusercontent.com/u/3646828/would_you_rather.py

Dan Anderson (@dandersod)Cool one. Depends on the n. Is (1/n)^2 > (1/2)^n? Here’s some python code to hack away at some small sample sizes: https://dl.dropboxusercontent.com/u/3646828/would_you_rather.py