Brainteaser - The Number Guessing Dilemma
The Number Guessing Dilemma
Reasoning
Three players act in order. Player 1 first announces an integer between 1 and 100. Player 2 sees Player 1’s choice and then announces his own integer (it must be different, but still between 1 and 100). Player 3 sees both earlier choices and then announces his integer, again different and between 1 and 100.
When all three numbers have been fixed, a random integer 𝑅 is drawn uniformly from 1 to 100. The player whose number is closest to 𝑅 wins; if two players are equally close, the tie is broken by a fair coin-toss.
Assuming Players 2 and 3 play perfectly rationally (each always picking the move that maximises their eventual probability of winning), what number should Player 1 choose to maximise his own chance of winning?
When all three numbers have been fixed, a random integer 𝑅 is drawn uniformly from 1 to 100. The player whose number is closest to 𝑅 wins; if two players are equally close, the tie is broken by a fair coin-toss.
Assuming Players 2 and 3 play perfectly rationally (each always picking the move that maximises their eventual probability of winning), what number should Player 1 choose to maximise his own chance of winning?