4 ms·

Although Ballmer could still be incorrect, because a 'sufficiently logical' player would also presumably know that he could pick numbers that'll be the most dif

by Closi 2y ago

Although Ballmer could still be incorrect, because a 'sufficiently logical' player would also presumably know that he could pick numbers that'll be the most difficult to find via binary-search, so by the same logic you could also meta-game it, and assume any number that can be found in 5 steps with a binary search is immediately out. This would narrow the search space to only 37 numbers, which can then easily be found within 5 guesses. But he also knows that you know that he could pick numbers that will be the most difficult... So could then pick one of the numbers that actually are guessable within 5 guesses to trick you. But then you also know that he knows that you know that he could pick difficult numbers too. I'm not entirely sure if this invalidates Ballmer's advantage, but I would be interested to know what the 'perfect' strategy would be for this game considering the meta-game.

Karliss 2y ago
There isn't much of metagame if number is only in Ballmers mind. No matter what guesses you choose he can force you to make at least log_2(100) guesses. Doing anything except splitting in half will only increase amount of guesses. There are two things that can change the game, requiring Baller to write the number on a piece of paper before the start. Other thing you could do is writing a number on piece of paper yourself halfway during the game. If opponent is changing the number adversarially with goal of maximizing guesses you can force them to "pick" a specific number. Afterwards you can open the piece of paper and claim that you actually guessed the number with the first attempt.
- Closi 2y ago
  This assumes Ballmer is cheating, rather than just behaving adversarially but within the rules. If we accept cheating is allowed, we can also potentially accept other 'cheating' scenarios where the player repeatedly punches Ballmer in the face until he discloses the number, thus winning. Or where the player just refuses to pay at the end. IMO the problem is only interesting if we assume any form of cheating isn't allowed.
  - uncanneyvalley 2y ago
    Do you want to catch a chair to the side of the head? Because this is how you catch a chair to the side of the head.

by Closi 2y ago

Karliss 2y ago

There isn't much of metagame if number is only in Ballmers mind. No matter what guesses you choose he can force you to make at least log_2(100) guesses. Doing anything except splitting in half will only increase amount of guesses. There are two things that can change the game, requiring Baller to write the number on a piece of paper before the start. Other thing you could do is writing a number on piece of paper yourself halfway during the game. If opponent is changing the number adversarially with goal of maximizing guesses you can force them to "pick" a specific number. Afterwards you can open the piece of paper and claim that you actually guessed the number with the first attempt.

Closi 2y ago
This assumes Ballmer is cheating, rather than just behaving adversarially but within the rules. If we accept cheating is allowed, we can also potentially accept other 'cheating' scenarios where the player repeatedly punches Ballmer in the face until he discloses the number, thus winning. Or where the player just refuses to pay at the end. IMO the problem is only interesting if we assume any form of cheating isn't allowed.
- uncanneyvalley 2y ago
  Do you want to catch a chair to the side of the head? Because this is how you catch a chair to the side of the head.