Skip to content

game theory

Optimal Strategy in a Number Guessing Game

You play a number guessing game in which you must pick a real number x, between 0 and 924. At the same time, the number y is uniformly and randomly selected from the same range. If x is greater than y, then you have to pay the square of the difference between the two numbers. If y is greater than or equal to x, you pay double the difference.

What number should you choose initially?

Read More »Optimal Strategy in a Number Guessing Game

Logical Pirates’ Treasure Split: Who Gets What?

A crew consisting of 3 democratic pirates finds a bounty of 100 coins.

The strongest pirate must propose a bounty split and all pirates vote. If the vote passes, meaning that it gets at least half the votes, his proposal is accepted. If the vote doesn’t pass, he is killed, and the process is repeated.

Knowing that all pirates possess perfect logic and their priorities are, in order to survive, then more bounty, then more deaths, how will the coins end up being split?

Read More »Logical Pirates’ Treasure Split: Who Gets What?