Guess my number 1

Optimal search strategy and expected cost in a guessing game

This is an easy probability question that tests whether you can combine game theory and information theory to find a fair price. It asks you to determine the expected cost of playing optimally against an adversary who knows your strategy.

The core challenge is to work out the optimal guessing strategy—that is, which sequence of guesses minimizes your worst-case or expected number of wrong guesses—and then calculate the expected number of guesses needed under that strategy. Once you know the expected cost, the fair prize is the one that makes your expected winnings equal to your expected cost.

• Binary search and information gain
• Decision trees and minimax reasoning
• Computing expected values over a discrete uniform distribution