Yao's minimax principle

Okay, here's a special principle named after a famous mathematician named Yao: the Yao's Minimax Principle! It sounds like a fancy name, but it's really just a way to help us figure out the smallest possible worst case scenario.

Let's say you're playing a game, and you want to make sure you have the best chance of winning, even if things don't go your way. Yao's Minimax Principle says that you should always choose your moves in a way that minimizes the maximum possible loss.

That might sound a bit confusing, so let's break it down using a really simple game called "Guess the Number." In this game, your friend picks a number between 1 and 10, and you have to guess what it is. If you get it right, you win a prize. But if you get it wrong, your friend gets to keep the prize.

Now, let's use Yao's Minimax Principle to figure out how to play this game to win. Since you want to minimize the maximum possible loss, you need to think about the worst-case scenario. That would be if your friend picks the number that's hardest for you to guess, which is 5, because it's right in the middle. So you need to make sure that even if your friend picks 5, you don't lose.

One way to do that is to guess the numbers in a specific order: start by guessing 1, then 3, then 5, then 7, then 9. If your friend picked any number other than 5, you'd win! And if they picked 5, then you'd have a tie, instead of losing.

So, using Yao's Minimax Principle helped us figure out the best strategy for "Guess the Number," and we can use it in all sorts of situations where we need to make decisions based on potential risks or losses. It sounds complicated, but it's really just a helpful idea to keep in mind!