Mind Performance Hacks

Hack #48. Don't Overthink It

When each side in a game—or an important decision—is trying to outsmart the other, it might be time to flip a coin.

On our third trek through the foothills of game theory, let's leave the wilds of Titanium Chef behind. Instead, imagine you are playing a game in which you hold a black Go stone in one hand and a white Go stone in the other. Your opponent must choose the hand holding the white stone. If she chooses correctly, she wins $1 from you; if she does not, she pays you $1.

Now imagine that your opponent is super-intelligent and will always outguess you. If you intentionally hide the white stone in your right hand, she will choose that hand. If you decide that she knows you will hide the stone in your right hand, and you try to outsmart her and hide it in your left, she will know that you know she knows, and she will decide to pick your left hand. No matter which hand you decide to hide the stone in while trying to outthink her, she will always be able to outthink you and pick the correct hand.

In this situation, the optimal strategy is to shake the Go stones in your cupped hands so that even you do not know which is which, and randomly take one in each hand. In fact, that is always your optimal strategy in this game against a rational opponent, and you must usually assume your opponent is rational. Similarly, your opponent's rational strategy is to flip a coin to determine which hand to pick. You can never expect to do better than 50:50 against ...