How John Nash Ruined your Childhood

Politeness. You allowed your friend to go first when you played tic-tac-toe, but, no matter how smart you thought you were, you could never beat him. Why? Well, I decided to seek out information regarding Nash Equilibrium to famous childhood games.

My source article started out as a simple explanation of the Nash equilibrium, but it quickly turned into a furious hunt for answers to some of life’s most basic questions: How can I never lose at simple games like tic-tac-toe and connect 4?

For starters, we have to explain what a Nash equilibrium is, and for that, I shall copy and paste a definition:

“In a Nash equilibrium, each player chooses the strategy that maximizes his or her expected payoff, given the strategies employed by others.”

So essentially, it’s your best move based on what you assume to be your opponents best move and, in games such as Tic-Tac-Toe, that best move is always in an attempt to win. Now, we’ve all lost games of tic-tac-toe (TTT) before, but the good news is, we do not have to ever again. Why? The Nash equilibrium of TTT is for it to always be a draw, essentially meaning that no one ever has to lose. This can be properly computed by doing a thought experiment not very far removed from the one conducted in class regarding the Christian and the Lion. What a player has to do is simply work backwards and eliminate his or her moves that are not optimal. This will form a sub-game perfect equilibrium.

Tic-tac-toe can always be a draw, but what about a more complicated game, like connect 4. One blogger has attempted to create a computer program that can master the game of connect 4, which essentially means that it will always play to it’s Nash Equilibrium. This is possible for connect 4, but there is one aspect of this that will make some players upset (exactly 50% of players). You must go first.

In both tic-tac-toe and connect 4, if you go first, you cannot lose. Now, if the other person is playing to their Nash equilibrium, you may not win, but you, if you use rational thought, will never lose. That may make the game lose some of its initial excitement, however, this is an extremely useful piece of information for when you decide to outsmart children at these games.

 

 

 

 

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2 thoughts on “How John Nash Ruined your Childhood”

  1. Checkers is another game that has been solved. The use of computers has allowed mathematicians to guarantee at least a draw from the start of the game, even if they are playing as the second player.

    Although computer power is what allowed them to say that definitively, there’s been little doubt for at least 150 years: In the 1863 World Championship of Checkers, the two finalists played 40 straight games to a draw. 21 of those 40 games were played exactly the same.

  2. “In both tic-tac-toe and connect 4, if you go first, you cannot lose.”

    This video explain how by going second, you can never lose in connect 4.

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