Noam Brown

You're going to have hands with your lose.

Even if you're playing the perfect strategy, you can't guarantee that you're going to win every single hand.

But if you play for long enough, then you are guaranteed to at least break even and in practice, probably win.

So finite's not a huge constraint.

So, I mean, most games that you play are finite in size.

It's also true, actually, that there exists this, like, perfect strategy in many infinite games as well.

Technically, the game has to be compact.

There are, like, some edge cases where you don't have a Nash equilibrium in a two-player zero-sum game.

So you can think of a game where, like, you know, if we're playing a game where whoever names the bigger number is the winner, there's no Nash equilibrium to that game.

Yeah, exactly.

18.

You win again.

I played a lot of games.

The zero-sum aspect.

So there exists a Nash equilibrium in non-two-player zero-sum games as well.

And by the way, just to clarify what I mean by two-player zero-sum, I mean, there's two players and whatever one player wins, the other player loses.

So if we're playing poker and I win $50, that means that you're losing $50.

Now, outside of two-player zero-sum games, there still exists Nash equilibria, but they're not as meaningful.

Because you can think of a game like Risk.

If everybody else on the board decides to team up against you and take you out, there's no perfect strategy you can play that's going to guarantee that you win there.