When John von Neumann came up with the principles of game theory, starting in 1928 with the minimax theorem, he loved using poker to analyze the way people behave in zero-sum situations. John Nash (the protagonist in the 2001 movie A Beautiful Mind) developed these principles further when he introduced the Nash equilibrium in 1951. Thanks to their work, and the advent of computers, we have something concrete we can use to play online poker: push or fold strategy.

You don’t need to be a mathematical savant to use these Nash push/fold strategies when you play poker online – you just need to download the charts and follow the instructions. But you’ll do a better job if you understand why they work, and when you’re supposed to use them. Wrapping your head around push/fold will help you make better decisions in other areas of the game. In many ways, everything the top pros are doing today is built on push/fold.


Unexploitable Play at the Poker Table

Nash push/fold strategies are useful for Texas Hold’em when it’s just you and one other player at the table. You could be playing heads-up cash poker at Ignition, or it could be a tournament where you’re down to the final two – although the presence of antes will change the math somewhat. Also, the stack sizes have to be small enough to warrant shoving instead of making a smaller open-raise.

The point behind using push/fold is to put your opponent in a position where she cannot exploit you. It’s kind of like playing for a tie, but hoping your opponent will make a mistake to your benefit. Let’s say you’re holding Ten-Seven offsuit and you’ve got nine big blinds left in your stack. According to the math, if you open-shove T7o every time you’re in this spot (antes notwithstanding), you will break-even in the long run – assuming your opponent also plays a “game-theory optimal” strategy.

Ideally, your opponent will fold too often and let you pick up the blinds. Nash equilibrium says if you’re the caller in this situation, you should swallow hard and call with hands like King-Four offsuit, Queen-Eight offsuit, even Ten-Eight suited. Not every player has the intestinal fortitude to call with a range this wide. If you spot a player like this, you can open-shove a wider range than the Nash charts recommend. Get acquainted with Nash push/fold if you want to make some immediate improvements at the online poker tables.