Nash Equilibrium
The equilibrium point where no player can improve unilaterally
Definition
The Nash equilibrium, theorized by mathematician John Nash, is the point where two players play their best possible strategies against each other. Neither one can improve their expected result by changing strategy unilaterally — both strategies are mutually optimal. In poker, the Nash equilibrium corresponds to pure GTO strategy. Applied to push/fold (the only two actions available when the stack is very short), Nash charts indicate exactly which hands to push based on your stack in big blinds, your position, and the number of players. These charts are mathematically optimal against an opponent who also plays optimally. In Spin & Go, Nash push/fold ranges are essential because blinds rise very fast. At 15bb heads-up, Nash tells you to push ~45% of hands from the SB (which is also the button). Deviating from these charts creates exploitable weaknesses against a competent opponent.
Nash push/fold charts indicate exactly which hands to push based on your stack (in bb) to be unexploitable heads-up. At 10bb BTN vs BB, you push around 60% of hands according to Nash.
Frequently asked questions
What is a Nash push/fold range?
It's the mathematically optimal all-in range when your stack is short (~≤ 15-20bb), built to be unexploitable if your opponent also responds optimally. It depends on stack in big blinds, position and the number of players still to act.
When should you use Nash charts?
Mainly in tournaments, Spin & Go and short-stacked heads-up, where push or fold are the only reasonable actions. Beyond ~20-25bb the push/fold model applies less and less, since limping, calling and 3-betting become relevant again.