Nash equilibrium

One spot, two players. They bet $100 into a $100 pot, with strong hands or bluffs. You call or fold.

Every point on this square is a pair of strategies: how often they bluff, and how often you call.

Your best reply depends on them. Left of the black line, fewer than a third of their bets are bluffs, so you fold. Right of it, you call.

Their best reply depends on you. Below the red line you call less than half the time, so they bluff more. Above it, they stop.

Now let each side keep switching to its best reply. You fold, so they bluff more. So you call, so they stop bluffing…

It never settles. Every switch is punished by the next one.

Except at one point, where the two lines cross. They bluff a third of the time, you call half the time. Neither of you gains by changing alone. That’s a Nash equilibrium.

Set both strategies yourself. Away from the crossing point, someone can always profit by changing.