Indifference Principle

Also known as: indifference, making opponent indifferent, indifference theorem

At equilibrium you size your bluffs/defends so the opponent's marginal hand has equal EV calling or folding, removing their edge.

The indifference principle is the engine of GTO: at a Nash Equilibrium, you construct your ranges so that the opponent's marginal hand is exactly indifferent between its options — same EV whether it calls or folds, bets or checks. When a hand is indifferent, the opponent can't gain by choosing one action over the other, which is precisely why your strategy is unexploitable.

It cuts both ways at a betting node:

• You set the bettor's bluff-to-value ratio so the caller's bluff-catcher is indifferent to calling.
• The caller defends at MDF so the bettor's pure bluff is indifferent to betting (it breaks even at alpha).

Indifference is also why mixed strategies exist: a player only randomises among actions that are tied in EV — and they're tied because the opponent made them so.

Key insight for exploiters: indifference makes the opponent's marginal hand break even, but it's a knife-edge. The instant you deviate to attack their actual tendency, their hands stop being indifferent — that's the whole basis of exploitative play. GTO defends the indifference; exploits weaponise the opponent's failure to maintain it.