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Poker Glossary

Indifference (Mixed Strategies)

Two actions are indifferent when they have the same expected value. At equilibrium the bettor bluffs just often enough that the caller’s bluff-catchers are indifferent between calling and folding, and that is why solvers show mixed frequencies.

In a balanced game indifference is not a coincidence; it is how equilibrium works. A bettor who wants his bluffs called sometimes but not too often sets his bluffing frequency so that the caller’s bluff-catchers win exactly the price — and then calling and folding pay the same. The caller, in turn, defends just enough that the bettor’s bluffs break even. At those points the frequencies you see (50/50, 70/30) are the mix that keeps the other player from profiting, not a sign that one action is secretly better.

Read a mixed frequency as information about the hand, not as an instruction to randomize to the decimal. A 70/30 hand is mostly a bet that sometimes protects the checking range; a 50/50 hand is one where both lines earn about the same. Against a balanced opponent you lose almost nothing by picking one action and playing it consistently. Against a real opponent who is not balanced, the tie breaks — and it breaks in the direction of his mistake. An indifferent spot also does not mean any action is fine: calling and folding may tie while raising loses.

Worked example

On K♠8♦4♣2♥9♠ you hold K♥6♥ and the button fires a pot-sized river bet, 20 into 20. Calling 20 wins 40, so you need 20 ÷ (20 + 20 + 20) = 33%. K-6 beats every busted draw and loses to every better king — a pure bluff-catcher. If one-third of his bets are bluffs, calling and folding are worth the same, and the course accepts both with call first. If only one bet in five is a bluff, fold; if half are bluffs, call.

FAQ

What does indifferent mean in poker?

It means two options have the same expected value, so you do not gain by choosing either. Equilibrium strategies make the opponent’s key hands indifferent; that is what stops him from exploiting you.

Should I copy solver frequencies like 70/30?

No. Read them as ‘near the boundary between two actions’. Against a balanced player pick one line and play it consistently; against a real opponent, lean toward the action that punishes the way he deviates.

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