Theory
GTO frequencies explained
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GTO frequencies are the exact rates at which a game-theory-optimal strategy takes each action so no opponent can exploit it. They fall out of one idea — indifference: you mix your bets and bluffs (or your calls and folds) at the ratio that makes every option equally profitable for your opponent, which leaves them nothing to attack.
What a “frequency” is
Open a solver and most hands don’t get one answer — they get a split: bet 60% / check 40%, or raise 25% / call 55% / fold 20%. That split is a frequency. It doesn’t mean the hand is worth exactly 60% of a bet; it means that across every time you hold that hand in that spot, betting it 60% of the time is what keeps your overall range balanced. The frequency is a property of the range, executed one hand at a time.
The indifference principle
A strategy is exploitable when one of your opponent’s options is clearly better than another. If you never bluff, folding to your bets is free money for them. If you bluff too much, calling is. Somewhere in between is the mix where calling and folding earn them the same amount — they are indifferent, and no adjustment they make gains anything. GTO frequencies are simply the mixes that sit on that indifference point across every spot.
This isn’t a poker invention. According to the standard account of a mixed-strategy Nash equilibrium, a player is only willing to randomize when the expected payoff of every strategy in the mix is the same. Poker frequencies are that condition applied to a betting round.
As the bettor: the value-to-bluff ratio
When you bet for value, you need enough bluffs alongside it that a hand which only beats your bluffs — a bluff-catcher — can’t profitably call or profitably fold. That balance point depends only on your bet size relative to the pot, because the bet size sets the price your opponent is getting:
| Bet size | Value : bluff | Bluffs as share of the betting range |
|---|---|---|
| ½ pot | 3 : 1 | 25% |
| Pot | 2 : 1 | 33% |
| 2× pot | 3 : 2 | 40% |
The pattern generalizes to value : bluff = (pot + bet) : bet. Bigger bets give your opponent a worse price, so you’re allowed relatively more bluffs; smaller bets, fewer.
As the defender: MDF and alpha
On the other side of the bet, you face the mirror question: how much of your range do you have to continue with so the bettor can’t just print money by bluffing any two cards? That floor is the minimum defense frequency:
MDF = pot / (pot + bet) and alpha = bet / (pot + bet) = 1 − MDF
Alpha is the flip side: how often your opponent must fold for a zero-equity bluff to break even. If you defend less than the MDF, their bluffs start auto-profiting.
| Bet size | MDF (defend at least) | Alpha (fold at most) |
|---|---|---|
| ½ pot | 67% | 33% |
| ⅔ pot | 60% | 40% |
| Pot | 50% | 50% |
| 2× pot | 33% | 67% |
Pure spots, mixed spots
Not everything is a mix. In plenty of spots the solver plays a hand as a pure strategy — one action 100% of the time — and some whole ranges simply check every hand on a given board. Mixing only matters where two actions are genuinely close in value; there, splitting them is what denies your opponent a read. Where one action is clearly best, you just take it.
Why you still deviate
GTO frequencies are the unexploitable baseline — the strategy that can’t be beaten. They are not always the strategy that wins the most. Against an opponent who makes a systematic mistake, the highest-EV response is to deviate from the balanced frequency and attack it: bet every time against someone who folds too much, stop bluffing someone who never folds, over-fold against someone who never bluffs. The balanced frequencies are your home base — what you return to when you don’t have a read, and what keeps you from being the one who’s exploited.
Key takeaways
- A frequency is how often you take an action across a range, not a per-hand verdict.
- Indifference is the goal: make every option equal-EV for your opponent.
- Bettor: value : bluff = (pot + bet) : bet — a pot bet is 2:1.
- Defender: MDF = pot / (pot + bet); a pot bet means defending 50%.
- MDF assumes zero-equity bluffs — a river heuristic, not a universal rule.
- Deviate to beat mistakes; return to balanced frequencies when you have no read.
Frequently asked
What is a mixed strategy in poker?
A mixed strategy takes one holding and plays it more than one way at set frequencies — for example, betting a hand 60% of the time and checking it 40%. Solvers output mixed strategies because always playing a hand the same way is a pattern an opponent can exploit.
What is the value-to-bluff ratio for a pot-sized bet?
Roughly 2:1 — two value bets for every bluff, so bluffs are about one third of your betting range. Bigger bets allow relatively more bluffs; smaller bets fewer. The general rule is value-to-bluff = (pot + bet) : bet.
What is minimum defense frequency (MDF)?
MDF is the share of your range you must continue with against a bet so the bettor cannot profit by bluffing any two cards. It equals pot / (pot + bet). A pot-sized bet gives an MDF of 50%. MDF assumes the bluffs have no equity, so it is a river-oriented heuristic rather than a universal rule.