In chapter 19 of The Theory of Poker, David Sklansky explains how game theory can be used to choose bluffing and calling frequencies that make you unexploitable — especially against strong opponents or those you don’t know well.
What Game Theory Is (and Why It Matters in Poker)
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Game theory is a mathematical framework for choosing strategies when you and your opponent are both trying to out-think each other optimally.
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Against weak players, you should mostly rely on judgment and exploit their mistakes.
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Against strong or unknown players, game theory lets you:
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Remove their edge in reading you.
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Force situations where they cannot gain by adjusting, no matter how clever they are.
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The key tool here is mixed strategy: making certain plays (like bluffs or calls) a fixed percentage of the time, but using a random factor (like unseen cards) so your opponent can’t predict when you’re doing it.
The Lowball Example: Turning a Losing Spot Into a Winner
Sklansky uses a draw lowball setup:
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You: pat 9-8 low.
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Opponent: draws one card; if they hit 5, 6, 7, 8, or 9, they make a better hand; otherwise they lose.
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That gives them 18 winning cards and 24 losing cards out of 42 unseen cards → they’re a 4-to-3 underdog.
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Both players ante $100; after the draw, the drawer can bet $100.
If the drawer:
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Always bets → you should always call and show a solid profit.
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Never bluffs (bets only with a made winner) → you should always fold, still profiting overall.
So far, you crush them either way.
But if they sometimes bluff, things change. By picking certain “bluff cards” (e.g., specific kings, jacks, etc.) and betting with those and with winning hands, they:
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Turn the situation from losing to winning, as long as the mix of value bets vs bluffs is chosen correctly.
The key turning point is when the ratio of:
Good hands : bluffs
matches
Pot odds you’re offered on a call
In the main example:
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Pot after bet: $300 (two antes + $100 bet).
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You’re getting 3-to-1 on a $100 call.
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If the bettor’s strategy makes the odds 3-to-1 against a bluff, then:
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Whether you always call or always fold, you lose the same amount in the long run.
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Any mix of calling and folding is equally bad.
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The bettor has reached optimal bluffing frequency for that spot.
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Optimal Bluffing Frequency in General
Game theory says:
To bluff optimally, choose a bluffing frequency so that
odds against your bluffing = pot odds your opponent gets when facing your bet.
So if:
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Your opponent is getting 6-to-1 from the pot on the end, your overall betting pattern should make it 6-to-1 against you bluffing in that situation.
In percentage terms:
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Figure out:
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Your chance of having a real hand.
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The pot odds your opponent is getting if you bet.
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Choose a percentage of extra bluff hands so that:
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Good-hand% : Bluff%matches the pot odds.
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Example structure:
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If you have a 25% chance of making your hand and the pot gives your opponent 2-to-1 on a call:
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Your good:bluff ratio should be 2:1.
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So you’d bluff half as often as you actually hit your hand (i.e., 12.5% in this case).
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To randomize, you use unseen cards:
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“If I draw one of these 10 cards, I have a real hand; if I draw one of these 4 extra cards, I bluff.”
Your opponent can know your method but not which unseen card you actually got — so they can’t exploit you.
When to Deviate From Game-Theory Bluffing
Pure game-theory optimal is best against:
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Very good players whose judgment is as good as or better than yours.
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Opponents you don’t know at all.
But real opponents:
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Some call too much → you should bluff less than game-theory optimal.
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Some fold too much → you should bluff more than optimal.
Sklansky shows that:
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Bluffing slightly less than optimal earns you more if your opponent calls too often.
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Bluffing slightly more than optimal earns you more if your opponent folds too often.
So judgment improves on pure theory when opponents are imperfect (which is… basically always).
Using Game Theory to Call Possible Bluffs
Game theory also applies when you’re the one facing a possible bluff.
If:
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Your hand can only beat a bluff, and
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You don’t trust your reads (strong opponent, minimal info),
then:
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Calculate the odds your opponent is getting on a bluff.
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Example: Pot is $100, they bet $20 → they’re risking $20 to win $100 → 5-to-1.
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To stop them profiting by bluffing here, you must call 5 times and fold once on average.
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That makes their bluffs break-even at best.
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Again, you randomize with unseen cards or some internal rule so your opponent can’t predict when you call vs fold.
Important:
Using game theory to call doesn’t create profit for you in that exact spot; it mainly prevents your opponent from exploiting you with well-chosen bluff frequencies.
Where Game-Theory Bluffing Applies (and Where It Doesn’t)
Game theory is most accurate when:
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The bettor either has the best hand or is bluffing; there’s no third category of “medium value” hand.
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Example: someone in stud betting a big obvious draw into your made hand — they either hit or they’re bluffing.
If the bettor might be:
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Value-betting a weaker made hand,
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Semi-bluffing in complex ways,
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Or in a multi-way pot,
then the simplified two-outcome model (“nuts or bluff”) doesn’t hold, and more nuanced analysis (like in Sklansky’s later chapter on heads-up endgame) is needed.
Big Picture Takeaways
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Game theory gives you a way to set bluffing and calling frequencies so that:
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Your opponent cannot gain by adjusting their strategy, no matter how smart they are.
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Optimal bluffing:
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Match odds against your bluff to pot odds on their call.
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Optimal calling vs bluffs (when you can only beat a bluff):
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Call often enough that the odds against you folding match the odds they get on their bluff.
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In practice:
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Use pure game theory against strong or unknown opponents.
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Adjust bluffing down vs calling stations and up vs folders.
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Always use randomization (via cards or internal rules) so your strategy can’t be read.
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Sklansky’s core message: game theory doesn’t replace judgment, but it gives you a safety net strategy — one that guarantees you won’t be mathematically outplayed in bluffing wars by anyone, no matter how sharp they are.