POKER MATHS · HEADS-UP SCENARIOS
Check a call, a bluff or a stack-to-pot ratio.
Three related questions, with separate inputs and clear pot definitions. Arithmetic you can inspect, without solver claims.
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Use one consistent unit inside each panel. No value is carried between panels: the call pot includes their bet; the bluff pot is before yours. Currency is only a unit label, not an FX conversion.
Calling
Pot now includes the opponent’s current bet. Only your call is added to reach the final pot.
Made with GoodRun · Simplified heads-up arithmetic.
How this works: calling
Break-even equity = call / (pot now + call). If equity e is supplied, call EV = e × (pot now + call) − call.
At a pot of 150 with 50 to call, the threshold is 25%. At 30% equity the simplified call EV is +10; at 20% it is −10. There is nothing to call when the call amount is zero; no 0/0 is shown.
EV assumes the call reaches showdown without further cost and that the entered equity is realized. No later betting, raises, rake, multiway calls or side pots are modeled. A positive simplified EV is not a real-world strategy recommendation.
Bluffing
One opponent either folds or calls the amount of your bet. No raise or later investment is included.
Made with GoodRun · Simplified heads-up arithmetic.
How this works: bluffing
For pot P before your bet B and called equity e: called EV = e × (P + 2B) − B. With fold chance f: total EV = f × P + (1 − f) × called EV.
If called EV is nonnegative, the model needs no folds to break even. Otherwise required folds = −called EV / (P − called EV). For a pure bluff this becomes B / (P + B). A zero pot can require 100% folds merely to break even; a zero bet is not a meaningful bluffing action.
Range coverage, chance of a fold, and equity when called are separate quantities. The formula assumes heads-up play, no raise, no future investment, no rake and full equity realization. It does not evaluate a player’s range or prove the action profitable in a real game.
Stack and pot
SPR describes how the effective remaining stack compares with the current pot.
Made with GoodRun · Simplified heads-up arithmetic.
How this works: stack and pot
SPR = smaller remaining stack / current pot. A remaining stack of 300 and pot of 100 gives SPR 3. A zero remaining stack gives 0; a zero pot needs a pot size before a ratio can be calculated.
This is a description, not an automatic stack-off, call or fold rule. More than one opponent or different side pots need a broader model.
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