Pot odds: price a call correctly

Define the decision

Let P be the chips already in the pot, including your opponent’s bet. Let C be the additional amount you must call. Let q be the probability you win. We assume a final call, no ties and no rake.

Folding has zero incremental value. Money put into the pot earlier is a sunk cost; it is not a new cost of this decision.

EV(call) = qP − (1 − q)C

Solve for the break-even probability

Set the EV equal to zero and solve for q. The cost of the call belongs in the denominator once.

If P = 120 and C = 40, the threshold is 40 / 160 = 25%. At 30% equity, calling earns 8 chips in expectation. At 20%, it loses 8.

q* = C / (P + C)

Avoid the common denominator mistake

A pot of 80 followed by an opponent’s 80 bet means P is now 160. Calling costs another 80. The threshold is 80 / 240, or one-third, rather than one-half.

In a real hand, future bets, ties, rake and uncertain equity may change the model. This calculation isolates the final-call decision so you can reason about price clearly.