Net payoff and sunk costs

Choose the decision point and count only the cash flows that change with your action.

10 minutes · intermediate · Original Poker4Quant lesson

What you will learn

Distinguish returned stake, net profit and earlier commitments in a final-call model.

Set the clock before counting

Expected value needs a precisely defined payoff. At a final call, take the current decision as time zero. Chips put in earlier are already committed and cannot be recovered by folding. Compare the incremental outcomes of the available actions from now.

If the existing pot is P and calling costs C, winning returns P+C but you supplied C at this decision. Your net win is P. Losing has net payoff −C. Counting P+C as profit would count your returned call as new wealth.

Whole-hand profit answers a different question

If you contributed S earlier, your total profit over the hand would be P−S on a win and −C−S on a loss after calling. Both call outcomes are shifted by the same −S. Folding also has whole-hand payoff −S, rather than zero.

Subtracting this common past cost from every action leaves their ranking unchanged. That is why sunk costs can be omitted from an incremental comparison. Do not omit a future cost that actually depends on the action: a later call, fee or extra bet is not sunk merely because you expect it.

Worked example

You previously contributed 40. The pot now contains 140 including the opponent’s bet. A final call costs 20. State incremental and whole-hand outcomes.

Winning the call returns 160; subtract the new 20 to get incremental +140.
Losing the call is incremental −20. Folding is incremental 0.
For whole-hand accounting, subtract the old 40 from all three: +100, −60 and −40.

The same action comparison can be made either way if the past cost is handled consistently. A new call is not justified just because earlier chips are at risk.

Common mistakes

Counting returned stake as profit.
Subtracting past contributions from the call but not from folding.
Treating a future conditional payment as sunk.

Keep these ideas

Define a common decision time.
Net payoff is receipts minus new payments.
Consistent subtraction of common sunk costs does not change the ranking.