Ties and shared pots

What you will learn

Price a heads-up final call when a stated probability of an equal split is possible.

Prerequisites: Expected value as a weighted average · Hand rankings and ties

A tie can have positive incremental value

In a heads-up final call, let the pot before your call be P and the call be C. If the final P+C is split equally, you receive (P+C)/2. Subtract C to get the tie’s net payoff (P−C)/2.

If P=90 and C=30, a tie returns 60 and nets +30 from this decision. The tie does not mean “no money changes hands” because some chips in the current pot were committed before the decision. Whole-hand accounting may tell a different story about past costs.

Equity weights shared outcomes

Let w be outright-win probability, t the tie probability and l=1−w−t the loss probability. Then call EV=wP+t(P−C)/2−lC. Under these exact heads-up, equal-split, no-fee assumptions, equity e=w+t/2 gives the equivalent formula e(P+C)−C.

Multiway pots, uneven split rights, side pots, rake and indivisible odd chips can require different outcome payoffs. Do not reuse half a tie mechanically when the split is not between exactly two equal claimants.

Common mistakes

• Giving a tie zero incremental payoff without examining the pot.
• Equating equity with outright win probability.
• Using a half-share for a multiway or unequal split.

Keep these ideas

• Compute the net receipt for each split.
• Keep win, tie and loss probabilities exhaustive.
• Use half-tie equity only under the stated equal heads-up split model.