Pot odds, with the assumptions visible.

After-play study. All scenarios are fictional. The calculations describe stated models, not recommended actions or solved ranges.

The price is exact. The range usually is not.

A useful hand review has two different jobs: reconstruct the money and decide what the opponent could have. Do them in that order. You can be certain that a call costs five big blinds while remaining uncertain whether the hand has enough equity to call. Keeping those two levels of confidence separate is more useful than an impressive-looking percentage with missing assumptions.

This workshop builds on the viewer's poker-math guide. Work in chips or big blinds, but use the same unit throughout one calculation. Put earlier contributions inside the pot. Do not charge yourself for them a second time.

One definition prevents most mistakes.

Let P be the pot already in the middle when it is your turn, including the opponent's latest bet. Let C be the additional amount you must call. If your call closes the action and all of that pot is available to you, the final pot is P + C. The break-even equity is C / (P + C).

Here, equity means your expected fraction of that final pot, including your share of ties. With no future betting, no deductions and no tournament-prize adjustment, the value of calling relative to folding is equity × (P + C) − C. This is a chip-value calculation. Tournament equity asks a different question.

Heads-up bet into a 12 BB pot, with no further betting or deductions

Opponent bets	Final pot after calling	Break-even equity
3 BB	18 BB	16.7%
4 BB	20 BB	20%
6 BB	24 BB	25%
9 BB	30 BB	30%
12 BB	36 BB	33.3%
24 BB	60 BB	40%

A raise-to amount is not the amount to call.

Start the street with 10 BB in the pot. You bet 4 BB. The opponent raises to 14 BB. The current pot contains 10 + 4 + 14 = 28 BB. You already contributed four on this street, so calling costs 14 − 4 = 10 BB. The final pot is 38 BB and the threshold is 10 / 38 = 26.3%.

Dividing 14 by the final pot would charge yourself twice for part of your original bet. Treating a raise to 14 as a raise by 14 changes the hand entirely. In a reconstructed vlog hand, write the word to next to the amount before building the graphic.

Check yourself: a bet of 2 BB is raised to 7 BB. What is still owed?

5 BB. The seven is the opponent's total contribution on this street, not seven more on top of your two. You still need the starting pot to calculate the percentage price. A correct call amount alone does not establish correct pot odds.

Seeing two cards and paying for one are different contracts.

Suppose exactly nine of 47 unseen cards would complete a particular draw on the turn. The next-card probability is 9 / 47 = 19.1%. If the same nine target cards remain relevant and you are guaranteed both remaining cards without another payment, the chance of hitting at least one is 1 − (38 / 47 × 37 / 46) = 35.0%.

Neither number is automatically your showdown equity. A completed flush can lose to a stronger hand; a pair might already be ahead; an opponent can improve too. The simple counting model also changes when additional dead cards are known. Its purpose is to make the assumptions visible.

A flop call that may face another turn bet does not buy a free river. Before using 35.0%, describe how the hand reaches showdown. Implied odds require an assumption about additional money won later. Reverse implied odds describe additional losses when you improve but remain behind. Neither should become an unexplained allowance that makes every call look attractive.

Multiway pots need another line of bookkeeping.

In a multiway hand, ask whether another player can raise after you call and which pots you are eligible to win. An all-in short stack cannot count someone else's side pot as a prize available to them. Refund uncalled excess before calculating the contested pot. Use the side-pot examples when the contribution levels differ.

A zero-equity bluff has a different threshold.

For a deliberately simplified heads-up river model, you bet B into a pot P. The opponent either folds or calls. You always lose when called, and there are no ties, deductions or tournament effects. The bluff breaks even when the fold probability equals B / (P + B).

This does not prescribe bluffing any particular hand. A hand with showdown value has an alternative in checking; a bluff that wins chips might still be worse than that alternative. An opponent's fold rate also depends on the actual range, board, size and history, not a universal population label.

Finish with a conditional conclusion.

A useful final note reads: “The call costs 10 BB into a final pot of 38 BB. It needs 26.3% equity under the no-further-betting chip model. My unresolved question is whether the opponent's raising range gives this hand that equity.” That sentence separates a calculation from a strategic judgment and gives the next study session a specific job.

Record the pot, incremental call, final eligible pot, assumed equity and the reason for that assumption. Then change one assumption. A conclusion that reverses under a small, plausible range change deserves a cautious explanation, not a confident verdict.