Understanding a preflop 3-bet bluff

Practice with exercises

Content by Tools of Poker Methodology and calculation assumptions

From an open raise to a 3-bet

Start with exercise 3.1, Steal, to understand risk and reward when nobody has raised. Here an opponent has already made an open raise. Hero considers raising again: a 3-bet. A bluff tries to profit from folds, although its cards may still have equity when called.

The big blind is the first bet, the open raise is the second and the next raise is the 3-bet. A 3-bet to 9 BB means a total live contribution of 9 BB; it does not mean adding 9 BB or always multiplying the open raise by three. The exercise supplies the size and the fold estimate; neither is a recommendation for the displayed cards.

Every generated spot has Hero in BB, one opener in CO, BTN or SB, and all other players folded. There are no antes, callers or rake. Hero’s cards are visible and the opener’s cards are hidden. Read the opener’s total, Hero’s posted blind and the proposed 3-bet total separately.

Read the betting sequence at the table

The table first shows the posted blinds, then the open raise and SB’s fold when SB is not the opener. The contributions increase beside each player’s cards and the active seat is highlighted. The sequence stops at Hero’s decision: the displayed 3-bet is a proposal, so Hero still has only 1 BB committed. Use the replay button to watch it again.

New rounds choose an open raise of 2.5, 3, 3.5 or 4 BB. The proposed 3-bet is 2.5, 3, 3.5 or 4 times that opening total. For example, an open raise to 3 BB and a 3-bet at 3.5 times that size means a 3-bet to 10.5 BB and 9.5 BB of additional risk. These sizes are supplied for practice, not strategic recommendations. The fixed reference example below still illustrates the same calculation.

Reference situation: CO opens, Hero is in BB

CO opens to 2.5 BB. SB posted 0.5 BB and folded. Hero posted 1 BB in BB. Everyone else folded and there are no antes. Before Hero acts, the pot contains 4 BB. Hero is considering a 3-bet to 9 BB, and CO is estimated to fold 70 percent against this size.

Current pot (BB)
2.5 + 0.5 + 1 = 4 BB
3-bet total
9 BB
Additional risk (BB)
9 − 1 = 8 BB
Minimum folds (%)
66.67%
EV
+0.40 BB

Step 1: count the pot you can win

The pot is the money already committed before the 3-bet. It includes the opener’s total, SB’s folded blind and Hero’s posted BB. A folded player’s chips stay in the pot. Hero’s proposed extra chips are not there yet, so do not add them to the reward.

Pot = opening total + folded SB blind + Hero’s BB
2.5 + 0.5 + 1 = 4 BB

Count a contribution once. CO’s open to 2.5 BB is already its total contribution, not 2.5 BB plus a separate call. If SB opens instead, its total includes its blind: an SB open to 2.5 BB gives 2.5 + 1 = 3.5 BB. There is no folded SB blind to add.

Step 2: calculate only the additional risk

Compare the decision with folding now. Folding requires no new chips. Hero’s 1 BB is already in the pot in either case; raising to 9 BB requires only 8 more BB. This incremental amount is what the model can lose when the opener continues.

Risk = 3-bet total - Hero’s posted blind
9 − 1 = 8 BB

Do not subtract the opponent’s open raise from Hero’s 3-bet. The calculation 9 - 2.5 = 6.5 BB measures the difference between two players’ totals, not Hero’s extra investment. Do not use the full 9 BB either: that counts Hero’s blind again.

Step 3: find the minimum fold frequency

The minimum fold frequency is the proportion of folds needed to break even under this model. Balance winning the current pot against losing the additional risk. This is a threshold, not an estimate of the opponent’s actual behaviour.

Minimum folds = Risk / (Pot + Risk) × 100
8 / (4 + 8) × 100 = 66.6666…% ≈ 66.67%

With the same pot, a larger additional risk needs more folds. With the same risk, a larger existing pot needs fewer folds. Using the full 9 BB incorrectly gives 9 / (4 + 9) × 100 = 69.23 percent, which overstates the threshold.

Step 4: use F to calculate EV

Use the supplied estimate of folds to the proposed 3-bet. Convert 70 percent to F = 70 / 100 = 0.70. The probability of continuation is 1 - F = 0.30. F must be between 0 and 1; entering 70 directly would confuse a percentage with a probability.

EV = F × Pot - (1 - F) × Risk
0.70 × 4 − (1 − 0.70) × 8
= 2.80 − 2.40 = +0.40 BB

EV is the average gain or loss per attempt relative to folding now. Here a fold wins the existing 4 BB and continuation loses the extra 8 BB. Over many comparable attempts, +0.40 BB means an average gain of 0.40 BB per attempt, not a guaranteed gain in this hand.

Compare positive, negative and zero EV

For the reference pot of 4 BB and risk of 8 BB, 70 percent folds gives +0.40 BB. At 60 percent folds the result is -0.80 BB. At exactly two thirds folds the result is zero. Above the exact minimum, EV is positive; below it, negative; at the minimum it breaks even against folding.

0.70 × 4 − 0.30 × 8 = +0.40 BB
0.60 × 4 − 0.40 × 8 = −0.80 BB
(2 / 3) × 4 − (1 / 3) × 8 = 0 BB

For an exactly representable zero example, keep CO’s open to 2.5 BB but consider a 3-bet to 7 BB: risk is 6 BB, the pot is 4 BB and the threshold is 60 percent. With F = 0.60, EV = 0.60 × 4 - 0.40 × 6 = 0 BB.

Keep full precision until the final answer and round to two decimals. The displayed 66.67 percent is a rounded threshold, not an exact two-thirds probability. Generated questions avoid a tiny nonzero EV rounding to zero; their zero answers are true break-even cases.

The model and its limits

Model: win the current pot when the opener folds; lose the additional risk when the opener continues. After a call, Hero can retain equity and play postflop. This is not the complete EV of a real 3-bet.

Continuation includes both a call and a 4-bet. For this exercise, both outcomes lose the additional risk, with no later winnings or bets. This deliberately isolates the value of folds. It does not claim that every called bluff is worthless, or that the model chooses the best real action.

To study postflop continuation, we would need Hero’s hand and the opponent’s calling and 4-bet ranges, equity against those ranges, position, effective stacks, the pot after a call, future boards, betting strategies, future investments and rake. Blockers can also change the fold estimate. Those inputs are outside this calculation.

How to practise this exercise

Beginner and easy ask for pot, additional risk, minimum folds and EV in four steps, with formulas and numerical substitutions. Intermediate asks for minimum folds and EV with symbolic formulas only. Difficult and extreme ask only for the final EV. Later calculations follow your chosen pot and risk; the result explains the solution at every difficulty.

The countdown covers the whole round. The result keeps the table, identifies each incorrect step and shows the calculations. If an earlier amount was wrong but the later arithmetic was consistent, expand the correction to compare with the actual scenario. Play again to practise another size and fold estimate.

Frequently Asked Questions

No. An open raise is the first raise preflop. A 3-bet raises an existing open raise; the big blind counts as the first bet in this naming convention. The name does not mean raising to three times the opening size.

Hero already posted 1 BB. Reaching 9 BB adds 8 BB. The posted blind belongs to the current pot and is already invested whether Hero folds or raises. Counting 9 BB as new risk would count that blind twice.

No. It is the rounded break-even threshold for the reference example. The supplied 70 percent estimate describes how often the opener is expected to fold in comparable situations. Use that estimate as F = 0.70 in EV, rather than replacing it with the minimum.

Only in this simplified model. After a call, Hero can retain equity and play postflop. A real 3-bet also depends on continuing ranges, position, effective stacks, future actions and rake.

Zero EV breaks even relative to folding at this decision. Positive EV gains BB on average; negative EV loses BB. Previously posted chips are already invested in either decision.

In guided rounds, later calculations use your selected pot and risk. If you calculate correctly with those inputs, that arithmetic step is correct even when an earlier identification was wrong. The round still marks the original error. In the result, expand the correction to compare with the actual hand’s pot and risk.

The opening total already includes SB’s 0.5 BB blind. An SB open to 2.5 BB creates a pot of 2.5 + 1 = 3.5 BB against Hero in BB, without antes. Do not add another 0.5 BB. The folded-SB term in the pot formula is zero in this case.