Understanding a semi-bluff all-in
Content by Tools of Poker Methodology and calculation assumptions
What does this calculation help you decide?
A semi-bluff can win in two ways: the opponent folds now, or calls and your hand wins at showdown. A draw alone does not make an all-in profitable. This calculation combines both possibilities to measure the average gain or loss of shoving instead of folding now.
Hero faces a bet on the flop or turn and has not invested on this street. The opponent covers Hero’s all-in and can only fold or call it. Folding is the zero-EV reference; this exercise does not choose between shove, call and other raises. There are no side pots or rake.
Convert percentages to probabilities by dividing by 100. Call probability is one minus fold probability. Equity when called belongs only to the calling range and includes half of ties.
Read the pot and the two new contributions
The displayed current pot already includes the opponent’s bet. Hero’s all-in is the entire new investment. The opponent only adds the amount still missing to match it. On a fold, the uncalled all-in returns to Hero, who wins the current pot.
Do not add two full all-ins to the displayed pot: that would count the opponent’s existing bet twice. A call can win the final pot, but Hero’s own new investment must be subtracted once to obtain net EV.
Worked example: two ways to win
There are 100 BB in the current pot, including the opponent’s 20 BB bet. Hero considers an 80 BB all-in. The opponent folds 40 percent and Hero has 25 percent equity when called. These are supplied assumptions for this size.
Opponent’s additional call (BB)
Final pot on a call (BB)
EV when called (BB)
A call loses 20 BB on average under these assumptions. That does not include the separate reward from folds.
All-in EV (BB)
The folds compensate for the losing call branch. Hero gains 28 BB on average compared with folding now.
A draw can still lose money; zero can be exact
Keep the first example but reduce folds to 10 percent. The same draw and call equity now produce −8 BB. Profitability depends on both branches, not on having a draw.
For an exact break-even example, use a 60 BB current pot including a 10 BB bet, a 50 BB all-in, 25 percent folds and 20 percent caller equity. The remaining call is 40 BB and the final pot is 150 BB.
Where does the all-in size come from?
The exercise samples a pre-bet pot and an opponent bet of 25, 50, 75 or 100 percent of it. Hero’s all-in is two to six times that bet, within the covered effective stack. Read the full all-in below Hero’s cards. You calculate its EV; you do not need to derive an optimal size.
This table keeps the current pot at 100 BB, the existing opponent bet at 20 BB, folds at 40 percent and caller equity at 25 percent. Only the proposed all-in changes. Real fold frequency and caller equity can change with the size.
| All-in risk (BB) | Opponent’s additional call (BB) | Final pot on a call (BB) | All-in EV (BB) |
|---|---|---|---|
| 40 | 20 | 160 | +40.00 |
| 60 | 40 | 200 | +34.00 |
| 80 | 60 | 240 | +28.00 |
| 100 | 80 | 280 | +22.00 |
| 120 | 100 | 320 | +16.00 |
Worked range: count folds, use supplied caller equity
Hero has Ah Kh on Qh Jh 2c 3d. Keep the 100 BB pot, existing 20 BB bet and 80 BB all-in. The assigned range folds 77 and calls QQ and JJ. Each pair has six original combos; the board blocks three QQ and three JJ. There are 12 available combos: six folds and six calls.
Fold frequency: 6 ÷ 12 × 100 = 50%
On this turn, the system checks all 44 legal rivers for each of the six calling combos: 264 outcomes, with 60 Hero wins and no ties. Caller equity is 60 divided by 264, displayed as 22.73 percent. That percentage is provided; you are not asked to count runouts.
For this exercise, use the displayed 22.73 percent exactly as an input. The unrounded enumerated equity would give a different final cent. The correction uses the visible percentage, so no hidden precision is required. Keep the exact fold fraction until the final EV rounding.
(6 ÷ 12) × 100 + (1 − 6 ÷ 12) × (−25.448) = 37.276 BB ≈ +37.28 BB
Assigned response range against the all-in
77
QQ · JJ
- Remaining combos
- 12
- Folding combos
- 6
- Calling combos
- 6
How is the supplied equity obtained?
The range exercise removes known cards and calculates equity only against callers. Turn rounds enumerate every legal river. Flop rounds use a deterministic simulation, with the same number of samples for each available calling combo; the approximate sign identifies this estimate. Ties count half. EV based on estimated equity is also an estimate.
Practice ranges are sampled from portions of existing preflop references using the shared hand order. Their survival to flop or turn and the assigned fold/call policy are educational assumptions. They are not a reconstructed hand history or a solver recommendation. In the frequency exercise both probabilities are supplied inputs.
How to practise this exercise
Both exercises always ask for all-in EV in BB relative to folding. Caller equity is supplied at every difficulty. Beginner/easy add the remaining call, final pot and conditional call EV; range rounds also ask for fold frequency. Intermediate asks call EV and all-in EV, plus fold frequency in range rounds. Advanced rounds ask only for all-in EV.
Frequency rounds allow 300, 240, 180, 120 and 90 seconds. Range rounds allow 360, 300, 240, 180 and 120 seconds. Each timer covers the whole round. Beginner/easy have three choices; other difficulties have four. Use the displayed equity, keep the exact fold fraction and round each requested answer only at the end of its calculation.
Results preserve the actual cards, amounts and range. A wrong earlier choice does not change later grading. The solution shows every operation with the real numbers; beginner/easy also show those numbers below each formula during practice.