Understanding a river hero call
Content by Tools of Poker Methodology and calculation assumptions
What is this calculation for?
Villain bets on the river and Hero must decide whether to call or fold. A bluff catcher wins only when Villain is bluffing. We calculate whether those wins compensate for the calls lost against value hands.
Minimum bluff frequency tells us how often we need to win to break even. Call EV tells us how much calling gains or loses on average with the estimated bluff frequency. Folding now has zero EV: positive call EV favours calling, negative call EV favours folding, and zero makes both choices equal.
The first exercise supplies the bluff frequency at every difficulty. The second obtains it from an assigned betting range after blockers. Both use the same final EV calculation, with no internal exercise selector.
Count the pot and the call once
There are 100 BB before Villain bets 75 BB. Hero faces 175 BB and must add 75 BB to call. The final pot after calling is 250 BB. The table displays the 175 BB pot faced, including Villain’s bet.
100 + 75 = 175 BB
175 + 75 = 250 BB
On a win, Hero’s own call comes back: the net gain is the 175 BB already faced. On a loss, the new 75 BB call is lost. Earlier streets are already invested. Heads-up, no rake, no raises, no side pots and no ties.
How many bluffs make a call profitable?
75 ÷ 250 × 100 = 30.00%
At exactly 30 percent bluffs this call breaks even. Above the exact threshold, calling earns more than folding; below it, folding is better. This threshold is the minimum required, not a prediction of Villain’s behaviour.
How does the opponent’s bet size change the threshold?
The exercise proposes Villain’s bet, usually 25, 50, 75, 100, 125 or 150 percent of the pot before the bet. With an initial 100 BB pot, a 75 percent bet is 75 BB. Some range rounds use other ratios to practise exact zero EV.
| Opponent bet (BB) | Final pot (BB) | Minimum bluffs (%) |
|---|---|---|
| 25 | 150 | 16.67% |
| 50 | 200 | 25.00% |
| 75 | 250 | 30.00% |
| 100 | 300 | 33.33% |
| 125 | 350 | 35.71% |
| 150 | 400 | 37.50% |
Worked call: 40 percent bluffs and 60 percent value
Average gain against bluffs (BB)
Average gain against bluffs = Bluff probability × Pot faced
0.40 × 175 = 70.00 BB
Average loss against value (BB)
Average loss against value = Value probability × Cost of call
0.60 × 75 = 45.00 BB
Call EV (BB)
Call EV = Average gain against bluffs − Average loss against value
Calling gains 25 BB per comparable attempt on average, compared with folding. This is a profitable call under the supplied assumptions.
An equivalent calculation weights the final pot and subtracts the call once. Both formulas measure the same net result.
0.40 × 250 − 75 = +25.00 BB
| Bluffs | Call EV | Decision in this model |
|---|---|---|
| 20% | −25.00 BB | Fold |
| 30% | 0.00 BB | Equal EV |
| 40% | +25.00 BB | Call |
Obtain the bluff frequency from a betting range
Hero has Jh Jd on Ks 9h 6c 3s 2d. The assigned bluffs are AQs, QJs and TT; the value hands are AKs, KQs and QQ. Hero beats every bluff and loses to every value combo. These are supplied scenario assumptions, not a universal betting strategy.
Remaining betting combos
Remaining betting combos = Original combos − Blocked combos
Hero’s two jacks block two QJs combos. The king on the board blocks one AKs and one KQs combo.
Bluff combos
4 + 2 + 6 = 12
Bluff frequency = Bluff combos ÷ Remaining betting combos × 100
Call EV (BB)
Keep the exact combo fraction until the final answer. Every remaining physical combo has equal weight; hand classes can contain different numbers of combos.
Assigned river betting range
AQs · QJs · TT
AKs · KQs · QQ
How to practise this exercise
With a supplied bluff frequency, beginner/easy guide final pot, minimum bluffs, average gain, average loss and call EV. Intermediate asks minimum bluffs and EV; difficult/nightmare ask EV only.
With range analysis, beginner/easy guide remaining combos, bluff combos, bluff frequency, final pot, minimum bluffs and EV. Intermediate asks bluff frequency, minimum bluffs and EV; difficult/nightmare ask EV only. Every difficulty analyses a range.
The timer covers the whole round: 300, 240, 180, 120 and 90 seconds. There are three choices in beginner/easy and four in the other difficulties. Formulas use full names; results explain the actual scenario at every difficulty.