Understanding a preflop steal
Content by Tools of Poker Methodology and calculation assumptions
Read the situation before calculating
A steal is an opening raise that tries to win the pot before the flop. Everyone before Hero has folded. From BTN, SB and BB still have to act; from SB, only BB remains. The cards identify Hero, but this exercise does not use their equity.
Read the proposed raise below Hero’s cards. It is the total live bet in BB, excluding antes. A raise to 3 BB reaches 3 BB in live bets; it does not add 3 BB on top of the posted blind. Total antes vary by scenario. No rake is included. The worked examples below use no antes unless stated otherwise.
Antes and a variable pot
New rounds randomly choose 0, 0.5 or 1 BB of total antes. Add this amount to SB’s 0.5 BB and BB’s 1 BB: the pot is respectively 1.5, 2 or 2.5 BB. The amount shown is the total already collected from the entire table, not an ante per remaining player. Do not multiply it by the number of opponents.
0.5 + 1 + 0 = 1.5 BB
0.5 + 1 + 0.5 = 2 BB
0.5 + 1 + 1 = 2.5 BB
Worked example with antes: Hero is in SB and raises to 3 BB. There is 1 BB of total antes already in the pot. The reward is now 2.5 BB, but the additional risk remains 3 - 0.5 = 2.5 BB. The break-even fold frequency falls from 62.5 percent without antes to 50 percent. If BB folds 70 percent, EV rises from +0.30 BB to +1 BB.
0.70 × 2.5 − 0.30 × 2.5 = +1 BB
The reference table in a question uses that round’s total antes. The tutorial reference table below uses no antes, so you can compare it with the original example.
Why can the exercise propose a raise to 4 BB?
The raise size is supplied by the scenario; you do not have to choose it. The exercise varies it between 2, 2.25, 2.5, 3, 3.5 and 4 BB to practise how the additional risk changes. A proposed 4 BB raise is not a recommendation for that hand or position.
Example from BTN: a raise to 2 BB risks 2 BB to win 1.5 BB and needs 57.14 percent folds. A raise to 4 BB risks 4 BB for the same pot and needs 72.73 percent folds. A larger raise therefore requires more folds in this model. In a real game, changing the size may also change the opponents’ fold frequency; this exercise supplies that estimate separately.
Step 1: count the pot you can win
The reward is the money already on the table at the moment of the decision, including Hero’s posted blind. Do not add the proposed raise: Hero has not made that investment yet.
Example: SB has posted 0.5 BB and BB has posted 1 BB. There are no antes or earlier bets, so the pot is 1.5 BB. This is true whether Hero is in SB or BTN.
Step 2: calculate only the additional risk
Subtract only Hero’s already posted blind from the proposed total raise. Antes are already in the pot, but do not count toward that raise. They neither increase the additional risk nor reduce the amount needed to reach the raise total.
Example from SB: Hero has posted a 0.5 BB blind and considers a raise to 3 BB. Hero adds 2.5 BB, with or without antes. From BTN, Hero has posted no blind, so the same raise to 3 BB risks 3 BB.
SB: 3 − 0.5 = 2.5 BB
BTN: 3 − 0 = 3 BB
Step 3: find the minimum fold frequency
This threshold answers: how often must everyone fold for the attempt to break even? Divide the additional risk by the reward plus that risk, then multiply by 100 to obtain a percentage.
Example from SB: the pot is 1.5 BB and the additional risk is 2.5 BB. The threshold is 62.5 percent. Above this frequency the model gains money; below it the model loses money. Exactly at this frequency its EV is zero.
Step 4: use F to calculate EV
EV means expected value: the average gain or loss per attempt if the same situation were repeated many times. It is expressed in BB, relative to folding at this decision.
F means fold frequency: the estimated probability that all remaining opponents fold to the proposed raise, expressed between 0 and 1. The exercise gives this estimate directly. It is not an announcement that they have already folded, and it is not the minimum frequency you calculated in the previous step.
Example: an estimate of 70 percent means that about 70 out of 100 comparable attempts end with everyone folding. In the other 30, at least one opponent continues. Convert it to F = 70 / 100 = 0.70; the probability that someone continues is 1 - F = 0.30.
With several opponents, use the joint estimate given for all of them folding. From BTN, 40 percent means SB and BB both fold in about 40 out of 100 attempts. It does not mean each opponent folds 40 percent of the time. Do not add individual percentages or multiply them without an independence assumption.
Multiply the reward by the probability of winning it, then subtract the additional risk multiplied by the probability of losing it. For the SB example, F = 0.70, pot = 1.5 BB and risk = 2.5 BB. The positive result is an average gain relative to folding now, not a guaranteed profit on this attempt.
Compare positive, negative and zero EV
Estimated folds and minimum folds are directly related to the sign of EV in this exercise model.
The minimum tells you how often everyone needs to fold to break even. The estimate tells you how often you expect everyone to fold to the proposed raise. Compare both frequencies for the same pot and additional risk; with several opponents, both refer to all of them folding together.
- Estimated folds > minimum folds: positive EV.
- Estimated folds = minimum folds: zero EV, break-even.
- Estimated folds < minimum folds: negative EV.
Example: keep the SB raise to 3 BB with no antes. The pot is 1.5 BB, the additional risk is 2.5 BB and the minimum fold frequency is 62.5 percent. If you estimate 70 percent folds, you expect more than the minimum needed, so EV is positive: +0.30 BB. With a 50 percent estimate, EV is -0.50 BB; with exactly 62.5 percent, EV is 0 BB. Folding at this decision is the zero baseline in all three cases.
0.50 × 1.5 − 0.50 × 2.5 = −0.50 BB
0.625 × 1.5 − 0.375 × 2.5 = 0 BB
Now use the BTN scenario with a raise to 4 BB and a joint fold estimate of 40 percent. Pot = 1.5 BB; risk = 4 BB; minimum folds = 4 / 5.5 × 100 = 72.73 percent. F = 0.40 is below that threshold, so the result is negative.
Why does this comparison work?
Write the minimum frequency as Fmin = Risk / (Pot + Risk), using a value between 0 and 1. The EV formula can then be rearranged as follows:
Pot + Risk is positive, so the sign comes entirely from F - Fmin. If the estimate F is above the threshold, the difference is positive; at the threshold it is zero; below it, negative. This shortcut tells you the sign of EV. Use the full calculation to find how many BB you expect to gain or lose.
Near break-even, compare unrounded values. A threshold displayed as 66.67 percent might actually be 66.6666… percent. An estimate of 66.67 percent is slightly above that exact minimum, even though both displayed percentages look equal.
For a BTN raise to 3 BB without antes, this difference gives an exact EV of +0.00015 BB at 66.67 percent folds. It is positive, but rounds to 0.00 BB. A displayed zero therefore does not always mean exact break-even. This conclusion remains specific to the supplied fold estimate and the simplified model; it does not guarantee the outcome of an individual attempt.
What does the exercise answer mean?
An EV of +0.30 BB means an average gain of 0.30 big blinds per attempt relative to folding now. Across 100 comparable attempts, the model predicts about +30 BB in total on average. It does not mean that each individual attempt wins 0.30 BB: each attempt either wins the current pot or loses the additional risk.
For example, if an EV were +1.8 BB, its meaning would be an average gain of 1.8 BB per attempt, or +180 BB over 100 comparable attempts on average. Results over a small number of attempts may differ. To convert BB into money, multiply by the value of one big blind at your stakes.
EV can never exceed the current pot in this model. Without antes, the pot is 1.5 BB, so +1.8 BB is impossible. With 1 BB of total antes, the pot is 2.5 BB and the theoretical maximum becomes +2.5 BB if everyone always folds. Always calculate using the scenario’s actual pot and fold estimate. In the no-ante BTN raise-to-4-BB example with 40 percent folds, the answer remains -1.80 BB: an average loss of 1.80 BB per attempt.
Steal reference table
| Raise to | Hero SB | Hero BTN |
|---|---|---|
| 2 BB | 50.00% | 57.14% |
| 2.5 BB | 57.14% | 62.50% |
| 3 BB | 62.50% | 66.67% |
| 4 BB | 70.00% | 72.73% |
SB has already posted a 0.5 BB blind; BTN has posted no blind. Antes are included in the pot, not subtracted from the raise. These are model thresholds, not raise-size recommendations.
The model and its limits
Model: win the current pot if all fold; otherwise lose the additional risk. EV relative to folding now.
If anyone continues, this model treats the attempt as losing all the additional risk. It assumes no later winnings or extra investments. This is not the complete EV of playing after a call: that would also depend on hand equity, future actions, future bets and rake.