Against this pool a cbet on Q♠J♥2♥ costs the BTN money: 0.21 bb per hand for a third of the pot and 0.45 bb for three quarters, compared with checking. Not because the pool defends the flop badly: it plays the flop like the solver. It is because after a cbet and a call it almost never donks the turn, after check-check it bets the turn more often and weaker than the solver, and on the river it hardly ever raises. The solver steers the hand exactly there. The full exploit gives the BTN +0.79 bb, the 50% version +0.39 bb.
This continues the GTO review of the same flop. There — how the solver plays against the solver. Here — how it plays against people.
This is the third version of the article, and it has a history. In the first, the pool was a mix of NL100–NL200, the BB's tree had only a 15% pot donk, and the tool threw away every pool donk larger than 24% — which came out as "the BB never donks". A reader spotted the mistake. In the second, the database was switched to a year of NL200, donks were counted honestly, and a 50% donk was added to the tree. That raised a hypothesis: maybe the solver donks the turn so much only because the raise against the donk is small (100% pot)? In the third version the raise was increased to 133% and the 50% donk replaced with 33%. The hypothesis did not hold up, more on that below. The main conclusion never changed, the numbers changed every time — that is normal, this is what checking looks like.
Where the numbers come from
Same spot: single-raised pot, BTN opened to 2.5 bb, BB called, flop Q♠J♥2♥, pot 5.5 bb, stack 97.5 bb, NL200 rake. Tree: BTN 33% or 75% on the flop, 75% and 135% on the turn, a 133% pot raise on the turn; BB first to act on the turn 33%, 75%, 135%, and after calling a cbet a 15% or 33% donk. It differs from the GTO review's tree in two ways: there the BB had only a 15% donk, and the BTN's turn raise was 100%.
The pool is the players in the BB from a year of PokerStars NL200: 9,188 hands of "BTN open — BB call". For every spot in the tree the pool's frequencies were counted and compared with the GTO of this flop. The frequencies are taken over all flops in the database, not only those similar to QJ2: on a single texture there are not enough hands for the turn and river.
How the exploit was computed:
- The BB's flop strategy was left at GTO. Only the turn and river were locked: the BB's frequencies were shifted from GTO towards the pool's frequencies on all turn and river cards. The previous version also computed a variant with the flop locked — it changed nothing, a hundredth of a bb, so it was not repeated here.
- The shift was shrunk towards GTO by sample size: at 100 hands half the difference is taken, at 1,000 almost all of it. Spots with fewer than 8 hands were left untouched.
- The BTN is free on every street; the solver finds its best response to such a BB. Response accuracy 0.01% of the pot.
What the pool does differently from the solver
The BB's frequencies in the database vs the GTO of the Q♠J♥2♥ flop (tree with the 133% raise). n is the pool's hands in the spot.
| Street | Spot | n | Pool | GTO | Difference |
|---|---|---|---|---|---|
| Flop | vs 33% cbet: call/fold/raise | 4342 | 47/38/14 | 55/35/10 | raise +4, fold +3 |
| Flop | vs 75% cbet | 1336 | 41/52/7 | 43/53/4 | raise +3 |
| Turn | after check-check: BB bets first | 3058 | 37 | 32 | +5 |
| Turn | after 33% cbet — call: BB donks | 2052 | 4 | 33 | −29 |
| Turn | after 75% cbet — call: BB donks | 543 | 7 | 41 | −34 |
| Turn | after check-check, vs 75%: call/fold/raise | 445 | 40/55/6 | 41/55/4 | — |
| Turn | after check-check, vs 135% | 48 | 23/71/6 | 32/66/2 | fold +5 |
| Turn | after 33% cbet — call, vs 75% | 523 | 50/42/7 | 45/49/6 | fold −7 |
| Turn | after 33% cbet — call, vs 135% | 272 | 32/66/2 | 37/60/4 | fold +6 |
| Turn | after check-raise and call: BB bets | 336 | 60 | 57 | +3 |
| River | BB first to act: bets | 4412 | 39 | 37 | +2 |
| River | vs a 60%+ bet after its own check | 863 | 33/62/5 | 30/60/9 | raise −4 |
What stands out: the familiar "the pool overfolds" is almost absent here. After check-check the pool defends the turn exactly like the solver, the river only 2 points worse. At NL200 people have learned to fold correctly. The mistakes are different ones.
The pool's three leaks
1. The BB almost never donks the turn after calling a cbet. In this tree the solver donks 33% of the time after a 33% cbet and 41% after a 75% cbet — and almost all of it is a 15% pot block bet spread across the whole range: from 21% with A-high to 40% with an OESD, top pairs and sets in between. The pool donks 4–7%, and mostly not as a block but at 25–80% of the pot. This is not the "cheap" leak it looked like in the first version: when the BB checks the turn, its range still holds every hand the solver would already be betting, and the BTN knows it. The pool's turn check after calling a cbet is noticeably stronger than the solver's — and the BTN's second barrel runs into a wall.
2. After check-check the BB bets the turn 5 points more often than the solver. 37% vs 32%. The extra bets are not strong hands but "well, I have to do something". The solver answers with a raise: against a 33% bet it raises 40% instead of 9% in GTO and folds 7% instead of 25%.
3. On the river the BB raises almost half as often. Against a 60%+ bet after its own check — 5% instead of 9%. It folds almost like the solver, 62% vs 60%. For the BTN this means one thing: a river bet almost never meets a raise, so you can bet wider — both thinner and as a bluff.
The pool plays the flop like the solver, with one correction: it raises the 33% cbet 4 points more often. A broadway board often hits the BB's range, there is nothing to fold, and the extra raise comes from boredom more than from strategy.
The raise hypothesis that did not survive
In the second version the solver donked the turn after calling a cbet 30–35% of the time, and a fair question came up: is that only because the raise against the donk in the tree was just 100% of the pot? A cheap raise makes a cheap donk. The raise was increased to 133%, the 50% donk replaced with 33%, and everything recalculated.
The solver donks 33% and 41%. That is the same, and after a 75% cbet even slightly more. The reason is simple: 30 of those 33 points are the 15% pot block bet, which the raise barely affects. A turn block bet is 1.4 bb into a 9 bb pot, and the solver bets it wide precisely because it is cheap — regardless of what the raise costs. The raise size affects only the big 33% donk: 2% of it is left. Conclusion: the pool's leak "does not donk after calling a cbet" is real, not an artefact of the tree. The pool does not block where the solver blocks with a third of its range.
How the solver uses it
The solver does not add aggression on the flop, it removes it almost entirely: the cbet drops from 43% to 3%. Against this pool the EV of checking the whole range is 3.82 bb, of a 33% bet 3.61, of a 75% bet 3.37. Checking beats a cbet by 0.21 and 0.45 bb per hand, that is 4% and 8% of the pot.
Those 3% are sets and two pair, and only with the 33% size. Nothing else bets the flop: not overpairs, not top pair, not flush draws. Played literally, your cbet on QJ2 would be a postcard saying "I have a set". Nobody takes that to the table, of course — more on that in the takeaways.
Why a check. After a cbet and a call the BB checks the turn with almost its whole range, strong hands included, and the BTN's second barrel hits a wall. After check-check, on the contrary, the BB reveals itself: it bets with weak hands, and when it checks, its range is already noticeably weaker. The solver steers the hand to where the BB speaks about its hand first.
Turn after check-check, BB checks (63%). Pot 5.5 bb. In GTO the BTN bets 32%, in the exploit 74%, of which 47% is a 135% overbet.
| Hand category on the flop | GTO: check / 75% / 135% | Exploit: check / 75% / 135% |
|---|---|---|
| Overpair | 32/41/28 | 16/75/9 |
| Top pair | 40/46/14 | 32/58/11 |
| Middle pair | 80/18/2 | 63/23/14 |
| Weak pair | 92/5/3 | 51/13/36 |
| A-high | 76/18/6 | 16/21/63 |
| Air | 50/38/12 | 11/21/67 |
| Flush draw | 36/46/17 | 28/42/30 |
| OESD | 35/45/20 | 21/33/46 |
| Gutshot | 58/31/11 | 18/27/55 |
Sets and two pair are not in the table: both in GTO and in the exploit they bet the flop. The picture is clear: strong hands bet 75%, and the 135% overbet is A-high, air, gutshots and weak pairs. The overbet here is a pure bluff, set up for a river where the pool does not raise.
Turn after check-check, BB bets 33% (13%). In GTO the BTN raises 9%, in the exploit 40%; it folds 7% instead of 25%. OESDs raise (68%), flush draws (54%), air (54%), gutshots (53%), A-high (46%). Made hands mostly call — they raise 17–38%.
Turn after check-check, BB bets 75% or 135% (23%). The shift here is more modest: against 75%, raise 6% instead of 3%, fold 29% instead of 44%; against 135%, raise 14% instead of 3%, fold 32% instead of 57%. Against big BB bets the pool simply folds less and calls more often with middle pairs.
River after the BB checks. In GTO the BTN bets 42% (3% all-in), in the exploit 87%, of which 24% all-in. The river check almost disappears.
What it is worth
BTN EV on the flop, bb per hand, pot 5.5 bb:
| BTN EV, bb | Who vs whom | vs GTO vs GTO |
|---|---|---|
| 3.04 | GTO vs GTO | — |
| 3.04 | GTO vs the pool | 0.00 |
| 3.43 | 50% exploit vs the pool | +0.39 |
| 3.83 | full exploit vs the pool | +0.79 |
Three conclusions.
First: on their own the pool's mistakes give a GTO player nothing. Zero. The solver strategy is protected from losses, but it does not collect money from other people's mistakes. To collect them you have to deviate from the solver yourself.
Second: the full exploit gives +0.79 bb, which is 14% of the flop pot. In the first version, on a mix of NL100–NL200, it was +1.11; in the second, +0.84. On pure NL200 the pool makes fewer mistakes and there is less to collect; changing the tree barely moved the number. It holds only while the pool does not notice that the BTN never bets the flop and overbets every turn. A regular with a HUD will notice.
Third: the money in this hand is on the turn and river. The pool's flop deviations (raising 4 points more often) were worth less than a hundredth of a bb in the previous check, and this is the fourth calculation in a row showing the same thing.
Exploiting in half the hands
A mix of "in half the hands the BTN plays the exploit, in half GTO". The EV of the mix is exactly the midpoint: 3.43 bb.
| Street | BTN spot | GTO | 50% | Full exploit |
|---|---|---|---|---|
| Flop | cbet | 43% | 23% | 3% |
| Turn | after check-check, BB checks: bet | 32% | 58% | 74% |
| Turn | … of which 135% overbet | 7% | 32% | 47% |
| Turn | BB bets 33%: raise/fold | 9%/25% | 28%/13% | 40%/7% |
| River | after the BB checks: bet | 42% | 71% | 87% |
In the check-check line the mix is closer to the exploit than to the midpoint. That is how it should be: the exploit brings its whole range into this line and GTO only half, so most of the hands that get here are "exploit" hands.
What the calculation does not know
Three assumptions, each pushing the answer its own way.
- The pool's frequencies are taken over all flops. Part of the difference from GTO may be texture rather than a leak. A year of database does not have enough turn and river hands for a single texture.
- The shift is the same for all hands. "Bet +5 after check-check" in the model means both a set and air bet 5 points more often. In real life the extra bets are mostly weak hands, but some strong ones too. Because of this the raise may be overrated in the model.
- The pool does not adjust. It is a mass of players, each of whom sees you rarely, so the assumption holds longer than against a single opponent. But "never bets the flop" is a stat a HUD will show within a couple of hundred hands.
The next step towards a precise answer is locks by hand category (strong hands bet, weak ones do not) instead of a uniform shift.
Takeaways for play as the BTN
What you can take to the table, with the assumptions above in mind:
- Check the flop far more often than the solver. You cannot play a full zero — it is readable, and "cbet only with a set" is readable even faster. But against the NL200 pool a cbet on this board does not make money and a check does. Bet the flop only with what wants to build the pot right now against a call: sets and two pair, plus a little for cover.
- After check-check bet the turn twice as often. Strong hands — 75%. The 135% overbet — bluffs: A-high, air, gutshots, weak pairs. The pool does not raise the river, so the overbet has a second barrel.
- Raise the BB's third-pot bet after check-check several times more often. Draws — raise, some air — raise, made hands — call more often. Almost never fold to such a bet.
- On the river after the BB checks — bet almost always. The pool does not raise, so a thin bet is not punished, and a bluff takes 62% of pots.
- After a cbet and a call — careful. The BB's turn check here is strong: it holds every hand the solver would have blocked with. Fire the second barrel only with hands that beat top pair.
The general idea: the solver does not "hit harder", it picks the line where the pool reveals itself first. On QJ2 that is check-check: a cheap flop, an expensive turn and river. The exploit is not about betting more. It is about betting where the opponent has already told you what they have.