The main point: on the flop the solver mixes almost every BTN hand category between check, 33% and 75%, so what matters is not the frequency of a single hand but the composition of the ranges. The key decisions are in the BB's response to the bet and on the turn. All numbers come from our GTO run; play against the pool is covered in a separate article.
Setup
Single-raised pot: BTN opens to 2.5 bb, BB calls. Pot on the flop 5.5 bb, effective stack 97.5 bb, rake 5% capped at 1.38 bb (NL200). On the flop the BB has 349.7 combos and the BTN 507.5.
Tree:
- Flop: BB check only (no donk), check-raise 60%. BTN bets 33% or 75%, raises 60%.
- Turn: BB 33%, 75%, 135% and a 15% donk after calling; BTN 75% and 135%.
- River: BB 33%, 75%, 135%; BTN 75%, 125% and all-in.
Solution accuracy 0.49% of the pot. Anything smaller than that in EV is treated in this article as noise, not as the solver's intent.
Who is stronger on the board
The BTN leads both in equity and in strong hands: 53.6% vs 46.4%, and 11.4% of its range has 80%+ equity vs 5.9% for the BB.
Where the difference comes from:
- Only the BTN has overpairs (2.3% of range): the BB 3bets AA and KK preflop, and those who do not never make it into a GTO run. The BTN also has more sets: 1.5% vs 0.9%.
- Two pair is more common for the BB (2.8% vs 1.8%): it has Q2s, a hand the BB cannot explain even to itself, but on this board it is the best one. The BTN opens Qxs from Q3s up.
- The main difference is at the bottom of the range. Hands with equity below 20% make up 13.1% of the BB's range and 2.8% of the BTN's. The BB defends the blind wide, and small cards get nothing on Q♠J♥2♥. Even the BTN's weak hands are broadways with gutshots and overcards. Even the BTN's air is more respectable.
| Category, % of range | BB | BTN |
|---|---|---|
| Set | 0.9 | 1.5 |
| Two pair | 2.8 | 1.8 |
| Overpair | 0.0 | 2.3 |
| Top pair | 12.2 | 12.9 |
| Middle pair | 10.9 | 11.8 |
| Weak pair | 11.7 | 11.1 |
| A-high | 25.3 | 27.9 |
| Air | 36.1 | 30.7 |
| Flush draw | 10.4 | 8.3 |
| OESD | 5.8 | 6.4 |
| Gutshot | 8.3 | 13.8 |
| Overcards | 0.0 | 3.1 |
Draws are counted separately from made hands: top pair with a flush draw lands in both rows. Hand weights account for the opponent's blockers, as with "Normalize" switched on in GTO+.
How the BTN cbets
After the BB checks, the solver bets 42% of the BTN's range: 15% at 33% pot and 27% at 75%. It checks 58%, yes, more than half: a 90% cbet on any board was not the solvers' idea. The bet is polarised: the strongest hands and hands with no showdown value go into the bet, medium made hands check.
| Category | % of range | Check, % | 33%, % | 75%, % |
|---|---|---|---|---|
| Set | 1.5 | 5 | 34 | 61 |
| Two pair | 1.8 | 10 | 16 | 74 |
| Overpair | 2.4 | 18 | 20 | 61 |
| Top pair | 13.0 | 52 | 16 | 32 |
| Middle pair | 11.8 | 75 | 17 | 8 |
| Weak pair | 10.9 | 85 | 6 | 9 |
| A-high | 28.4 | 64 | 14 | 22 |
| Air | 30.3 | 46 | 17 | 37 |
| Flush draw | 8.2 | 42 | 17 | 40 |
| OESD | 6.3 | 33 | 21 | 46 |
| Gutshot | 13.8 | 45 | 15 | 40 |
What the table shows:
- Strong hands almost always bet, mostly at 75%. Sets, two pair and overpairs go into the bet 82–95% of the time.
- Top pair splits in half: 48% bet, 52% check.
- Middle and weak pairs mostly check (75% and 85%), A-high checks 64% of the time. These hands win at showdown and prefer to get there cheaply.
- Air and draws bet more often than medium pairs: 54–67%, with the same lean towards 75% as the strong hands. So the 75% betting range is made of strong hands and bluffs, with almost no medium pairs in it.
Why it works this way: what EV says
On the flop the BTN mixes almost every hand category between check, 33% and 75%. In equilibrium this happens only when the hand is indifferent: the EV of the actions is the same for it.
The category EVs show why. For most of them the EV of check, 33% and 75% differs by no more than 0.03 bb. If you have ever spent half an hour deciding whether to bet second pair 33% or 75%, the solver did not care, but you did. The decision matters noticeably for only two categories:
| Category | EV check, bb | EV 33%, bb | EV 75%, bb | Takeaway |
|---|---|---|---|---|
| Set | 11.13 | 11.32 | 11.35 | betting beats checking by 0.22 bb |
| Weak pair | 2.34 | 2.32 | 2.18 | checking beats a 75% bet by 0.16 bb |
It does not follow that the BTN can bet or check its whole range. The EVs stay equal only while the BB responds to the solver's betting range. If the BTN starts checking everything, sets and two pair end up in the checking range, the BB readjusts and takes the difference. Only a rerun would show what such a simplification costs: BTN strategy locked, BB free.
That is why you should look not at the frequency of a single hand but at the composition of the ranges: what goes into 75%, what into 33%, what into the check. A single hand can pick any of the actions, but if the whole range shifts, the BB's response shifts with it.
The same holds for the BB's check-raise. If the BTN does not adjust, a BB without a check-raise loses 0.10 bb against 33% and 0.13 bb against 75%. If the BTN adjusts, the loss is bigger: knowing there is no raise, it starts betting wider.
BB vs the 33% and 75% cbet
Against 33% the BB folds 34% of its range, against 75% — 52%. That is more than MDF allows: by MDF the fold should be no more than 25% and 43%. The BTN's bet is made of strong hands and bluffs, and the bottom 13% of the BB's range is not worth defending, however often you hear "defend your blind". Check-raise: 11% against 33% and 5% against 75%.
| Category | % of range | 33%: fold/call/raise | 75%: fold/call/raise |
|---|---|---|---|
| Set | 0.9 | 0/3/97 | 0/28/72 |
| Two pair | 2.8 | 0/54/46 | 0/80/20 |
| Top pair | 12.2 | 0/89/11 | 0/95/5 |
| Middle pair | 11.0 | 0/98/2 | 1/95/5 |
| Weak pair | 11.2 | 0/93/7 | 70/28/2 |
| A-high | 26.3 | 58/37/5 | 82/16/2 |
| Air (draws included) | 35.6 | 52/34/14 | 61/33/5 |
| Flush draw | 10.3 | 0/70/30 | 0/83/17 |
| OESD | 5.9 | 0/69/31 | 0/85/15 |
| Gutshot | 8.5 | 0/77/23 | 38/55/6 |
Three groups make the difference between the two sizes:
- Weak pair never folds against 33% and folds 70% of the time against 75%. Against 75% its call is already losing: −0.11 bb.
- Gutshots all defend against 33% and 62% of them against 75%.
- Sets and two pair check-raise more often against the small bet: 97% and 46% vs 72% and 20%. The BTN's 33% range is wider and weaker, and it is a pleasure to attack.
Draws do not fold against either size and supply more than half of all check-raises. For them call and raise are almost equal in EV (a 0.00–0.04 bb difference), so the exact share of draw raises does not matter.
The suit decides: a heart in the hand
For hands with no pair and no draw the solver looks at one thing first: is there a heart in the hand. A heart together with the J♥ and 2♥ on the board gives a backdoor flush draw, and the A♥ a backdoor to the nut flush.
| Hand | Heart | BTN cbets, % | BB defends vs 33%, % | vs 75%, % |
|---|---|---|---|---|
| A-high | A♥ | 58 | 88 | 5 |
| A-high | another heart | 51 | 32 | 0 |
| A-high | no heart | 19 | 1 | 0 |
| Air | with a heart | 68 | 13 | 0 |
| Air | no heart | 33 | 0 | 0 |
For play this gives two simple rules:
- The BTN bluffs with hands that hold a heart. With one, A-high bets three times as often and air twice as often. Such a bluff has a backup plan on the turn.
- The BB defends A-high against 33% almost only with a heart. A♥x defends 88% of the time, the same A-high without a heart 1%. One card of one suit, and the hand goes from "fold without looking" to "call without looking". Against 75% the backdoor is no longer enough: even A♥x folds 95% of the time.
Pure blockers (how a card in the hand changes the opponent's range) cannot be separated from the backdoor in this run: that would need the EV of every combo, and the export gives EV by hand class.
The turn after calling a 33% cbet
After calling the 33% bet the BB has more equity (54.2% vs 45.8%), but almost all the strong hands belong to the BTN. 8.9% of the BTN's range has 80%+ equity vs 2.3% for the BB: the BB nearly always check-raised its sets, and the calling range holds 0.1% of them. The BTN's range is polar: strong hands plus 34% air and 26% A-high. The whole turn strategy follows from that.
| Turn | BB equity, % | BB EV, bb | BB leads (15%), % | BTN after check: 75%/135%, % |
|---|---|---|---|---|
| 3–7 non-♥ | 55.3 | 3.90 | 6 | 1/37 |
| 2 | 55.1 | 3.65 | 2 | 3/43 |
| 8 | 53.3 | 3.82 | 14 | 16/24 |
| 9 | 53.9 | 3.78 | 2 | 33/12 |
| T | 50.9 | 3.32 | 0 | 18/28 |
| K | 49.3 | 3.51 | 7 | 44/0 |
| A | 47.0 | 3.01 | 0 | 34/21 |
| Q, J | 56.2 | 4.24 | 43 | 24/18 |
| ♥ | 55.0 | 4.14 | 36 | 31/6 |
The pot on the turn is 9.14 bb. For card groups the figures are averaged over the cards in the group: "3–7 non-♥" is 15 cards without a heart, "2" and "Q, J" pair the board, "♥" is any of the 11 hearts that complete the flush.
Three kinds of turn:
- Blank cards (3–7, 2) — overbet. The BB almost never leads, the BTN bets 38–46% and almost always 135% pot. The card changes nothing, the BB still has no sets, and the BTN pressures its top pairs and middle pairs. A five on the turn changed nothing except the bet size.
- Overcards A and K — the best cards for the BTN. BB EV drops to 3.0–3.5 bb, the BB does not lead. On a K the BTN bets only 75%, no overbet; on an A — both sizes, 55% in total.
- A heart or a paired Q or J — the best cards for the BB. Only here does the BB often lead with a small 15% donk (36–43%), and the BTN almost never overbets after a check.
After calling the 75% bet the picture is the same, only sharper. On blank cards the BTN bets 51%, and on a paired J the BB leads 15% with almost its whole range (96–99%).
Takeaways for play
As the BTN:
- Bet sets, do not bet 75% with a weak pair. The rest of the hands mix: the exact frequency of each does not matter, what matters is that the composition of the ranges does not shift.
- The 75% bet is polar: strong hands and bluffs with a draw or a heart in the hand. Medium pairs and A-high without a heart mostly check.
- On the turn after a 33% call: on a blank — a 135% overbet, on a K — 75%, on a heart or a paired Q or J — more careful, almost no overbets.
As the BB:
- Against 33% defend all pairs and all draws. Defend A-high only with a heart, preferably the A♥.
- You have to check-raise: without it the BB loses at least 0.10–0.13 bb. Sets go into the check-raise almost always, draws a third of the time.
- Against 75% weak pairs and A-high mostly fold, even with a heart.
- Donk the turn only on a heart or a paired Q or J.
The river is not covered in this article. It deserves one of its own: that is where the biggest pots and the most expensive mistakes are.