Flopped a Set: When Solver+ Fast-Plays It and When It Slow-Plays

A flopped set is the hand players are most sure about and most often misplay. One school slow-plays it to "let them catch up". Another fires big to "protect it". Solver+ does neither. Across seven flops, button versus big blind at 100bb, the set almost never decides its own action. It c-bets when the range c-bets, at the size the range uses, and the one real choice it makes comes later: whether to raise or call when the pot gets big, and which set size gets to slow down. The answer depends on which set you hold, not on how strong it is.

1The Spot and the Boards

Every number here comes from one Solver+ tree: 100bb cash, the button opens to 2.5bb, the big blind calls, and the flop arrives with 5.5bb in the pot and 97.5bb behind, an SPR of about 17.7. That is deep enough that a set can win a stack over three streets, which is exactly why the slow-play temptation is strong.

A pocket pair flops a set or better 11.8% of the time (two of the 50 unseen cards match your pair, so the chance that none of the three flop cards does is C(48,3)/C(50,3) = 17,296/19,600 = 88.2%). You will see this spot about once every eight or nine pocket pairs that see a flop, so getting it right is worth more than most bluff spots.

Seven flops cover the main textures:

One structural fact shapes everything. The big blind 3-bets most of its big pairs preflop, so its flat-calling range rarely holds the top set on K72, A94, J53 or T86. The button opens every pair. When this post says "top set" in the big blind, it usually means the highest set the big blind can actually hold.

2Button With a Set: Bet, at the Range's Size

Start with the seat where slow-playing feels most natural: in position, preflop raiser, the big blind has checked. On dry boards the button checks only 5-16% of its range, and it checks none of its sets. On connected boards it checks about a third of its range, and it still checks none of its sets.

The pattern to take away is not "sets bet". It is that the set uses whichever size the whole range uses. On K♠7♦2♣ and A♥9♦4♣ that is the 25% bet, so KK and AA bet 1.38bb into 5.5bb, a size that looks like a range bet because it is one. On T♥8♦6♣ and 9♠8♦4♣ the range shifts to the 80% bet and the sets go with it. A set that picked its own size would tell the big blind what it has. Hidden inside the range's normal action, it gets paid by the top pairs and draws that continue anyway.

The exceptions are small. On J♠5♦3♣ the low sets take the big size about 30% of the time, more than the range does (22%), most likely because the 5 and 3 leave the big blind straight draws worth charging. On 9♠8♦4♣, top set 99 uses the small bet more than any other set (17%). The paired board is where checking first appears: trips with a weak kicker (98s, T8s, 87s) check 17-20%, because on K♠8♦8♣ there are few hands left for the big blind to pay with. The full houses still bet 91-99%.

3Big Blind With a Set: Check, Then Raise or Call

Out of position the question is different: lead, check-call or check-raise. The first answer is clean. The big blind checks its sets 100% on K♠7♦2♣, A♥9♦4♣, J♠5♦3♣, T♥8♦6♣, 9♠8♦4♣ and K♠8♦8♣. It leads 1-2% of its range on those boards and none of that is sets. The exception is 6♠5♦4♣, where the big blind leads 70% of its whole range and the sets lead 88-97% along with it. That is the same rule as the button: the set does what the range does.

After the check, the size of the c-bet decides how the set plays.

Against the 25% c-bet the set raises, almost always to the big size (6.21bb, 90% pot). The small bet invites a raise: the big blind's range is full of hands that continue, and the bet is too small to fold to.

Against the 80% c-bet the sets split, and this is the most useful pattern in the post. On A♥9♦4♣ the 9s call 83% and the 4s raise 91%. On 9♠8♦4♣, 99 calls 99%, 88 calls 74% and 44 raises 87%. On T♥8♦6♣, 88 calls 85% and 66 raises 62%. The higher set slow-plays and the lower set raises.

The likely reason is card removal. When the big blind holds 99 on 9♠8♦4♣, it removes the 9x hands the button would call a raise with. When it holds 44, it blocks almost nothing the button continues with. The set that blocks the opponent's pairs has fewer hands to get paid by after a raise, so it calls and lets the button keep betting. The set that blocks nothing raises, because the button's range still has plenty of top pairs to pay it. The grid tab shows the full picture on 9-8-4: two pair 98s raises 99%, 44 raises 87%, 99 calls almost always, and small pairs like 77 fold to the big bet.

Two boards break the split. On K♠7♦2♣ and J♠5♦3♣ both sets raise against the big bet, because the button's 80% range on dry boards is narrow and strong enough to pay either set. On 6♠5♦4♣, the board where the big blind's range is strongest, the split flips: 66 raises 89% and 44 calls 67%. Treat "higher set calls" as a strong tendency on boards the button bets big, not a law.

4Button Facing the Check-Raise: Bottom Set Re-Raises

Now the button has c-bet its set small and the big blind check-raises. This is where the same card-removal logic shows up most cleanly.

How often the button 3-bets its set (to 7.59bb) after c-betting 1.38bb and facing the big blind's small 3.45bb check-raise. Everything else calls. Against the big 6.21bb check-raise the button calls with every set on K72, A94 and J53. Source: Solver+.

Against the small check-raise to 3.45bb, read across each row. On A♥9♦4♣, AA 3-bets 1%, 99 9% and 44 74%. On K♠7♦2♣, KK 9%, 77 53% and 22 77%. On T♥8♦6♣, TT 17%, 88 67% and 66 87%. On every board except 6-5-4, top set 3-bets least and bottom set 3-bets 67-100%. Top set holds the card the big blind's top pairs need, so it calls and leaves those top pairs in. Bottom set blocks nothing, so it builds the pot now.

Against the big check-raise to 6.21bb the decision collapses: every set on K♠7♦2♣ and A♥9♦4♣ calls 100%, and on J♠5♦3♣ 91-100%. With about 91bb behind and a raise that already represents a polar range, the button keeps its sets in its calling range, which protects the calls it makes with top pair. 6♠5♦4♣ is again the exception: every set calls the small raise about 95% of the time, because the big blind's raising range there is heavy with straights and two pair.

This lines up with what Solver+ does with top pair facing the same raises in our check-raise breakdown: small raise, merged response with some 3-bets; big raise, call and never re-raise. For the big blind's side of those sizes, see check-raise sizing from the big blind.

5The Flop in One Tree

6Turn: Where Top Set Slows Down

The flop c-bet was called and the big blind checks the turn. The pot is 8.26bb after a small flop bet, 14.3bb after a big one. This is the street where the real slow-play appears, and only one set does it.

On blank turns the low sets choose the 135% overbet almost every time: 22 on K♠7♦2♣ 4♥ overbets 97%, 99 and 44 on A♥9♦4♣ 2♠ overbet 98-99%. The overbet is how the button gets the most from top pairs that cannot fold. Top set does not join in. KK on K♠7♦2♣ 4♥ uses the 80% size 59% and the 25% size 35%. AA on A♥9♦4♣ 2♠ checks 99%, and on the 7♠, K♠ and 3♥ turns it checks 83-89% (58% on the T♥). You will rarely see a set checked with this confidence anywhere else in the tree.

The reason is the one from the flop. AA removes two of the three remaining aces, so the big blind's range has few Ax hands left, and Ax is the main thing that pays a turn overbet on an ace-high board. KK on K♠7♦2♣ blocks the Kx hands the same way, less severely, so it bets but smaller. An overbet with top set mostly gets folds from hands that were never paying. A check lets the big blind bluff or improve to a second-best hand on the river. This fits the wider pattern in overbetting one pair: the size of the turn bet follows what the opponent can call with, not how strong your hand is.

When the turn is a high card the logic reverses. On K♠7♦2♣ A♣, KK overbets 100%. On J♠5♦3♣ K♠, JJ overbets 87%. The new card gives the big blind fresh top pairs that top set does not block, so top set goes back to building the pot.

In the big blind, the sets that called the flop's 80% bet check the turn 95-100%. Facing the button's overbet the split appears again: on A♥9♦4♣ 2♠, 99 calls 81% and 44 jams 91%; on T♥8♦6♣ 2♠, 88 calls 94% and 66 jams 91%. Facing the 80% turn bet, the sets mostly raise to 28.6bb, except on 9♠8♦4♣ 2♥, where top set 99 calls 100% and keeps slow-playing and 88 splits 50/50.

7River: The Slow-Play Gets Paid

Follow the clearest slow-play line to the end. You hold A♠A♦ on the button.

Flop A♥9♦4♣: you c-bet 1.38bb into 5.5bb (AA uses the small size 100%) and the big blind calls. Turn 2♠: the big blind checks, you check (99%). River 7♥: the pot is 8.26bb and you each have 96.12bb behind.

Your turn check changes what the big blind does on the river. After a turn that checked through, the big blind leads the river 43% of its range: 3.3bb (40% pot) 25.7%, 7.85bb (95%) 14.4% and 12.39bb (150%) 3.1%. Those leads are the payoff for the turn check, since a hand that would have folded to a turn overbet now puts money in. If it bets small, AA raises to 9.9bb 100%. If it bets 95% pot, AA moves all in 98%. If it checks, AA bets 7.43bb (90% pot) 100%. The hand that checked the turn is betting or raising on every river branch.

The same top set versus bottom set gap runs through the river after a bet-bet line. On K♠7♦2♣ 4♥ 9♥, with the button having bet the flop small and the turn 80% (river pot 21.48bb, 89.51bb behind): KK bets 90% pot 74% and jams 21%, 77 bets 150% pot 65%, and 22 jams 88%. Top set keeps choosing the smaller size, all the way to the river.

8Quick Reference

Four rules for a flopped set:

1. On the flop, play the range, not the hand. Bet if your range bets, at the size it uses. In the big blind, check if your range checks.

2. When the pot can grow, ask what your set blocks. The set that holds the opponent's top-pair card (top set, or the higher of two sets) calls and waits. The set that blocks nothing raises.

3. On blank turns, top set sizes down or checks; low sets overbet. When an overcard arrives, top set goes back to betting big.

4. A checked turn earns a river bet. The big blind leads 43% after a turn checks through, and top set raises it.

Rules are easier to read than to apply at the table. Postflop+ deals you set spots across these textures and grades the size and line you pick against the solved answer, so the blocker read becomes automatic. If you want to see why a top-pair hand calls the raise you are about to make, the blocker and check-raise glossary entries cover the basics, and the delayed c-bet breakdown shows which other hands Solver+ likes to check before betting.

All data: Solver+, BTN vs BB single-raised pot, 100bb cash, BTN opens 2.5bb. Per-hand frequencies are hand-class averages; specific suit combinations can differ by a few percent.