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Just using this hand as an exercise for myself.
Hmm, ace-rag is not found in many 13% ranges. Even if we rule out broadways and say he only raises pairs 77+, including ace-rag already gets us up to 18%. Of course sample size is an issue, but it would be nice to know which ace-rag hand you've seen. Like, was it suited? Was the rag card specifically 5 or was it 8+? Also, what position was he in when he raised that? CO or BTN? What's his steal %?
The KTo is part of the 30% range (VP$IP) so that's reasonably expected.
In the absence of the suited / kicker / positional information I'll define his CO opening range as follows:
22+,A2s+,KTs+,QTs+,JTs,T9s,98s,ATo+,KTo+,QTo+,JTo (21.0%)
This includes a limited propensity for raggy aces and offsuit broadways and hits a reasonable position adjusted percentage of hands.
Against that range you have 48.0% equity before the flop and know you are playing OOP.
Wait, 40? Is that aggression factor of 40? Not 4.0? Or is it actually the steal % I was asking about? Normally when 3 stats are listed it's VP$IP/PFR/AF and if either of the stats you list is not one of those, it'd be helpful to mention it.
If it's the steal % then 21.0% is probably too narrow for a CO opening range. Let's try to get closer to 30%.
22+,A2s+,K9s+,Q9s+,J9s+,T8s+,98s,87s,76s,65s,54s,A 2o+,KTo+,QTo+,JTo (30.6%)
Against this range we have 47.6% equity preflop.
Come the flop against the 30.6% preflop range our equity is 54.2%
Come the flop against the 21.0% preflop range our equity is 61.4%
If we have a look at the opponents range on the flop we notice a lot of weak top pairs - since he's playing all aces - and a lot of broadways that have become second pair or gutshots. Whether it is correct for you to bet out on the flop depends a bit on if you put him on the narrower or the wider range and on whether you think with multi-street betting it's possible to get him to fold his worst aces, and conversely if you think by you betting he is likely to call rather than fold his gutshots and weaker kings.
Going to just do a breakdown of the wider 30.6% range.
Set and two pair: AA (3), KK (1), 99 (3), AK (6), A5 (9) = 22 combos
Top pair: A2-A4 (36), A6-AJ (72), AQ (9) = 117 combos
Second pair: KQ (6) KJ-KT (18), K9s (2) = 26 combos
Third/fourth pair: 22-44 (18), 66-JJ (36) = 54 combos
Gutshot: QJ -QT (24), JT (16) = 40 combos
Worse: Q9s (3), J9s-T8s (8), T9s-76s (16), 65s-54s (6) = 33 combos
Total: 292 combos
We want to pick a line on the flop that maximises our EV. Considering our opponents range where is the EV hiding?
If we bet we can probably assume he folds worse and third/fourth pairs (87/294 combos = 29.8% of the time). He could also fold gutshots (127/292 combos = 43.5%). So if we ignore later street actions (deciding to check/fold any card) a bet size that requires 43.5% folds to be profitable if the opponent folds 127 combos is worth identifying. It turns out that that bet size is about 77% of the pot.
If we think he folds 127 combos just betting out $0.70 might be a +EV line, as long as we know to proceed with caution if we are called, as we will assume we are almost always crushed if we do not improve. If we think he calls those hands that we beat betting may also be +EV, but then we have to play potentially unimproved against a range that includes both hands that we beat and hands that beat us on a turn.
Check/raise is another interesting line. If we check, how many combos will he bet? He might check behind gutshots (40 combos) second pairs (26 combos) and third/fourth pairs (54 combos), which enables us to fire most turns to get almost all of those to fold. T-Q turns are at risk of improving our opponent to a straight, but may also make him strong enough that we can get value from a worse pair. Similarly lower pairs that have checked through might call the turn to catch you bluffing, so you could get value from those.
When we check I think he almost certainly bets sets, two pair and top pair hands (139 combos) for value. He needs to price out the apparent flush draw and the likely gutshots. He might bet the worse hands also (33 combos). So, if we check, he bets and we raise - what hands are folding? Worse, if they are in his range for sure. A2-A4 and A6-AQ are definitely maybes. So 22 combos continue for sure (and might even make the decision super simple by raising), 33 combos fold for sure and a whopping 117 will... sometimes fold and sometimes call. If he calls A3o, will he then fold to a turn bet if you lead out? Probably. So, if he calls the raise widely you can bluff lead the turn and get many folds, if he raises his sets/two pair hands 100% of the time that means if he calls it's basically a green light to try to push him off his (potentially weak) top pair hand. Since it's exploitable to raise only nut hands I would tend to think that he will call his sets and two-pairs if you raise. And while he may fold some of the lower aces, the question is whether he folds enough for it to be profitable for you to c/r.
Bluffing is expensive, and I think the opponents range is strong enough here that I don't particularly prefer a check/raise line. I think both leading out and check/calling have merit. If you lead out you risk getting hands to fold that might pay you a bet in a later street, but you also reduce the risk of them improving to beat you or successfully bluffing you out. If you check/call you are looking for a cheap showdown unimproved and since you are OOP there are no guarantees. If he checks behind you may want to put some money in on a later street, but consider that he could easily check a few of his weaker aces and still have it be significant compared to the lesser hands in his range (which may improve). I tend to prefer leading out here. We realise what fold equity we have and if called and unimproved I would then tend to look to get out of the hand or see a free showdown only.
As played the turn does shake things up a bit. Let's assume that the bet indicates a range of sets, two pair, top pair and the worse section, along with any heart draws from other sections (ends up being just JhTh with the Qh blocker):
Sets: AA (3), KK (1), 55 (3) = 7
Two pair: AK (6), AQ (6), A5 (9) = 21
Top pair: AJ-A6 (6 * (1 + 5 + 6)), A4-A2 (3 * (1 + 5 + 6)) = 9 (flushes) + 45 (flush draws) + 54 = 108 combos
Gutshots turned flushes (and straight): JhTh = 1 combo
Worse turned flushes: Jh9h, Th8h, Th9h-5h4h = 8 combos
Worse not turned flushes: Q9s (2), J9s-T8s (6), T9s-76s (12), 65s-54s (6) = 26
Total: 171
We are now beaten by 7 + 21 + 9 + 1 + 8 = 46 combos (26.9%)
We are now beating strongish hands 45 (flush draws - 26.3%) + 54 (top pair - 31.2%)
We are beating weak hands: 26 combos (15.2%)
The question is if there is value in putting money in here. The opponent is keen to at least bet 53.2% of his range (all that beats us and the flush draws). If we lead out the weaker hands will fold, but since that's only 15.2% there's not a lot of equity realised by his folds. The flush draws might call given good odds if we bet too small, and if we bet too big they might raise thinking (probably correctly given our line) that they have fold equity and that combined with their flush draw (and indeed draw to two-pair that beats ours) makes raising +EV. They might also raise some of their nut range, but some of the nut range will call also, so if called we cannot assume on the river that we are automatically up against a top pair hand - although top pair will probably be the majority. If we bet the turn and are called we should wish for the river to go check/check. If we go check and he bets a top pair hand unimproved he will be turning it into a bluff - so the question is if he is capable of turning a made hand into a bluff.
Ok, so if we check and the opponent checks behind we assume he has top pair without flush draw or a weak hand and we bet the river for value. If we check and he bets into us we assume he has sets, two pair, flushes and flush draws and we what? We almost have to consider folding. We have 4 outs against the hands that beat us (and some are sometimes compromised like when he gets a better full house) and the hands that we beat have typically 12 outs against us. So we're slightly ahead or way behind. With the dead money folding may not be required, but it's worth considering. Especially if we consider his river tendencies. We would expect to arrive on a river unimproved and if it's not a heart we expect to be ahead of half the opponents range. It's probably more like 40% that we're ahead on no heart as some cards will give him a better (aces up) two pair hand. We can at least decide also to not continue on any 5. So that's 11 hearts, 3 5s that we don't continue on and 2 kings and 2 queens that we stack off on (sometimes to a bigger full house) and 28 cards we are looking for the right way to continue on against a range that is probably 60% ahead and 40% behind.
The turn again can be either bet/fold or check/call, and I think I prefer bet/fold.
Once the river lands we are in the situation I just described. If we check and he bets we need to judge whether he is ever turning unimproved top pairs into bluffs (or mistakenly think he's betting them for value). If we don't think he bets naked aces we can confidently fold. If we think he bets naked aces quite often we can confidently call. A better line imo is bet/fold. Make sure to bet an amount that he will not raise with naked aces. So if he raises you know you are beaten and can confidently fold. If he calls you will sometimes - maybe even often - win the pot. The perfect bet size is one that is raised by all hands that beat us and called by all hands that we beat. I don't know if a perfect bet size exists but my gut feeling is suggesting it should be somewhere around 40% of the pot. Like $2.20 or so.
So yeah, I could argue here for bet/fold flop, as played bet/fold turn, as played bet/fold river and as played.... make a read. Is he bluffing often enough that you can call? I don't know the opponent so can't really tell.
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KQ 2p on wet board
, K
, 5
(2 players)
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