On the 6643dd board, there's two opposite pressures going on --

1) In big pots 30-100bbs we are at a substantially disadvantage here with big regions of overpairs which are bluff-catchers.
2) In small pots 10-20bbs, we are actually have a nice range advantage against the huge number of offsuit overcards that have odds to call the flop. And since many players are biased against calling some Ace-Highs on turn, we actually have a nice bluffing opportunity on the turn.

PIO is going to mainly pot-control these boards with checks to keep from generating big pots with a range disadvantage, but exploitatively sizing down to target the over-folding over-card region is plausibly quite valuable if our opponent doesn't counter with lighter calls and more semi-bluff checkraising. He chooses the latter option here, but then I think gets little carried-away with having to win the pot.

The turn I think is where the mistake was made. K8o has really terrible card-removal against the turn-folding range, blocking random Kx combos is going to have a big impact on fold frequency, because they always fold.

With K8o on the river, A52JT board, I actually kind of like the bluff on the river -- it's one of the few board textures that generates like 40% jam from IP on the river. (The straight gets there and given positions we can jam something like AT, AJ or better for value). I think it's informative though that K8o actually has to be a plus EV bluff here to make it, because of the small region of flush draws that give +1 bbs or so to the check.

On the T74K board with the small flop bet, ranges are actually pretty symmetrical here (all overcards are modeled as +EV flop floats). I think PIO prefers slightly larger like 110% of pot, but doesn't really do much geometric growth overbets.

From a more exploitative idea, betting small on the turn should create more turn calls, which increases river fold frequency. It's transparent if you know what to look for, but can be tricky to play against if you aren't aware of the trick.

I would just also factor in Q8o not opening the button 100% of the time, so a lot of the 1 club combos I think will come from two overs without sdv in the KJ, KQ, QJ region. I double checked this on wizard, but the bet size is going to be different in the video. Where the HH shows min open, 33%-100%-100%. On wizard I have 33% - 125% as the main sizes for the one I chose. But I wanted to look at the turn strategy. I thought KQ would barrel a bit more with a club, but I guess KQ has too much sdv and it mostly starts around the KJ region. But I wanted to point out the KJo / QJo hands seem to barrel regardless of the suits and then the suited hands are just barreling clubs and spades. Wizard turn sim.

So If I understand turn correctly the
value region: AT+
bluffs coming from KJo/QJo & FD. Then some low KX/Qx combos. I have a really hard time finding those K3dd Q2hh combos. I guess blocking some 4x..

Looks like way more bluffs than value on the turn.

So the idea is that from the flop -- we have about 160 combos of unpaired one-card flush backdoor flush draws. They are going to be the best bluffing combos so PIO is going to choose some subset of them to triple barrel. PIO fractionalizes these combos to minimize the impact of card-removal in a our opponent's hand. And it's necessary to follow through often on flush-completing rivers if we bet turn, but as your sim points out they aren't 100% finishes -- in game with the pressure to win pots -- I think this can get overridden by the strong desire to win the pot along with the fact that most bluffs are very close to 0 EV in these games, so always finishing isn't a big impact on winrate.

The struggle comes is that if we go pot-size or bigger on the river -- our value region is only going to be about 30-40 combos when the flush comes in. So doing some rough math, we end up with between 16-22 bluffs at slightly overpot size or 10-15% of the original region. To get to 16-22 combos with a random number generator we have to be very careful with the fractions to come up with these numbers. If we say bluff 100% on the flop, 50% on turn and then finish 50% on the river we'd come up with roughly 40 river bluffs.

Without preplanning this region before the game with the right fractions, there's no realistic way not to overbluff these spots. Given that lots of players pretty much instantly bet these spots, I get really skeptical that they are approaching this from PIO perspective instead of some heuristic like bluff every offsuit one-club hand worse than KJ.

Tyler Forrester

we have about 160 combos of unpaired one-card flush backdoor flush draws

When you say things like this I'm always amazed at how you come up with the number of combos so fast. The numbers come to you so easily some times its like you are making them up, but usually pretty spot on. Just depends on how many A3o, K8o-98o hands are in the opening range. If its A3o+, K7o+ J8o+ etc ends up being 216, but that is at full frequency.

Given how easy it is to over bluff, would you just pick the AcX, KcX, QcX, and JcX to lower the bluffing frequency and block the higher flushes? So eliminate the kickers like Ax8c, Kx9c, Qx9c etc?

RunItTw1ce

You could do something like this where you chose the 8c and 9c hands to bluff. The main challenge with this approach is that something like QcTd is going to have a 3-5bbs worth of EV as a river call, because of the card removal. There's really not a simple approach to bluffing here that doesn't leak EV if your opponents know your strategy. We can see this in the sims with the complicated mixing to try to minimize card removal effects.

There's a relationship between hand-strength and pot-size. It's not obvious in the sims, but I think the extreme examples make it pretty clear.

We make money two ways, by bluffing or value-betting. We can make bluffs indifferent or -EV by calling at some frequency at each betting node. At some point (roughly when mdf becomes about 1% of original range), we only have to pay off with the nuts to make bluffs indifferent. So this means that on any board, there is actually a cap to the amount of money that can go in, before we only get called with the best possible hand.

The trick here is to realize that each hand class has some amount of money that goes in before it becomes a bluff-catcher. On a 6643 board, overpairs can get called by worse in small pots (but always become bluff-catchers in big pots). This gives the player with more overpairs, more value bets in small pots, but more bluff-catchers in big ones, because MDFs dictate calls with many worse hands in small pots, but few worse hands in big pots (Trips is about 5-8% of oop players range).

Yes, basically sizings go up (assuming opponent can raise, otherwise we just bet hand-strength) when we have a many more strong hands than our opponent, so on T74K, a big flop bet folds things like KJ, KQ, K9, Ks6s at pretty high frequencies, so we this is a much better turn for us at a pot-sized flop bet, then 1/3rd pot. At 1/3rd pot, nothing with two-overcards or good back-door flush draw is supposed to fold, so the king is much more neutral than in the big bet scenario.

Actually given the worse odds we lay our opponents, we can actually give up more on turn and river after a big flop c-bet, because the weak draws pay more money to hit their weak draw or to bluff river after we check. The main difference on the big flop c-bet is that on certain cards like the Kx or 7x in this example the ranges swing heavily in favor in the IP player and the OOP player. Bigger c-bets should increase OOP donking on favorable OOP cards and IP barreling on favorable IP cards.

Tyler Forrester I have a question about SRP OOP as the PFR. On ignition there are always blasters. On these low 644 boards I'll do a lot of range checking OOP, but IP seems to use large flop & turn sizes at a high frequency. Because you talked about over pairs being bluff catchers in larger pots and value bets in smaller pots, what is the best way to approach these pots? I thought maybe I should start betting more often OOP for 1/3 size as bluff raises are less frequent than large float bets. High frequency check raise was another thought that seems to do pretty well. I'll post two hands below that demonstrate indifference with these over pairs, mainly JJ. I guess part of my question is when pool is using "incorrect" bet sizes or just clicking buttons rather what would you recommend OOP as the PFR? I guess I should node lock this for IP to stab more often for larger size and see how PIO responds, but curious to your overall thoughts on this as well. Playing small / medium pots against these guys seems rather difficult. At what point do these over pairs stop being bluff catchers and just value against these players? There are some other hands where players will 3bet TT and take it to the house 3 way in on 765 boards. I'll end up folding my JJ and someone else will stack off A7s. Its like I kick myself some times for trying to play correctly based on solver outputs instead of just being more merged against the pool. The JJ vs Q2 hand I called off the other one I folded being a SRP and just thinking my range is protected here. The play seemed suspicious at the time, but I figured I can just call my 2 pair+ here or hands like T9s that have better blockers.

The JJ vs Q2d hand, villain called 3bet, then donk bet 3 streets.
K8s XC75-XC75-donk all in.

The board pair in the 2nd hand improved almost none of the players range and made trips+ very unlikely. The first hand was a more natural runout where more two pairs were available so sizing scheme has to be smaller.

Thanks TruePower!

I think it's important to focus on the differences between GTO and heuristics. Diamonds are poor bluffs in GTO, so lots of people round that idea to never bluff. Wherease GTO sometimes bluffs them to make calls like this closer to 0 value.

People struggle with frequencies here. There's maybe 35 combos of TT+ so he needs around 20 combos of bluffs. QJo,QTo,JTo is 36 combos without even addressing things like J4s (4 combos) or Q3s-Q4s (8 combos), so it's very easy to overbluff.