Sweet man!

I was also curious about your question so looked at some different river cards and how AKo plays each of them. Links below for each one. I looked at where club / heart completes and also with A or K comes on the river that doesn't complete the flush.

Th-4c-3h-5c-Qh - shoving with AxKh but not AhKx.... This is a spot I messed up the other day blocking with the nut blocker instead of 2nd nut blocker.

Th-4c-3h-5c-Ks - I have no idea what is going on with the suites here. You see some KJh / K9h blocking the river as well, but not KJc/K9c. Then AKo Not sure what is going on with the suites.

Th-4c-3h-5c-Ah 10% pot is being used here even with KJh K9h hands and then KQh jams as well as 55 and 8h8x (no club). I thought K9h would jam more than KQh here unblocking some higher flushes?

Th-4c-3h-5c-Jc - doesn't like clubs to bluff. On Ac river it blocks 10% with a lot of AQ/AK hands and on Kc it blocks 1/3, but no all in.

Despite what wizard says here, still interested in Tyler Forrester thoughts from a more practical stand point. Seems like when you make a pair it's mostly block betting 1/3 or 10% depending on A or K and when front door flush completes does some shoving but never with the back door flush. Maybe can simplify all of this to 25% donk bet on the river on hearts or A/K regardless of suite and our hand strength if we are in SB's shoes.

I didn't do a deep dive into the c/c line with AK here. My sense of these mixes is generally they exist to accomplish three goals.

1) To keep IP from expanding his flop floating range
2) To force IP to continue to value bet/bluff with extra hands on different runouts -- this adds value to the nutty parts of our hand ranges
3)To force IP to check slightly more often on the turn (this adds value to the check/folding regions)

I think donk leading Kx river especially is appealing and having some donk bluff leads on the Qh makes sense though PIO will claim it doesn't add value to the strategy unless our opponent overfolds.

In the sim we looked at, I didn't give OOP the ability to donk lead, because it's a reasonably rare thing from the player pool and I didn't want to model my opponent being stronger than he was.

P.S. I should note that the exact frequency of AK calls here is likely very very important. Too many and villain starts playing really aggressively on rivers and too few, likely the Tx region on blanks starts to become more check-heavy.

RunItTw1ce

The donking lines in these situations are really complicated and challenging. Something like AK on the Ks river is clearly ahead of our range, but it's not necessarily dominate after two straights complete on the turn. I think that's why you are seeing the block mainly. The other idea is that the bluff-jams in PIO land aren't making any money, just forcing calls when we have the nuts, so from an EV perspective, it doesn't make check-calling AK better here.

I think this spot plays much much tighter on average than the pool plays this situations. It's a counterintuitive board where we have many dominate hands as a portion of range. In that sense the model is very broken compared to what we see in practice from the pool.

First sim Qh...I wonder why we jam the kh but not the Ah.

This has to do with blocking the cbet range and XC turn range. You want to unblock a XC XC XF range. That is not the line, but how to think about it. More so when flush draw bricks though.

I wonder how often sb is suppposed to barrel heart draws on turn given a lower spr spot.

Hearts are almost never barreling! There are some Ah7h & Ah6h that barrel 20-30% of the time, but all the KQh QJh KJh etc are 0%! But clubs are 50-90% depending on how weak of a kicker you have (no sdv). I just realized having KhXh QhXh doesn't block any top pairs! Because the "Th" is on the board you want to block more of the top pairs, so solver is choosing clubs over hearts.... That is my guess. I'll switch some suites around and put clubs as front door and hearts as back door and see if it changes. Frequency goes up, where it starts to barrel QJh but the KQh KJh are still checking... Also frequency goes up with AhXh as well blocking ATh I guess. But honestly idk the answer to betting back door vs front door. Maybe too many single heart combos that float the flop? Like AhQx, AxQh that float the flop and fold the turn? So blocking TP + blocking the (call + fold) range? I'm sure Tyler will chime in soon and provide us some answers :-) Good discussion though!

RunItTw1ce

I think the obvious explanation for not barreling say QJhh, Ah7h is that the only folds on this board for IP is a backdoor 1 heart floats, so taking out KdQh or AdJh is a real problem for fold equity.