I think vs lead our hand is just a call. We do fine vs the leading range but not as well as vs a check and certainly not well enough to raise. Probably the threshold is somewhere around a strong 7 but that's just a guess

I think it's just a call but could be convinced otherwise.

I think we want to pick a big sizing here as we're only betting Ax+ for value (and they can all pot it or something similarly large.) This allows us to put in the maximum number of bluffs.

Yeah this hand was really interesting for me I think mostly b/c of the relatively "null" 3 turn (though less null given it's a BB defend vs. an LP open so he should have an appreciable proportion of 3x in his range)--do we agree that some Ax for Hero should be checking turn (to place a large bet [b75-b125 range]) when checked to on most rivers? If so, I imagine the weakest Ax would be what PIO would choose to place in this region, with greater preference toward those Ax that do contain a diamond (the ones that do not obv. unblocking IP's diamond draws). I could be wrong about this and may run this spot and report back with my findings. I'm in total agreement that AT+ (approximately) loves bigbet on turn. Just thinking that it must be the case that we need to partition off some small proportion of Ax into a turn check/river bigbet range--this also allows us to bluff stuff like 98ss when checked to on river, combos that have no hope on turn (utter lack of draw/equity I imagine makes PIO not super enthused to bluff it on turn), but that likely seek to bluff OOP out of better unpaired combos/some Kx when checked to on river--i.e., crap combos that don't like bluffing turn, but do like bombing river when checked to. Will run this if I get time tomorrow.

Ok, so here are the PIO results. The two images I'm posting in this comment are IP's turn strategy (A4o highlighted), and then IP's river strategy on a bricky card (7s), given turn checked through, with A4o highlighted. As we can see, on the turn, A4o (and more generally, the weaker Ax combos) check as their most frequent action--when betting, they opt for b66. We can also observe that these combos then b100 on the river as their most frequent action when checked to--I think I captured the intuition behind this spot in my other comment but very much welcome others' input on this if they have more to add.

In the next comment, I will post my tree settings as well as the IP & OOP ranges I used. Wish I could just post the tree itself in a succinct manner, but such a manner isn't coming to mind.

I realize now the images are too low-res to see much detail--it was my first time posting images on RIO--if anyone is interested I can just host them on Imgur and post the links, which is what I now plan to do in the future

Thanks for doing all that Angel_zera.

I think I played the spot alright given your outputs. I essentially clumped all my bets into a single size (I think it was probably too big and in hindsight I sort of prefer like B80).

And then I just rolled. I segmented my range roughly as your intuition suggested. Placing a small premium on betting "stronger" Axs because they have a bit more EV (win on the K river). I also preferred betting w/o diamonds (want to force out or charge diamond draws. I think it's also worth factoring in the relevance of broadway cards here. (though its a bit tricky because those are obviously getting a premium from being stronger). I then just tried to roll for the rest of the combos (specifically A9-A4!d) so that villain can never find some magic blockers against me