Ha, that's not surprising to me at all. I've recently started playing chess for fun and can definitely see how this will hold even more so true in chess since so much can change depending on one small thing, whereas poker is more generally principled. (Don't want that to be misinterpreted - obviously chess is a very principled/theoretical game, but I mean that in the sense that for example in poker once you figure out minimum defending frequencies, you can can apply that to all betsizes, and if you miscount/forget one combo it's not a huge mistake, whereas in chess if you miss a move sequence you're just screwed).

Probably my favorite chess quote ever, from Mikhail Tal:

"You must take your opponent into a deep dark forest where 2 + 2 = 5 and the path leading out is only wide enough for one."

Glad to hear that!

Yes, I think it's useful but like you said it's time consuming. If you're playing part time and have something like 20 hours a week to devote to poker you're probably better off just picking up bits here and there rather than building trees yourself. If you devote all of your work week to poker I'd say it's borderline a necessity to keep improving in today's game environment. So it really depends on your situation.

Thank you!

Hi Duke,

I would expect the leading frequency to be a little different if BB had an option to x/r flop, but not by much.

CO does not have the stronger range when the 9s peels off, especially because the BB does not have a x/r range. CO will win (just barely) over half the pot, but that is solely because of positional advantage. BB will have a ~53/47 equity edge, as a result of CO c-betting ~100%.

Independent of who has the equity range, CO chooses to check back turn more than half the time. When such a large chunk of his range is checking back, naturally some hands in the BB's range will be incentivized to do some specific thing against that part of CO's range.

Looking at what the BB leads, a rough breakdown would be that we see some strong hands (especially 22), quite a lot of middling hands (KQ), some good bluffs (nut FDs, FD+) and some bad bluffs (AsTx, 86).

Leading hands like KQ is good because of how polarized CO is barreling - generally it is either hands that are better than KQ or bluffs. So we are getting value from weaker Kx, 9x, TT, JJ type of hands which would always check back if we checked. In effect, we are messing up the effectiveness of villain's polarized range, which would make KQ indifferent on a lot of rivers after we x/c turn.

Leading good bluffs makes a lot of sense given that they are iffy to continue with against a bet in the first place, and the value of a free card is OK but not super great.

The fact that developing a leading range allows is to have bad bluffs in our range is what makes leading so great. We are not profiting with hands that cannot be x/called and make for lousy bluffs on the river if the turn goes check/check. Leading hands like AsTx to bomb spade rivers is obviously great, leading 86, T8 so make very non-obvious nut hands on by the river is great also.

What's really cool about developing a leading range here is that it doesn't actualyl hurt our checking range. We do take some hands out of our range that would be some of our best ones to continue with versus a turn barrel, but we also take out a lot of obvious check/folds, so our folding frequency isn't impacted too much. As such, there isn't an incentive for CO to start barreling turn more than ~40%.

Thank you!