So my brain is nowhere near ready to play the tournaments I had planned for today, the upside being that I can dive into this right now. I’ll start by giving BTN a somewhat tight but totally reasonable shoving range of AA-99,AQ+. That leaves a calling range that should look something like:

88-44,AJs-A2s,K5s+,Q8s+,J8s+,T8s+,97s+,87s,76s,AJ-AT,KJ+,QJ

Of the 164 combos in that range, I have villain continuing vs. a cbet with 98/164 combos or 59.8%. That is comprised of 3 sets, 11 combos of 2 pair, 26 combos of top pair, 21 combos of 2nd pair, 2 combos of 76s+BDFD, 4 OESDs, AJ and AT gutshots (but not J9s or T9s), and A9s/A8s/J9s with BDFD.

Without considering our range yet, we can see that unless villain stretches to find more calling combos, we have an immensely profitable opportunity to make a 1/3 pot cbet (~8k). Our cbet only needs folds 25% of the time to break even, so even if we add a relatively large risk premium of 10% (representing the value of our tournament life), we’re still getting enough folds (40.2% vs 35%) to really benefit from betting. Even giving villain every combo of slowplayed AA that only increases their calling rate by 0.8%.

We do need to consider possible bluff raises for the villain, but our range is strong enough that they’re unlikely to have more than a few. I don’t have PIO yet so I’m winging it, but I imagine the most natural bluffs being something like the combos of J9s,T9s,A7s,87s with BDFDs, and maybe ATo or AhTh. If they bluff all of the A7s/T9s/87s that adds 8 more combos to their continue range. So now our 1/3 pot cbet fails to immediately win the pot 109/164 times or 66.5% of the time (still including the slowplayed AA). We’re 1.5% short of enough folds to justify a 1/3 cbet if we include the 10% (again, relatively high) risk premium.

Considering that we’ll occasionally take down the pot with further bets, I can’t see a way that cbetting isn’t profitable with 0% equity (and our A5s has a fair amount more than 0). We can also use a smaller cbet sizing considering the shallow SPR, and unless villain widens their range considerably (and sets themselves up with very hard ranges to play against further betting), a 1/4 pot cbet (~6k) is extremely profitable even if we always lose when the villain doesn’t fold.

I still haven’t talked about our range (and won’t in this post), but I’ll leave you with two more thoughts. Range advantage becomes less of a factor as the SPR becomes shallower. Holdem becomes much more a game of protection and equity realization rather than range vs. range considerations when people are priced in with weaker holdings. I don’t understand the reasons for that well enough to properly explain it, but it seems to be the general consensus among players that understand these concepts better than me.

That leads to my second point. We want to be cbetting an increasingly polar range as the SPR gets smaller, because the middle of our range and our strong draws really can’t call raises but also can’t fold to them (obviously they need to pick one of the mistakes which usually means folding). I much prefer cbetting a hand like A5s BDFD instead of hands like AJs BDFD or AQ/QJ/QT/JTs here.

Lol, I think I’m going about the flop bet backward because I’m not a computer program. Not sure how you expect me to calculate multiple ranges with any kind of precision in a forum post, although I do very much appreciate you sharing insight from your PIO results. I kind of assume it’s understood that villain can and will vary their range based on our bet sizing.

If they were playing GTO they certainly would continue with at least 70% vs a 1/3 bet pot. I’m trying to give a logical range based on my experience of ranges that I want to play and how I tend to see most other (even very good) players play, which is defending a lower frequency than solvers vs. small bets. Personally, I knowingly pass on small parts of my range that I ‘should’ call with because I prefer making small mistakes than getting myself into situations on later streets where I’m liable to make big mistakes. It’s suboptimal, exploitable, and still very profitable. It’s also worth noting that (AFAIK) PIO doesn’t adjust for tournament considerations which make under-defending better.

I’m curious when you say PIO bets 1/3 pot with basically its entire range, does that include JT and all the queens? If so, I’m guessing it’s using a pretty passive strategy for the villain. This was one of my main issues with crEV for a long time, it kept finding equilibriums on low SPR flops where it bet hands that I thought were foolish. Eventually figured out that it was raising flops very little compared to what I regularly see (and do) at the tables. When I locked in more flop raises and check-raises, it started betting much more polar (although still seemed to overly favor betting draws). No idea if that’s what PIO is doing here, but I’m still going to advocate being very selective with betting strong (but not monster) draws and middle pair type hands.