So on the monotone flop I assume I get a ton of calls from hands with one heart in them so have clear value. I'm not sure that that makes it clearly better to bet for value than checking though. It isn't clear to me that I have two streets of value here though and checking the turn in a pot twice as big while out of position and with a gazillion hands with one heart getting to realize their equity and possibly bluff me off the pot seems pretty gross.

Don't know, interested to hear what people think about this spot. It seems like a very odd board rangewise because something like a third of the time I'm guess over 60% of the caller's flop calling range is going to end up being a flush on the river, and a lot of my flop betting range will too.

c/f'ing but happy to see showdown if it happens somehow. Using this hand to bluff now seems bad since I'm blocking a lot of his folding range.

I just have to c/f here and he has to bet all his range, right? This was the interesting spot because of how the math changes when the chance to chop is introduced. Am I actually the person who is meant to bet a ton because I get the first shot at it? It's hard for me to have a big heart but not impossible, I have definitely aspired to be like Tony G in the past and checking the Qh or Jh seems fine on the turn to me and I probably have every 2h in my range still.