3-bet preflop, checked on 2 streets, bet size on river?

There's never a cookie cutter answer. It always depends on your villains, what you range them on, and how much you think they would call. In this hand I would probably bet 100 even.

In future hands be sure to post your exact position and the stack sizes because 100 IP is a little too much (not that we always have to 3bet tens).

If you get into these situations, just stop, breath, and think. Don't worry if the dealer is saying "it's on you", just take a deep breath, relax, think, and act.

Doesn't appear that anyone has anything. So bet small.

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H was in the cut-off.

ight jus go (20+20) X 2 = 80 then.

How much would you bet with an Ace-King-high bluff here? Bet that much. 😉

I really think the answer is “a ton.”

This is what I tried to do.
I paused for about 6 seconds and bombed the river for $300.
V actually tanked for 1-2 minutes, which had me hoping, but ultimately folded.
Then I started thinking I made a big mistake, that $300 was way too much, and he probably would have called something in the $100-150 range if that prolonged tank meant anything.

I’d be curious to learn whether it’s a “solver-approved” sizing. My thinking was:

1) We are going to very often arrive at this River with a medium-strength hand that’s happy to check down. AA, KK, AQ, KQ, AJ, etc, these are all hands we just want to check back and get to showdown. (We will have bet all our sets earlier.)

2) Therefore, the only hand we’ll want to bet for value will be a straight, and the only straights we’ll have here are TT and ATs.

3) The only hand we’ll have that needs to bluff is exactly AK. Everything else has some showdown value.

4) Since we are very rarely betting on this River—since our betting frequency is very low—therefore, our betting size should be huge.

But as I said, would be happy to hear from the actual experts here. But I’m pretty sure OP is right to overbet with TT (so long as he’d do the same with AK!)

I would have bet around $100.

It doesn't appear V has anything strong, and there's four to a straight on board. The best you can hope for is that maybe he has 9X. He probably has less than that.

I get what you're going for, trying to make your hand look like a bluff with something like AK, but you could also have some decent 1P hands here that likely beat whatever V has.

If $300 got Villain to tank, you didn’t want to bet only 100.

Let me explain. Let’s suppose for argument’s sake that you are right that he would have called $100. And let’s say he always calls that.

In that case, if he calls $300 more than one-third of the time, you would rather bet $300 than $100. And the fact that he tanked means he probably actually calls a pretty good deal of the time, enough to make $300 worth it.

The real question is whether you could bet something like $250 and disproportionately increase his calling frequency.

All due respect, if we were to bluff here, we wouldn't need to bet very big when V has checked to us three times. This seems like one of those spots where if we even breathe on the pot, V will fold. If we were to bet $50 here as a bluff, we'd probably be printing. Even betting $100 may be too much.

We should recognize that we made a pretty large 3B pre, yet we checked back flop and turn, and V didn't even attempt a stab at it on the river.

I might actually like a reverse blocker bet here, like $40 or $50, hoping to induce a raise from V.