I've been messing with a hand range calculator of sorts, and this is what I'm coming up with.
- Let's assume our opponent is very loose, playing ~50% of his hands. I'm assuming any pair, any 2 broadway, any 2 suited, and some connected cards. The actual distribution doesn't really matter, as long as we lump in all the hands he could possibly have on the turn.
22+,A2s+,K2s+,Q2s+,J2s+,T2s+,92s+,82s+,72s+,62s+,52s+,42s+,32s,A2o+,K9o+,QTo+,J9o+,T9o,98o,87o,76o,65o,54o
Of this hand distribution, given the board and our 2 cards, he has:
A straight (Kx): 0.1807 => 18% [our equity = 12.5%]
Better 2 pair or a set (AQ,AJ,AA,QQ,JJ,TT): 0.0402 -> 4% [our equity = 10%]
Lower Straight (98): .0321 => 3% [12.5%]
Same 2 pair (AT): 0.0080 => 1% [50%]
Worse 2 pair (QJ,QT,JT): 0.0422 => 4% [90%]
A heart draw (xhyh): 0.0863 => 9% [80%]
Something else: 0.6104
Let's assume that he wouldn't play "something else" in this manner. Therefore, our opponents' rebalanced holdings are:
A-hi Straight: 47%
Better 2pair/set: 10% (probably way less likely - most people raise big pairs preflop)
Low Straight: 8%
Same Hand: 2% (unlikely, but low percentage anyways)
Worse 2pair: 10% (probably not likely - i think people check/call with these hands)
Heart draw: 23%
Even if our opponent could have any 2 hearts, he still has the ace high straight at least twice as often.
Pot should be like 7BB on the turn right? I see 15SB after flop = 7.5BB on the turn (minus rake => 7BB). After villain's turn bet, we're getting 8:1 immediate odds.
Let's say he's only betting a flush draw (33%) or the nut straight in this situation (67%), and will follow up with a river valuebet/bluff 100% if we don't raise the turn. Let's also assume that he'll bet/call the river if an ace or T comes. However, if we raise the turn, he'll 3bet w/ the straight and call with the flush draw (but not bluff the river). I'm also ignoring chops (3 kings left)
Strategy #1: Call turn, call river (raise if we boat up)
- result 1: we boat up/he has a straight (+10) * (.08)*(.67)
- result 2: we miss / he has a straight (-2) * (.92)*(.67)
- result 3: we boat up/he misses a flush draw (+9) * (.08)*(.33)*(.8)
- result 4: we miss / he makes a flush (-2) * (.92)*(.33)*(.2)
- result 5: we boat up/he makes a flush (+10)*(.08)*(.33)*(.2)
- result 6: we miss/he misses a flush draw (+9)*(.92)*(.33)*(.8)
Total: +1.6 bets
If he never bluffs the river, and we still pay off every time, we're +1.36 bets
Strategy #2: Call turn, fold river unimproved
If he's bluffing 100% of his missed flush draws, we're -.14 by calling and folding the river.
If he bluffs 50%, we're +0.95 bets
So it seems like if we expect our opponent to play turned flush draws in this manner (and he has a flush draw this often), calling turn/river unimproved seems ok.
Strategy #3: raise/call turn, check/fold river unimproved (assuming our opponent doesn't bluff)
We're +0.37 bets
Note that these are very optimistic assumptions -- we're assuming that our opponent could hold any 2 hearts in the deck when he bets out on the turn. If we assume our opponent has a straight 80% of the time and a flush draw 20%, calling down is still ok at +0.5 bets; raising and getting 3bet on the turn becomes a disaster (-.84). Calling and folding becomes an option vs an opponent who never bluffs the river, but call/calling remains a reasonable option.
So in conclusion:
raising turn = bad
calling down = ok, but only if your opponent might donk a flush draw a reasonable % (like, at least 15% or so) and not just the nuts.