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.
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.