Math question - unsure how to figure best play versus $$ return

[na4bart]

Played this hand in a 20/40 game a couple of months ago and was thinking about it recently. Can't figure out if my play gave me the best return on the dollar long run versus the other obvious option.

I held A [img]/images/graemlins/spade.gif[/img]A [img]/images/graemlins/club.gif[/img] UTG+1 and raised. All folded to sb who called. bb mucked. $100 in the pot preflop.

Flop 2 [img]/images/graemlins/club.gif[/img]6 [img]/images/graemlins/club.gif[/img]Q [img]/images/graemlins/club.gif[/img] $80 each goes in on the flop (bet, raise, 3 bet, 4 bet) making the pot $260.

The turn is the A [img]/images/graemlins/diamond.gif[/img] and sb check raises my bet.

Now this is where I get lost in the math. I am acting on the assumption sb does have the second nut flush. Is my return greater if I just call his raise and hope to hit one of my 17 nut outs and get a hopefully extra bet on the river or 3 bet with the intention of showing down the river if I miss. the sb plays well enough to not 4 bet the turn without the nuts, but I still give that possibility about a 10% chance. Given the size of the pot at the point sb check raises the turn where do I earn the most: calling the $40 raise, 3 bet for another $80 and maybe have to put in $120 if I get 4 bet?

I caught a Q to win the pot and was paid off. Whether or not I won is not my question. I understood the situation was profitable, I just don't know which of my options would have given me the greatest long run profit.

Sorry if all this is a bit rambling, but I just do not write very well to go along with my crappy math. Would very much appreciate some feedback on how to figure return in these types of situations. Especially any short cuts that can be used in the heat of the moment. Much thanks in advance to all you math types out there.

[pfkaok]

calling is better if you know he has the flush... you have a lot of outs, but you're still less than 50% to win, so you lose money on each extra bet going in on turn, b/c its not like he's ever going to fold his flush, and, if anything, capping the turn might get you less action on the river if you hit.

[na4bart]

Thank you. See, didn't even occur to me about losing $$ on each bet going in on the turn assuming sb had the flush. All I knew at the time was that I would make the nuts a tiny bit less than 40% of the time. BTW, sb showed K [img]/images/graemlins/club.gif[/img]7 [img]/images/graemlins/club.gif[/img]

[pfkaok]

Well yeah, i mean you're not losing a lot... but if you 3-bet, and then he caps it, you'd be losing almost half a BB ( 4 bets go in, and you get .4 * 4 of those back on avg).

so pretty much you lose .2 on each extra bet that goes in.

[na4bart]

Again, thanks. Sometimes I just see stars shinning when I pick up a hand with all of its outs being to the nuts. A draw like that is so rare that I just get carried away. Fun, but not good poker...lol

[flawless_victory]

if the river is the 3 [img]/images/graemlins/diamond.gif[/img], are you gonna pay it off? if the answer is no, call... if yes, threebet.