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The math in the above post is not correct. This is actually a scenario where even though you’re drawing for the nuts, your opponents cards really matter quite a bit.
The 35% to win is assuming only the nut flush would be good, meaning your opponent has AJ. Also, this and every other percentage below are assuming you see a river which I mention more below. You’re only 19% to catch on the turn, so you need to calculate the odds you think you’ll pay if you get to the river.
Any opponent other than AJ materially changes the odds. Any other pair of jacks or pockets better than your 9 (as turned out to be the case) increases your outs by 3 aces to 12 total, up to about 45% before we take away his 3 king & 2 jack redraws. Call it 44%. In this case the pot was 3-ways with Jx mucked meaning 7 redraws, call it 43%
However, if your opponent has 2 pair or a set already, not only is your ace not good, but you’re dodging far more redraws. J5, 75, or any set take away the 5d from your outs. Other 2 pair/sets make 4-10 cards in the deck into full boat cards which backs you to ~31% (j7), ~28% (J5,75), ~23% (any set).
So the reason I responded here is to note how nut draws are often oversimplified, even though it seems like they’re straight forward. 23% to 41% is a huge difference (and this doesn’t count opponents like 8d6d or 6d4d where you’re way in the lead).
The percentage regarding the direct odds for your first call would be $150 for a pot of $400 total after the call, or 37.5%. That’s irrelevant because it just seems too unlikely you’ll see the river without paying more. Implied odds here are likely UTG folds and all-in on the turn so $450:$1000 (45% i.e. fold), or if the UTG calls or shoves $450:$1400 (31% i.e. ehhhhhhh?).
In hindsight it was a good call. 3-way pot against players sharing top pair, your ace is good means 43% from the first bullet point means you’ll put in 100%/43% * $450 = $1047 to get $1400 in the long run. Had UTG folded it would have been a bad call. Had any opponent had a set it would have been a bad call. 2-pair and it’s break-even at best.
I would almost never make this call. While pro players can concern themselves with the “correct” play nearly 100% of the time, most of us have other things to think about. Getting it in with a draw on a pot you’re stuck $15 in means you are PROBABLY going to lose money right now, even though your eventual profits might exceed losses. And even though the UTG calling is what is giving you the odds, it pretty much means you’re never against Kd3d+ or other hands you’re way ahead of. Another draw like this next hand and chances are you’re down $900 or felt in a hurry trying to get a small profit. If this guy is playing as aggressive as it sounds I would wait for a spot where I’m ahead. I don’t know what your bankroll is like, but I’m a rec player and most players like me are not comfortable getting stuck that much trying to catch draws I’d so far paid $15 for. If I was up and had $1,700 instead of $700 I might give it more thought, but then again I’d usually rather allow it to play out and try to stack the aggressor on a different hand.
Squeezing with a 3-bet from the button would not have been a bad move, although in this example I think if 2 players are getting it in with top pair OK kicker I doubt the outcome would have been different.
You’re not going to “out play” loose players without high-equity hands.
