Am I thinking correctly here about +EV decision?

[storm75m]

I just want to see if I'm thinking this through correctly... I didn't save the HH so I'll try to remember the details.

25NL 6 Max on Party (.10/.25 blinds)

UTG just bought in for another $25 after loosing two buy-ins in the past 20 minutes. Plays a little too over-aggressively, and has run into some big hands. He had a decent stack when I got to the table, so I figure he might have a little brains... I've pretty much been playing ABC poker, (but pulled a couple of big tricky moves) and built my $15 buyin up to $35.

UTG raises preflop to $2.5 (kinda big, but he seems to be betting hard). I call on the button with pocket fives, everyone else folds. Flop comes 467, rainbow, giving me an OESD. UTG bets $7, overbetting the pot. I immediately push all in for the rest of his stack (~$15).

Here is my reasoning...
I think there is probably a 10%-20% chance that he will fold right there and give me credit for a set, given the quickness of my raise. (Not TOO likely because he's probably tilting a little)

There is probably a 20% - 30% chance that he is just playing overs and completely missed the flop, meaning my fives are good.

Then there's the ~35% chance that I make my OESD by the river to beat whatever he could be holding anyway.

So do all these percentages make this a +EV decision in the long run, even though my hand isn't really that strong? I think I already know that this was a good play, I just want to make sure that my thought process was correct.

Results in white below:
He calls with KJs, hit a K on the turn, and I hit my 3 on the river to make the straight.

[LeFou]

i'm really not an EV calculator, but this looks fine to me. You have multiple ways to win the hand (don't forget the two fives in addition to the OESD ... catching a 5 is not likely to make opp a straight here)

I might even raise this smaller, for value. Advantage being that a play-back would indicate a higher pair than fives, and you just calculate the call based on the 10 outs.

[dalecooper]

If he's as aggressive as you say I'd say 20% chance of folding is generous. He's probably calling with overcards and definitely calling with an overpair. I'd put that around 10%. If he calls you, I'd say it's basically 50/50 that he has an overpair or overcards (he's more likely to have overcards, but also more likely to fold overcards; he probably doesn't ever fold overpairs). So:

- pot as of the flop is $5
- he bets $7, making it $7 to you on a $12 pot
- you put him all in for another $15 approx.
- if he's on overcards you're like 80/20 to win
- if he's on an overpair you're about 40/60 to win

So 10% of the time he folds and you win $12. 45% of the time he calls, and you're 80% likely to win $27. 45% of the time he calls, and you're 40% likely to win $27. Cost to you is your $22 bet.

If I'm doing the math right, your expected value for the hand is about +7.86. Which is obviously quite high, so I think that's a good move. If we said he would call every time and had an overpair every time, this is a terrible move and -EV, but the strong probability of him calling with a worse hand, plus the moderate possibility of a fold, make it a good play.

Of course, I'm taking your word for it that he's so aggressive that he'll call with overcards in this situation. If he probably would fold something like AK here, your EV drops dramatically.

[storm75m]

Of course, I'm taking your word for it that he's so aggressive that he'll call with overcards in this situation. If he probably would fold something like AK here, your EV drops dramatically.

Nice math, good analysis, thanks. So even though I still make money if he folds his overcards, the decision would be less EV if say he wasn't on tilt and could let go of his hand? I guess this is because it doesn't make up for the additional money that I would make with him calling the extra $15 with the worse hand?

Think I just learned something new today, yippee.

[dalecooper]

Right - because you're betting $22, you'll only win $12 if he folds the worse hand, but you may lose $22 if he calls with an overpair. Of course your outs are still good for a 40% win rate even if he calls with an overpair, but still your EV is a lot lower because he's not artificially inflating it by calling with a much worse hand.

This is why, even though they deliver many infuriating bad beats, loose players are good for your bottom line. The more of your bets they call with bad hands, the better off you are.