Button is a drooler playing 80%. SB is a somewhat competent, but overaggro LAGGy type (AZjennyjones on FTP).

Full Tilt Poker $2/$4 Limit Omaha Hi/Lo - 6 players
The Official 2+2 Hand Converter Powered By DeucesCracked.com

Pre Flop: (1.5 SB) Hero is BB with K A 2 3
3 folds, BTN raises, SB calls, Hero 3-bets, BTN calls, SB calls

Flop: (9 SB) J Q 5 (3 players)
SB checks, Hero bets, BTN calls, SB calls

Turn: (6 BB) 6 (3 players)
SB checks, Hero bets, BTN calls, SB calls

River: (9 BB) J (3 players)
SB checks, Hero ?

You need to figure out a) how often do you win unimproved and how does Button's bluffing tendencies factor into it; b) how often do you win when you bet; c) how often do you bet and get 1 or the other to fold; d) how often do you bet and get them both to fold.

Looking at propokertools, vs. an 80% button range and a 15% SB calling range, you have 2.79% pot equity.

So your EV of checking, assuming BTN checks behind is:

0BB(.9708) + 9BB*(.0279)=+.25 BB

It gets worse if you think he will try and steal the pot and you fold, say, 50% or 75% of the time:

(.50)(.25)+(.50)(0)=+.13 BB
(.25)(.2511)+(.75)(0)=+.063 BB

Let's solve for an outcome if he bets 50% of the time. The outcome has to be >.13BB.

Now you need to find the EV for:

SB calls and wins/button folds, Button calls and wins/SB folds, Button folds and SB folds.

If the EV is greater than .13 BB, than betting is better than checking it down.

As a shortcut, I am plugging in your hand as A2Q3 vs 80% range and 15% range on this board to determine % fold. This is a tricky way of saying 'how often can TPTK beat the other two hands' and saving a lot of time. We can assume SB or Button is not calling or raising the river without at least top pair or better and folding everything else (missed lows, crappy one pairs). We are also assuming you are betting once and then done with the hand if there is any action.


So you are risking 1 bet to win 9. Let's keep it simple and not factor in ties. 43% of the time you scoop/win the high outright. 24.7% of the time you lose one bet and the button wins; 32.3% of the time you lose one bet and the SB wins.

(9BB)(.4296)+ (-1BB)(.5713)= 3.87BB - .57 BB= 3.3 BB

Conclusions:

It is better to bet in a pot this size than check it down and it is not even remotely close.

Button's bluffing range has basically no effect on this decision since you're likelihood of winning the pot unimproved is so small.

Even in smaller pots it is better to bet out although the edge decreases.

Against two other players, one or both are very often drawing to the low. It is profitable in a pot given passive postflop action to keep betting missed low draws.

You have "nothing" but the betting initiative.

SB could have A2 (got only one low on the flop) and something, why not 5, 6 or Q giving two pairs on the river. If he has that, he may very well call a river bet from hero, taken into account the failed low and flush board + pot odds.

Alternatively BTN may have a pair in addition to the J:s. He may (though unlikely) have a J and raise a bet. BTN may even reraise with two pairs (queen high), seeing the failed low an failed flush.

SB could also gamble with a J in the hole, attempting check raise (could win four BB.s). Someone of the two may very well call a bet from Hero (pot odds!) and win.

Both have stayed in the pot, which raises probability they have something (unlikely both chased a good low). If all have only high cards Hero will win the pot anyway with AK. Maybe Hero should check and hope button checks too.

Edit: while I was thinking, Gildwulfs post came in. My answer is written without the knowledge of that. I see he came to a different conclusion.

F the overthinking. You know how many times morons chase both streets for a low/low EV open-ended straight draw?? Dont give LO8 morons too much credit. Fire the 3rd barrel!

check and call the button if sb folds... i don't see any fold equity in betting and ck-call only risks a few accidental value bets from the button

Gildwulf - thanks for the great insights and maths behind it.

-wack

+10

It's a question of tenacity on the river of both of your opponents against Hero. Will either call with only two pairs in the face of a possible better hand held and bet by Hero?

If so, either bet to encourage them to continue their tenacity on the river, or check to save a bet. Most likely hand for either opponent on the river is two pairs. (But someone might have made three of a kind, a full house, or quads on the river).

If Hero bets the river, either opponent is getting 10 to 1 to call, and may call with only two pairs because he suspects Hero of bluffing - or simply because he's stupid, stubborn, or both.

It's all about knowing what these particular opponents are likely to do. You know these particular opponents better than I do.

Buzz

People don't fold when the low bricks. I'd rather vbet 77 than bluff AK here.

np

It still may be the best hand, will you check and fold?

No. This post makes sense to me. Excellent spot to Hero call if SB folds.

Here is the problem I see with a check on the river. Say I check and BB bets (bluffing or not), but now SB realizes his crap 2P might be best and that I was bluffing/semi-bluffing the whole way and decides to call thinking that this 80VP$P drooler on the button is just bluffing in position in a big pot. Now I should probably fold in that scenario because I am facing a bet and a call and I'm surely beat. But if I bet, I have the only chance to win a reasonably sized pot and if I get called and lose I definitely gain some calls in the future when I have the goods. When I do bet, both players might have me beat, but the button might fold thinking the SB is going to call and the SB might be weak enough that he folds as well, or he might have been the one drawing and missing. No one has shown any liking to this pot other than me so I see no reason to not bet unless I am just throwing in the towel and don't care about the reasonably good pot that has been built. That just seemed too weak for me. In the end I bet and they both folded - but I posted the hand because while I felt that was a great result, I wasn't sure it was the most optimal play. I now think without a doubt it was. I risked 1BB to win 9BB in the most generic terms and in more specific terms, Gildwulf laid it all out.

I'm a big fan of sprinkling semi random numbers to prove a point, but only thing Gildwulf proved was that betting is better than checking IF both your opponents fold all hands worse than Qxxx on the river and i think most of us would come to the same conclusion intuitively.

You also very likely have more than 2.74 equity in this pot based on the known characteristics of the sb, texture of the board and the action on the flop and turn also i think it's safe to assume that sb's range is wider than 15% and every action they have taken suggests that the top of their range is much less likely than middle or bottom.

And yes when you bet you can make the worst hands fold and no that is not a gain of 9BB, just a missed opportunity to induce a bluff, also known as a loss.

ps. nobody is suggesting overcalling here

I'd much rather check to one very aggro opponent than check 3way to a drooler and an aggro opponent.

If ev calcs about a straightforward one street math problem is 'sprinkling semi-random' numbers then I am guilty as charged.

You are right though that my calling range might be a little tight vs. a loose player.

So let's change it to they call with a 6 or better. That is a pretty wide range on this flop, no?

Your equity drops down to just 19%. That is a big change.

Still doesn't matter though:

.191 *9bb + (-1bb) (.809)= 1.72bb - .81 bb = 0.91 BB. Still much greater EV then checking, although it is closer.

Even if you get called 80% of the time it is more +EV to bet!

Let's say the SB is a bit looser like you say...is 40% ok?

You still have 19% equity. Almost no difference on this board. So still better than checking.

Funny enough, your equity actually gets worse the bigger the SB's range is. At 40% SB calling range, your equity drops to just over 2%.

To me the bet seems like a no-brainer, and I'm not nearly as smart as any of you.

Megabrick on the river, in a 9BB pot, and you only need to make two people fold???

I don't have your instincts yet, since I just switched from midhigh limit holdem to midhigh 08 so I have to work it out on my own

Seems like a lot of my opponents are calling me here very often when any 2P hand EVERY time. There are certain opponents I would certainly check the river against and know if they bet I can safely fold.. this setup of opponents was much more interesting than the average super LP who never folds and never raises w/o the absolute nuts.

Another point to consider for those people considering a check/call instead of a check/fold: one of them may bluff with a hand that actually beats you (2237, for instance) but will probably fold it it if you bet (especially the button). In that sense you don't even really have a bluffcatcher.

You'd be absolutely crazy to fold 2pair vs. anyone in this spot. As for the river bet, it's probably pretty close to ev neutral, so I say go for it. I have been called by hands like 2334 here though.

2.74 % or whatever are based on the assumption that opponents meekly call with their whole range on every street regardles of the board cards (you can throw some weight to the missing btf cap bet also). That is almost always a wrong assumption and sims based on that assumption give very unaccurate estimates.

Propokertools just isn't a reliable program for these type of problems. Guesstimating your equity here is something like 7-15%. As for the button, most mouthbreathers don't value bet very lightly here, but even dimmest players realise that A489 is prolly not the best hand here and will atleast be tempted to bluff. Also you almost never risk folding the best hand here if sb decides to call or raise.

As i said before only risk of ck-calling is accidental value bets, but even those are slightly diminished by the mouth breathing tendencies of the button (his likely making a hero call with pair 2's if you bet and sb ends up cussing after folding 5xxx or some other random crap)

And to add to my earlier post it really is just drawing the line as best as you can. I hope there's no disagreement in ck-calling with A344 in this spot or betting A9xx. Since neither opponent is described as weak tight AKxx must be pretty close to the spot and i'm betting everything worse than that.

I think you pretty much had it all along Wack... 9:1 odds + when you get called you give drooler "permission" to chase you down with all kinds of crap, right? Easy math is if they fold once out of 8 times, you are making money. I can't imagine that AK has that much showdown value either.

cool math and good to see EV conceptualized, but you have to account for the fact that your "top 15% calling range" is an inappropriate for SB. he's closing the action and will call with bottom pair more than 0% of the time.

i tailor my river bet accordingly to tough opponents but i know that my general looseness and aggression tends to get very light calls. I agree with cero_z that the river bet is close to break-even.