Bet or check this river?

[Catt]

[ QUOTE ]
That's incorrect. On the river, hero risks 1 BB to win 6.5 BB. If his opponent folds 50% of the time, Hero's EV != 0. His EV = (.5)(-1) + (.5)(6.5) = +2.75 BBs.

[/ QUOTE ]

There's no +EV to Hero's bet and Villain's fold unless Villain folded a better hand.

[SippinSoma]

Okay, I understand where we're confused. I don't care what Villain holds and folds, as long as he does it. I don't know this villain well enough to know if he got here with a better hand or not. He could have overcards, trying to incorrectly spike a pair. He could have a small pocket pair that he's calling down with the whole way. He could have a weaker Ace. There are too many possibilities. And he doesn't know me - he may think firing a final barrel is the sign of an overpair. There is just not enough information. So I'm not going to analyze any of this unless I have taken notes on this.

I consider the river bet to be a steal. Its not a value bet, but it can be +EV because of the size of the pot. You were analyzing whether the bet in a bubble; as if the pot were 0 BB. But it's not.

[mantasm]

If he has a missed draw that hasn't paired he'll fold. If he has a pair, pretty much any pair, he'll call. Sometimes he'll call with ace high but way more than half the time he calls he will have paired. He'll call with a pair of 3's here because he thinks you have overcards. You lose money by betting. Check behind and expect to win some of the time when he has a missed draw or random unpaired cards.

[SippinSoma]

Catt, I agree (although you forgot to mention when villain calls down with a weaker hand). However, we do not know Villain's folding tendencies on the river so I think this river bet has more merit than everyone is giving it.

I don't think Hero got here correctly. I don't usually bet every street with AK UI. But the past does not matter. I'm at the river. The pot is 6.50 BB. Villain checked to me. I can check behind and stay neutral with EV. She won't go out to dinner with me, but she's not screening my calls. Sometimes I'll win this 6.5 BB pot, most of the time I won't. But if I bet, I might be increasing my chance to win this 6.5 BB pot, sometimes win a 7.5 BB pot, or just lose 1 more BB. And I think in a lot of cases, EV just noticed I've been packing on some muscle. And she likes it.

I'm not saying this is correct. But we do not have enough information on villain to say what he folds or calls down with. So there's no point in trying to analyze it. This is why taking notes is so important. Betting this river and seeing what hand villain calls me with is huge for note taking.

I'm done for now, I still need to eat breakfast. Join us in #sstakes @ efnet.

[DBowling]

[ QUOTE ]
I consider the river bet to be a steal. Its not a value bet, but it can be +EV because of the size of the pot.

[/ QUOTE ]
You are correct, this is where we differ. I think if you are attempting to steal with AK high you are making a mistake in most instances. This may work against an opponent who chases underpairs to the river and then gives up. However, in my experience, most dont give up. Dont try to bluff a calling station.

[ QUOTE ]
You were analyzing whether the bet in a bubble; as if the pot were 0 BB. But it's not.

[/ QUOTE ]

again, if we are talking about a value bet, the size of the pot does not matter. if it is a steal, you are correct, pot size must be taken into consideration.

[mantasm]

Betting the flop and turn is the best way to play it. You have a very strong draw headsup in a medium sized pot. If you bet the turn he'll probably fold between a third and a half of the time, so the bet shows immediate profit. Plus you improve to top pair on a fairly dry board or a flush pretty often. And you may have the best hand. No reason to take a free card. Or give one.

Oh and betting doesn't really increase your chance to win the pot because not one better hand will fold. The board is dry, you raised preflop, he thinks you have overcards. He will call with any pair, you're not stealing anything.

[SippinSoma]

Great. And FWIW, Hero didn't list any worthwhile stats here, so everything is completely up in the air. A WTSD would have been nice.

Seacrest out.

[W. Deranged]

There has been a lot of confusion in this discussion, it appears to me, because different posters are considering different reasons for a river bet and are using different lines of reasoning to argue for or against a bet. If you look at the bet purely in terms of value, you are looking for a call and consider only the effect of the final river bets, not the amount of money already in. If you are thinking in terms of a bluff, you consider the whole pot. To clarify, I'll give a shot at how I think the calculation looks.

The key point to remember is that we are looking at how much a river bets gain OVER CHECKING. We therefore only count the whole pot in our EV in cases when checking behind would not have won that money.

We consider two cases: villain has a better hand or a worse hand.

If villain has a better hand (with probability B), then the EV of a bet is:

(-1)*Cb + 6.5Fb,

where Cb and Fb are the probabilities villain calls with a better hand or folds with a better hand. We assume that hero folds to a check-raise so we count checking-raising and calling with a better hand to be the same thing. We will note the possibility of opponent check-raise bluffing the turn but not include it in the calculation because it is extremely unlikely.

If he has a worse hand (total Prob. W), EV for the river bet is:

1*Cw + 0*Fw

Note that the EV is 0 when your opponent folds a worse hand, because that gains nothing over checking.

So, total EV for the river bet is:

(-1)*Cb + 6.5*Fb + 1*Cw + 0*Fw

or

6.5Fb + Cw - Cb

This gives the result many people have explained:

6.5Fb + (Cw - Cb) > 0

is the condition for +EV

In other words, we need the equity from bluffing (6.5Fb) and the value equity (the Cw - Cb, the expectation for a pure value bet) to be positive.

Clearly, Cb (the prob. villain will call with a better hand) is pretty large. So we need the sum 6.5Fb + Cw to be very high. As a few posters have mentioned, these two numbers tend to be negatively correlated... players don't often call down with worse hands a lot and fold the best hand a lot.

Hope this helps.

[TiltsMcFabulous]

[ QUOTE ]
Great. And FWIW, Hero didn't list any worthwhile stats here, so everything is completely up in the air. A WTSD would have been nice.

Seacrest out.

[/ QUOTE ]

WTSD = 69%

Villian was a station. I had seen him call with A high before, but generally he just mindlessly calls with any pair or hope of improvement.

I think the river bet was a poor choice.

[Catt]

[ QUOTE ]
I don't think Hero got here correctly. I don't usually bet every street with AK UI. But the past does not matter. I'm at the river. The pot is 6.50 BB. Villain checked to me. I can check behind and stay neutral with EV. She won't go out to dinner with me, but she's not screening my calls. Sometimes I'll win this 6.5 BB pot, most of the time I won't. But if I bet, I might be increasing my chance to win this 6.5 BB pot, sometimes win a 7.5 BB pot, or just lose 1 more BB. And I think in a lot of cases, EV just noticed I've been packing on some muscle. And she likes it.

[/ QUOTE ]

I wasn't trying to argue that the EV is checking is greater than the EV of betting, though that may very well be the case. I was commenting on your view that, if Villain folds 50% of the time, the EV of betting is +2.75 BB. That is not the case. That would be true if Villain always has a better hand and folds 50% of the time to the bet. If Villain has a worse hand and folds to your bet, that bet has neutral EV (other than meta game considerations like not having to show your hand). You would have won whether you bet or checked.

I agree with you that we need a lot more information to accurately gauge the EV of a river bet. We need to know what Villain is likely to take to the river; and we need to know what Villain is likely to call the river bet with. If Villain always calls with any small pair to the bet and always folds A-high, then the river bet has -EV. If Villain calls with any pair and with A-high (or worse) hands, then the river bet might have +EV depending on the likelihood of him being on the river with no pair versus a pair (the no pair hands would obviously have to substantially outnumber the pair hands). If Villain is willing to fold a small pair a decent portion of the time (like 15%+ of the time) and always folds no-pair hands then the bet has +EV because we fold a better hand often enough to justify risking the 1 BB with a worst hand.

My only point is that there is no way the river has +EV of 2.75 BBs when Villain folds 50% of the time unless Villain is folding a better hand 50% of the time and/or making up for it by calling with a worse hand a significant portion of the time.