Getting the last word (bet) on the river...

[Mathieu]

This post started as an off topic tangent to an another thread and I decided to give it it's own thread.

Here's the deal:

You are on the river, out of position with a strong hand, and you and villain have been gunning it on the turn. Villain capped the turn, so he obviously likes his hand.

If the river is a card that should not have helped neither you or villain, and the "dialogue" that started on 4th street has reached a point where if you bet and get raised, it will mean that you should just call the raise.

Do you bet/call, or check call, and what are the factors to consider?

OK this is too vague so lets look an example:


Preflop: Hero is SB with Q[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/diamond.gif[/img].
1 fold, UTG+1 calls, 1 fold, MP1 calls, 4 folds, Hero raises, 1 fold, UTG+1 calls, MP1 calls.

Flop: (7 SB) 9[img]/images/graemlins/club.gif[/img], 8[img]/images/graemlins/spade.gif[/img], Q[img]/images/graemlins/heart.gif[/img] (3 players)
Hero bets, UTG+1 calls, MP1 folds.

Turn: (4.50 BB) A[img]/images/graemlins/spade.gif[/img] (2 players)
Hero bets, UTG+1 raises, Hero 3-bets, UTG+1 caps, Hero calls.

River: (12.50 BB) 2[img]/images/graemlins/spade.gif[/img] (2 players)

Hero..

This was my question to Aaron regarding the river bet:

[ QUOTE ]

Why do we (many of us do it) bet the river HU when our opponent has shown a lot of strength and we think that if we get raised it will be bad news.

I think if the raise will mean that we are more likely to be behind, then we should just check-call. This way we don't allow our opponent to get 2 bets in when we are behind.

My point is that it seems like we often bet hoping that our opponent will "just call" in situations where our opponent got the last raise on the turn and is obviously going to bet if we check.

So I think that for the bet/call to be better than the check/call we have to think that a raise by our opponent will imply that our winning chances are around 50%-65%. If there are any higher we should bet-reraise and any lower we should check-call.

Do you agree?


[/ QUOTE ]

Special thanks to Aaron for responding to my post. I will post his analysis as a reply to this post in order to allow grunching.

[Mathieu]

As promised, here is Aaron's analysis:

[ QUOTE ]

Aaron,

I know this is off topic, but I have theory question regarding the river bet.

"Why do we (many of us do it) bet the river HU when our opponent has shown a lot of strength and we think that if we get raised it will be bad news."

I think if the raise will mean that we are more likely to be behind, then we should just check-call. This way we don't allow our opponent to get 2 bets in when we are behind.



[/ QUOTE ]

But then you also don't win a bet when villain has a hand which is worse than your and checks behind. In this case, I don't want him to check behind with two pair because he's afraid of the flush.

[ QUOTE ]

My point is that it seems like we often bet hoping that our opponent will "just call" in situations where our opponent got the last raise on the turn and is obviously going to bet if we check.

So I think that for the bet/call to be better than the check/call we have to think that a raise by our opponent will imply that our winning chances are around 50%-65%. If there are any higher we should bet-reraise and any lower we should check-call.

Do you agree?


[/ QUOTE ]


The short answer is that the bet-call and the check-call lines are both close in value, and it goes either way unless you have extra information. HPFAP suggests that you want to believe you have the best hand 55% of the time when you are called to make a river bet correct. Since I'm always getting called here, that would imply I want to have the best hand 55% of the time to make betting correct (55% instead of 51% to cover the times I get re-raised and lose).

But that's only an estimate based on your assessment of your hand ONLY and (as I recall) is more about value betting than value calling (inducing a bluff... or in this case, getting villain to bet a strong hand that's worse than yours). I'm not going to worry about the bet-3-bet line because you've got to have a very very strong hand to get capped on the turn and still 3-bet the river.

Here are the four things that can happen (Hero is OOP):

1) check-check
2) check-bet-call
3) bet-call
4) bet-raise-call

We need to assign various probabilities to these. To do this, we need to give villain a hand range:

Hands that beat me
AA = 3 ways
JT = 16 ways
Flush = 3 ways (estimating that it's about a likely as AA based on the action)
Total = 22 ways

Hands that I beat
99 = 3 ways
88 = 3 ways
AQ = 3 ways
A9 = 9 ways

A8 = 9 ways
Q9 = 3 ways
98 = 9 ways
Total = 39 ways

This is about 65-35 for me to be winning. Since I'm not folding this, all we need to do is compute river EV on the extra bets we're putting in.

1) check-check -- This happens is more a function of how villain plays than what he holds. I suspect this gets checked through 20% of the time when villain gets cold feet because of the flush. Checking through is 0 EV because I don't win or lose any bets on the river, and it's just a showdown computation.

2) check-bet-call - So the 80% of the time villain bets the river, and I win 65% and lose 35% of these cases.

What is the EV of checking?

EV = 0 + (.80*.65)*(1) + (.80*.35)*(-1)
= .52 - .28
= .24

The betting line is much harder to compute because we just don't know what villain's playing style is. To make things concrete, we'll assume he raises A9 and better and calls everything else. You can tweak this around to see what other assumptions give.

3) bet-call - Villain here is on one of the 21 ways of holding two pair worse than A9. This is 21/61 of the possible hands. We win one bet from this situation.

4) bet-raise-call - Villain does this with the rest of his hands. We win two bets out of 18/61 of these and we lose two bets with 22/61 of these.

What is the EV of betting?

EV = (21/61)*(1) + (18/61)*(2) - (22/61)*2
= .34 + .59 - .72
= .21

Obviously, you don't do this in the game. And you can see how very close in value this runs (espcially considering that .03 BB is a tiny fraction of the 12 BB pot to start the river action.

What are the key factors?

1) How often does villain check behind? If he checks behind more, EV of checking goes down.
2) How aggressive is villain? More aggressive villains will call your river bet with fewer hands and re-raise more of them. This means you get two bets with the best hand more often than you get just one.
3) What range of hands does villain have? In this case, if you were to take away the flopped straight possibility, betting goes way up in value because now the number of hands which beat me is greatly diminished.

That was probably about ten times longer than you expected.

[Mathieu]

Aaron,

Thanks for the analysis, it was very instructive, here are my comments.

[ QUOTE ]
But then you also don't win a bet when villain has a hand which is worse than your and checks behind. In this case, I don't want him to check behind with two pair because he's afraid of the flush.

[/ QUOTE ]


This is the Key factor #1 that you mentioned:
"How often villain will check behind with a weaker hand?"

I totally agree that this is a Key factor, but I think we disagree about how often villain might check behind with a weaker hand.

In this case, the flush is backdoor, and you and villain already indicated that you liked your hands on the turn. So I don't think villain, after capping the turn, will check very often here (say less than 5%).

This is one of the main reasons why I reccomend check calling that river. I am simply convinced that after capping the turn, villain will bet this river if checked to.

Key Factor #2 "How aggressive is villain"

[ QUOTE ]
More aggressive villains will call your river bet with fewer hands and re-raise more of them. This means you get two bets with the best hand more often than you get just one.

[/ QUOTE ]

Here I agree with you 100 %. However, there is another factor which is related to this one. How good is villain? Can he understand the dialogue that is going on?

When we bet into him after he capped, we give him an extra piece of information about the strength of our hand and we allow him to use it by either just calling or raising. If villain often overplays his hands, he may not exploit this, since he will raise when he should realize that his hand does not warrant it anymore.

I think factor #2 turns out to be somewhat equivalent to "What will a raise from your opponent imply?". In other words: "How does our hand compare with the range of hands that he will raise with?

[Jarcon]

I think it depends who are you against? If opponent is good player, I think he caps only sets and straight. Then you should check-call.

If your opponent isnt that great player and caps 2 pair also I think you should bet-call.

[DrunkHamster]

I appreciate the analysis here, it seems well thought out and reasonable. However, I think that I prefer checking and calling by a fairly large margin.

Firstly, in my experience, people who cap a street RARELY check through the next one. If he had raised the turn, and we had called, I can easily see a donkbet being right. But seeing as we 3 bet and he still capped, I would think it is extremely unlikely for him not to bet.

Secondly, how many villains will cap a relatively weak 2 pair hand against consistent opposition? Only extremely aggressive ones IMO. Taking out a couple of these hands from the range gives us a significantly worse chance of winning. And if the opponent is extremely aggressive, what is the harm in c/c this street? I think betting is a lose lose proposition.

Also, I think we need to be more than 55% sure that we have the best hand here. Normally when I use this figure to see if a value bet is worth doing, it is after I have been the aggressor. The thing here is that we are far more likely to be raised than usual, simply because the villain capped the turn. I would like to be 65% sure I was ahead to bet out here, because I'm pretty sure I'm going to be paying 2 bets.

[Mathieu]

DrunkHamster,

Thanks for sharing your thoughts. I would like to add something to the numbers that you used.

By saying that we need to be a 66 % (2-1) favorite, we are assuming that villain will only raise with better hands. If villain will raise with weaker hands, we don't need to be this much of a favorite.

I think it is also important to estimate how does our hand compare with the hands that villain will raise with.

For example, we could be 60 % favorite given what we know so far, but if we are still above 50% vs villains' raising hands, then betting would still be profitable I think.