A little game-theory question: catching river bluffs

[Hielko]

Assume the following action:

An early position players raises, you 3bet.

Flop comes: 2 [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/diamond.gif[/img] 3 [img]/images/graemlins/spade.gif[/img]

He check, you bet, he calls.

Turn comes: 7 [img]/images/graemlins/heart.gif[/img]

He checks, you check.

River: 6 [img]/images/graemlins/heart.gif[/img]

He now bets.

He also knows that your range is now 99,9% A-high hands with a lot of AK/AQs. You knows that he know, he knows that you know that he know.... etc

How often should you be calling if villain is not bluffing to much, but also not too little?

Bonus question: If you know how often you should call, what's the easiest idea to implement this.

PS. Beforce answering the main question you should figure out how much of his range is beating you, before he bets the river. If he would be beating you a lot here you can never call, altough he is also bluffing. But I don't think that's the case here [img]/images/graemlins/smile.gif[/img].

[Sushiglutton]

This can easily get very complicated. If villain bluff too much u should always call. But this will cause villain to never bluff and then u should always fold etc. However there is a break even point were both of u bet and call with exactly correct frequency. If one of u are to deviate from this strategy u will lose money. This steady state is called "Nash equllibrium" (as in Nash from "a beautiful mind").

Here is how to calculate this equillibrium. Suppose villain will beat u with x% of his range. He should now bluff so often that ur pot-odds for calling is excactly as big as the chance u are winning. Suppose after he bets u will get pot-dds of P:1. He should then bluff y% so that:

x/y = P.

Notice that it now doesn't matter if u call or fold. To force him to play like this u should call with the same frequency as the pot-odds he is getting on his bet. He is getting (P-1):1. So u shold call 1/(P-1)% of the time.

Now this is an equllibrium because neither of u will make money on playing in an other way. Rarely u will face a villain like this, so normally it is better to try to take advntage of his tendency to bet too much or too little.

[Reaction]

*grunch*

@ 5:1 you need to be good 20% of the time to call. Which means that we need to be 60/40 to the good before he bets. Since the assumed hand range for hero dominates or beats a portion of his range before villain bets and without doing the combos or stove (@work) I will say this is a good assumption. I would only call if it is within 12min till the hour (20% of 60min is 12min).

[marchron]

Not to piss on your parade, but this should never happen, because you should almost always bet the turn with anything you have in this spot. If I'm checking the turn, it's with the specific intention of calling a river bet no matter what comes.

[Hielko]

[ QUOTE ]
Not to piss on your parade, but this should never happen, because you should almost always bet the turn with anything you have in this spot. If I'm checking the turn, it's with the specific intention of calling a river bet no matter what comes.

[/ QUOTE ]
I think that this is a good spot to check behind against an aggressive player, and to call any river bet. That said: if I see a good player use this line on this board I'm valuebetting every pair, but certainly not bluffing every hand. Sometimes folding here is certainly the right play if you don't want to be exploited. And there are a lot more situations where it is very probably that villain has just A-high and may or may not fold for a single bet.

I realize that most of the time you want to be exploiting other players instead and counting on him bluffing to much or to little. But sometimes you don't know and then you could take the safe route of the optimal calling frequency.

But that's not the only answer this thread can provide. If you know how often to call, you also know how often you should bluff here if you would be the villain. If you bluff with the right frequency you force villain to call also your valuebets, making you money.

[Buzz-cp]

If this is the scenario, then I will be betting the turn again.

counter = Bluff raise river? I really dunno..

[Aaron W.]

As hero, there are only a couple ways to look at this:

Check turn --> Call river bet
Bet turn --> River check unless you have a good value bet

Hero should think about what to do on the river before he checks behind on the turn. AK/AQ are clear value bets.

If I were villain, I would almost never bluff on the end, knowing that Hero si going to call a bunch. Therefore, almost all my bets are value bets. I would potentially bluff some of the weaker non-pair hands in my range, like QJs or JTs because now I win if I get hero to fold his K-high hands. Basically, it follows the rule of bluffing from the bottom hands in your range and value betting the top ones.

Although as villain, I would have check-raised the flop with any pair, so I wouldn't be in that situation much, either.

[Reaction]

[ QUOTE ]

Although as villain, I would have check-raised the flop with any pair, so I wouldn't be in that situation much, either.

[/ QUOTE ]

I was having trouble coming up with a range that fit into when we should call on the river. I thought of what is quoted but it didn’t click till now (maybe not even).

Following in the spirit of the OP, you (villain) should c/r bluff a losing portion (10%) of your range and call to c/r the turn with a winning portion (20% [img]/images/graemlins/confused.gif[/img] doesn’t seem right), yes? Then when the hero checks behind, you wind up in a position when you are calling the flop with draws that miss and a few winning pairs.

[Shillx]

Think about what the guy is check/calling the flop with. Does he really have KQ or AT? Your AK is going to be in bad shape. Anyway the GT here is complex but it shouldn't be too tough to visualize.

If the guy has something like AQ he should sometimes bet and he should sometimes bet a hand like 88 or 99. It gets more complex if you think you can bet AK for value on the end but doing so is a mistake against a smart player. If you will bet when checked to, he should go for a check/raise with said hands some % of the time. The problem with value betting is that he figures to either fold or raise so it has no value with AK. You have to be able to show up with a hand like AA or KK to make it work. It is risky since you might lose value on 4th street but you should do it against a good, tricky player.

Your optimal strategy would be to check big pairs some % of the time on 4th (and bet AK/AQ some % of the time) and bluff and bluff-raise AK some % of time on the end.

[Gap23Razor]

here's my guess...(i hope i pass the test as i need to keep my B average so i can get into grad school [img]/images/graemlins/wink.gif[/img])

assuming there are 8 small bets (after rake) in the pot by the time we get to the river, the early position player should bluff 1 time for every 5 times he has a solid hand as he will be offering 5 to 1 odds (10sb to 2sb needed to call) to the other player to call

the caller needs to call around five out of every six times he is in this situation...an easy way to randomize calling would be to look at your watch or cellphone...if the second hand is within the first 10 sec of the minute, fold
late edit---
OOPS DID NOT SEE SOMEONE HAD ALREADY ANSWERED AS I DID...I GUESS I DON'T PASS [img]/images/graemlins/frown.gif[/img]