Checking Behind Turns Versus TAGs

[gaming_mouse]

Here is a hand against against a TAG that I botched nicely. This guy had a turn AF of 6 after about 30 hands. Clearly it was idiotic to bet, and I should have checked behind. Assuming that I did, would you c/call the river, or c/fold it?

In general, should it be standard practice to check behind versus TAGgy players who like to c/r? Let's assume they do it both as a bluff and for value. Obviously this kind of play puts the TAGs opponents (me, in this hand) to a decision -- they either bet and risk losing an extra BB when behind, or risk giving up a free card when ahead. Which is worse? How would analyze the situation (hand reading + math) on the turn in this particular case?

Also, I challenge anyone to come up with a line that loses more chips than mine.

Party Poker 3/6 Hold'em (9 handed) converter (http://www.selachian.com/tools/bisonconverter/hhconverter.cgi)

Preflop: Hero is CO with T/images/graemlins/spade.gif, T/images/graemlins/club.gif.
UTG calls, <font color="#666666">2 folds</font>, <font color="#CC3333">MP2 raises</font>, <font color="#666666">1 fold</font>, <font color="#CC3333">Hero 3-bets</font>, <font color="#666666">3 folds</font>, UTG folds, MP2 calls.

Flop: (8.33 SB) 6/images/graemlins/spade.gif, 6/images/graemlins/club.gif, Q/images/graemlins/heart.gif <font color="#0000FF">(2 players)</font>
MP2 checks, <font color="#CC3333">Hero bets</font>, MP2 calls.

Turn: (5.16 BB) 3/images/graemlins/spade.gif <font color="#0000FF">(2 players)</font>
MP2 checks, <font color="#CC3333">Hero bets</font>, <font color="#CC3333">MP2 raises</font>, Hero calls.

River: (9.16 BB) A/images/graemlins/club.gif <font color="#0000FF">(2 players)</font>
<font color="#CC3333">MP2 bets</font>, Hero calls.

Final Pot: 11.16 BB

[Shillx]

Checking behind is too risky imo. With TT there are just too many ways you can offer him a free card. When he check/raises the turn and the river comes an ace, I think you can find a fold. Even if he has something like AK /images/graemlins/spade.gif you are now beat.

Brad

[PancakeBoy]

Fold the turn! What are ya doing....u have only 2 outs

[Alexthegreat]

Against a TAG I'm folding to the checkraise, or at the most checkfolding the river...He's pretty much owned you at that point if you pay him off...

[gaming_mouse]

[ QUOTE ]
Checking behind is too risky imo.

[/ QUOTE ]

really? so you like my turn bet, but just think i should have folded the river?

the thing is... i don't see him folding to my turn bet, because of the steal war thing going on. so i'm actually not risking much with the free card -- i'm only missing a bet the times i am ahead. whereas the times i am behind, i lose 2 BB.

so do we think i am ahead here, after his flop call, at least 1/3 of the time?

[Alexthegreat]

[ QUOTE ]
In general, should it be standard practice to check behind versus TAGgy players who like to c/r? Let's assume they do it both as a bluff and for value. Obviously this kind of play puts the TAGs opponents (me, in this hand) to a decision -- they either bet and risk losing an extra BB when behind, or risk giving up a free card when ahead. Which is worse? How would analyze the situation (hand reading + math) on the turn in this particular case?


[/ QUOTE ]

I don't have any math figures for you, but if you can bet and fold to a checkraise, it's the best line...you won't lose any more than one bet, and you won't give him a free card...If you are worried about being bluffed off hands too easily, call down every once in a while...

[gaming_mouse]

[ QUOTE ]
Against a TAG I'm folding to the checkraise, or at the most checkfolding the river...He's pretty much owned you at that point if you pay him off...

[/ QUOTE ]

well, he's also owned you if you he pushes you off the best hand w/ a c/r bluff, which this guy was capable of.

thinking in terms of being owned will probably make you play emotionally and make poor decisions. i think it's better to think about it objectively, and understand that sometimes you get owned by making the right play. not that i played this hand well, mind you...

[gaming_mouse]

[ QUOTE ]
If you are worried about being bluffed off hands too easily, call down every once in a while...

[/ QUOTE ]

this is the whole thing. how often is once in a while? when do you decide to do it? keep in mind that at 3/6 turn raise bluffs are VERY common.

[Alexthegreat]

I know i know, I'm not mocking you or anything, it just looks like he's got you in bad shape with his turn play.....How often do you think he would follow through with a bluff turn raise on a blank river?? I think you can call him down if it's a blank, but I think the A helps him most of the time if he was indeed just running a high card bluff on the turn

[Alexthegreat]

Well, if they are more common then legit turn check-raises, then you call them down....

I'm not sure if you can figure that out, but with a super high TA factor, which I'm guessing is aggression? (don't have pokertracker)

I guess I would call him down if I'd seen him bluff raise with worse than A-high...(this is the other problem with this hand..the A may have bailed him out on the river)

[gaming_mouse]

[ QUOTE ]
I think you can call him down if it's a blank, but I think the A helps him most of the time if he was indeed just running a high card bluff on the turn

[/ QUOTE ]

oh yes. this has already been agreed. i should have folded this river for sure.

this question is... should i have checked behind on the turn, and called any river instead? or something more nuanced like:

1. call any broadway river, except an A, which i fold. or can you not fold once you check behind the river?
2. call any A, and raise any non-braodway.

the dilemma comes down to: Do you prefer risking a free card, or a c/r?

i am still not satisfied on how to answer this.

[Alexthegreat]

I like the idea of checking behind and calling the river...you avoid getting checkraised...and, since I suspect he will bet any river, I think the times where his free card beats you will be offset by the bets you accumulate when he bets with nothing

[gaming_mouse]

[ QUOTE ]
Well, if they are more common then legit turn check-raises, then you call them down....

[/ QUOTE ]

no, they are not that common. but they don't have to be. in this case, eg, he risks two to win six (if he successfully pushes me off the best hand). so if i fold 25% of the time, he automatically shows a profit. so if he's doing it only 40% of the time, and i never call down, he also shows a profit.

[AngryCola]

Well, I realize these numbers won't tell you the EV of any play here, but they may prove useful.


I'm giving this player QQ-99, AKs-ATs, KQs-KJs, AKo-AJo, KQo.
(NOTE: This is the range of hands I give the villan before the flop. After the flop it becomes murkier.)

3,432 games 0.005 secs 686,400 games/sec

Board: 6s 6c Qh 3s
Dead:

equity (%) win (%) / tie (%)

Hand 1: 48.7179 % [ 00.48 00.01 ] { QQ-99, AKs-ATs, KQs-KJs, AKo-AJo, KQo }
Hand 2: 51.2821 % [ 00.51 00.01 ] { TsTc }

It's very close.



[ QUOTE ]
i don't see him folding to my turn bet

[/ QUOTE ]

Bet the turn, but after the raise you must take into account the chances of your opponent doing this as a semi-bluff or total bluff. Really, since the range of hands here is so close, the decision on whether or not to call the turn raise is heavily based on the likelyhood of your opponent trying to bluff here.

I would call the turn raise, because I don't think folding or calling is particularly bad. But giving up the pot is always worse in close situations.

Fold the river.
The A/images/graemlins/club.gif is obviously a horrible card for you.

[axioma]

bet the turn and fold to the raise. the C/R here says your beat the vast majority of the time.

[Shillx]

GM,

Let's say that on average the villian will have 6 outs against us (if he is behind).

So if we get check/raised (and fold) we lose 1 BB. If we bet and get called, we make .74 BB. Notice that if he folds his 6 outs, he isn't make a mistake in this spot. By checking we are offering him 6 outs of a 5 BB pot. That eqates to .65 BB/Hand. So he loses .09 BB/Hand everytime he calls with 6 outs.

So let's say that he will fold 20% of the time, call 40% of the time and check/raise 40% of the time.

Our EV in this spot is: .2*.65 + .4*.74 - .4 = .026 BB/Hand

So what you need to do is determine how many outs he has on average and his % of check/raising. The fewer outs on average he has, the less chance he will call and the less EV you give up by checking. The more outs he has, the greater the chance that he will call and the more EV you give up by checking. It is hard to calculate how often he will check/raise but no one said that poker is easy.

Let's just say that he can have AKo and AQo in this spot. If he has AQo he will check/raise (and you fold) and if he has AKo he will always call. In this case there are 6 combos of AQ and 9 of AK...

EVbet = -.4*1 + .6*.74 = .044 BB/Hand

EVcheck = .4*.05 = .02 BB/hand

So in this case a bet would be better then a check (not counting implied odds). Notice that your EV for the check includes those times that you spike a ten on the river against his AQ. Against AK you get nothing on the turn by checking.

Brad

[AngryCola]

You're the man, Shillx!

I'm horrible at doing the exact math for these types of situations, because it requries a lot of speculation.

I don't doubt that there is a solid mathematical way to approach this, but having a good feel for the game and a read on your opponent helps to solve so many of the variables. It's hard for me to do that when judging other people's hands.

[gaming_mouse]

Brad,

Thanks very much for the thoughts. There is still more to consider tho:

Notice that your EV for the check includes those times that you spike a ten on the river against his AQ. Against AK you get nothing on the turn by checking.

I think it's likely that he bets w/ AK and like hands if we check behind the turn.

EVcheck = .4*.05 = .02 BB/hand

I don't understand the .05. But the real EV of a check the turn/call the river must include the times we lose the whole pot to a t/r bluff. Given AngryCola's range of hands (minus QQ, JJ, which I think he would have capped w/ PF), he is about 26% to have Q. So .76*(his bluffing percentage)*(entire pot) must be added to the EVcheck.

Unless I'm misunderstanding you???

[gaming_mouse]

My last reply may have been confusing. But I think:

EVcheck = (pot)*(our equity in pot)*(his bluff raise percent)

If he's bluffing 30% of the 76% of the time he doesn't have a Q, his bluff raise percent is .228, so we'd have:

5*.65*.228= .74

which seems quite a bit larger than EVbet. Am I missing anything?

[spydog]

Just an extra thought on this situation.

If you plan on betting the turn and calling down if raised then consider 3-betting the turn and checking behind on the river (or folding to a cap). Crazy? Well, if you suspect villian is on a bluff he will likely fold to your 3-bet, thus relinquishing his 2-6 outs. If he has a legitimate hand then you will lose the same by calling down as you will by 3-betting/checking behind on the river. Plus, you might fold JJ or a weak queen (QTs, QJs, KQ) if he can make a tough laydown. Plus, you might spike a T on the river and get an extra bet.

Seems ballsy, but I don't think it's that risky when you are way ahead/way behind.

[gaming_mouse]

[ QUOTE ]

If you plan on betting the turn and calling down if raised then consider 3-betting the turn and checking behind on the river (or folding to a cap). Crazy? Well, if you suspect villian is on a bluff he will likely fold to your 3-bet, thus relinquishing his 2-6 outs. If he has a legitimate hand then you will lose the same by calling down as you will by 3-betting/checking behind on the river. Plus, you might fold JJ or a weak queen (QTs, QJs, KQ) if he can make a tough laydown. Plus, you might spike a T on the river and get an extra bet.

[/ QUOTE ]

very nice. other level thinking --- i like this alot.

[chesspain]

Calling the river here is bad. Folding is best, with raising as a distant second in an attempt to have him drop hands like KQ, KK, JJ.

[chief444]

I'd have to question not just if your opponent likes to check/raise semibluff turns a lot but more importantly if he would check/raise with a Q. If he's holding AQ,KQ, or QJ he's probably showing down and he doesn't really gain anything with the check/raise since only worse hands with two outs fold. That doesn't mean this particular opponent thinks that way. But I'd be tempted to 3-bet and fold to either a cap or river bet.

[colgin]

[ QUOTE ]
In general, should it be standard practice to check behind versus TAGgy players who like to c/r?

[/ QUOTE ]

Checking the turn in this hand would be awful, simply awful. You simply can't give hands like AK or AJ a free card here.

If opponent is a TAG who only C/R's with top pair or better than this is an easy fold. If he is tricky and you think he may be trying to push you off the best hand then I call down UNLESS an Ace hits. Calling the river here is just dreadful IMO. There are pretty much no reasonable holdings for villain that you beat.

[Elizabeth]

[ QUOTE ]
My last reply may have been confusing. But I think:

EVcheck = (pot)*(our equity in pot)*(his bluff raise percent)

If he's bluffing 30% of the 76% of the time he doesn't have a Q, his bluff raise percent is .228, so we'd have:

5*.65*.228= .74

which seems quite a bit larger than EVbet. Am I missing anything?

[/ QUOTE ]

Something is wrong -- the value of checking cannot be dependent on his bluff frequency because he's not getting a chance to bluff raise you.

For each card that falls on the river, and the outcome is the same in the case that he bluffs 50% of the time versus the case where he bluffs 100% of the time. The EVs cannot be different.

Plus you should note that for a player who never bluffs, your equation gives an EV of 0 for checking.

[gaming_mouse]

[ QUOTE ]

Something is wrong -- the value of checking cannot be dependent on his bluff frequency because he's not getting a chance to bluff raise you.

[/ QUOTE ]

elizabeth,

you are right. but something is also wrong that this chance is NOT being factored into anyone else's calculations. the decision of wheather or not to check behind clearly must be based on this. 3-betting can also come into play.

i still cannot figure out the proper way to analyze this. i'll keep trying....

[gaming_mouse]

[ QUOTE ]

Checking the turn in this hand would be awful, simply awful. You simply can't give hands like AK or AJ a free card here.

[/ QUOTE ]

why?

please offer some analysis to back this up. i'm not saying you're necessarily wrong, but if he is c/raising with a proper frequency, i don't think it would be awful at all. and i still think against certain opponents it is better.

i feel like there is general tendency on the forum -- and again, i could be wrong, which is why i want some more anlysis -- to overestimate the damage of giving a free card to a tricky opponent. it seems the general philosophy is that nothing is worse than giving a free card, and i'm just not convinced this is true.

[colgin]

[ QUOTE ]
Checking the turn in this hand would be awful, simply awful. You simply can't give hands like AK or AJ a free card here.
[ QUOTE ]
why?

please offer some analysis to back this up. i'm not saying you're necessarily wrong, but if he is c/raising with a proper frequency, i don't think it would be awful at all. and i still think against certain opponents it is better.

i feel like there is general tendency on the forum -- and again, i could be wrong, which is why i want some more anlysis -- to overestimate the damage of giving a free card to a tricky opponent. it seems the general philosophy is that nothing is worse than giving a free card, and i'm just not convinced this is true.

[/ QUOTE ]

[/ QUOTE ]

I thought I did give the general reason -- a free card is very dangerous here. This is not a way ahead or way behind situation. Your opponent may very well have 6 clean outs against you. Giving him a free card as opposed to, IIRC, around 6:1 odds to call your turn bet is very bad. Although I don't have my copy at work with me, I am pretty sure that betting the turn when you have few outs to improve and are susceptible to overcards (which you very much are here) is straight out of HPFAP. Against most opponents you could fold to a checkraise. Since there is no draw, it would be a very aggressive move to C/R the turn with just overcards. You won't see that too often at this level but if you think you are against that opponent by all means call down. But most times you can safely fold a hand you would only infrequently draw out on with at the river to win had you in fact taken the free card. Far worse IMO is giving overcards a free look at the river.

[ QUOTE ]
it seems the general philosophy is that nothing is worse than giving a free card, and i'm just not convinced this is true.

[/ QUOTE ]

There are times that it is OK to give a free card. Not too long ago I posted a hand where I checked the turn with pocket Jacks on a board of KKAx. In that hand the overcards I was worried about were already outh there and I figured a free card was more likely to help me than my opponent. Sthief09 still said I was too weak but I believed (and some others agreed) that this was correct. In this hand, where you are ahead a good amount of the time but very vulnerable, I think a free card is bad.

[gaming_mouse]

[ QUOTE ]

you are right. but something is also wrong that this chance is NOT being factored into anyone else's calculations. the decision of wheather or not to check behind clearly must be based on this.

[/ QUOTE ]

Okay. I think I got it. It should be factored into EVbet. Brad's original formula had (for an oppo who folds 20%, calls 40%, and raises 40%):

EVbet = .2*.65 + .4*.74 - .4 = .026

The final term is incorrect, as it should include the pot equity we lose those times we are being bluff-raised. Again, putting our oppo on:

TT-99, AKs-ATs, KQs-KJs, AKo-AJo, KQo.

His prior chance for having a Q is (12+3)/58, about 26%. This means that if he bluffing 40% of the time, 14% of those must be bluffs. Now, when he does not have a Q, we have 85% pot equity, which comes to 5*.85=4.25. So we can now rewrite:


EVbet = .2*.65 + .4*.74 - .4(1 + 4.25*.14) = -.21

And this is for a fairly low bluff percentage. It will only get worse if he bluffs more.

On the other hand, by checking behind your EV is simply your equity of the current pot, which is about 65%, a positive number. Of course, you will also lose 1 more BB about 12% of the time (when he hits 1 of 6 outs), but that should be compensated for by the times you induce a bluff, and even if it isn't, checking is still clearly better than betting.

Against an opponent who bluffs here a decent percent of the time, though, 3-betting is probably the best play.

I'd really appreciate further comments on the above, to make sure I didn't make a mistake

Thanks,
gm

[BigEndian]

Against a reasonable opponent, I lay this down to the CR on the turn. What hand do you put him on when he CRs you? What % of the time do you think it's a hand you beat against the 2BB to the pot to call down?

I bet the turn pretty much 100% of the time though.

- Jim

[BigEndian]

Think of it this way, what % of the time do you think it's a bluff and what are your effective odds? I would put it at less than 10% to be a bluff.

You can't win every hand, let this one go.

- Jim

[gaming_mouse]

[ QUOTE ]
Against most opponents you could fold to a checkraise. Since there is no draw, it would be a very aggressive move to C/R the turn with just overcards. You won't see that too often at this level

[/ QUOTE ]

I see turn bluff c/raises all the time at 3/6. Does your experience not agree with that? I suppose it's possible that memory overemphasizes them, but I don't think so. Also, this oppo had a turn AF of 6, as I noted.

I should really write a pokertracker query to figure this out. It would be useful to know the percentage of t/r bluffs you face versus an average opponent, or an oppo with an AF &gt; 2, things like that. Getting a good statistical estimate would be difficult, because often hands are not shown down, but I think you could get a rough measure...

[gaming_mouse]

[ QUOTE ]
Think of it this way, what % of the time do you think it's a bluff and what are your effective odds? I would put it at less than 10% to be a bluff.


[/ QUOTE ]

See my (most recent) analysis above. If he is bluffing 10% of the time, it is far better to c/behind or 3 bet than it is to bet and fold to a raise.

[BigEndian]

Where's the AA-JJ? How do those numbers take into account his propensity to bluff more with one type of hand than another? How about the type of hands he's likely to see the turn with after being 3-bet preflop?

- Jim

[gaming_mouse]

[ QUOTE ]
Where's the AA-JJ?

[/ QUOTE ]

He would have capped.

[ QUOTE ]
How do those numbers take into account his propensity to bluff more with one type of hand than another?

[/ QUOTE ]

They don't, but I don't see how that affects the validity of the EV calc.

[ QUOTE ]
How about the type of hands he's likely to see the turn with after being 3-bet preflop?

[/ QUOTE ]

This is an argument in favor of checking behind. That is, removing hands like KJs makes it more likely that he has a Q, and thus more likely that he will c/r.

What the other calculation proves is that even a small chance of being bluffed makes the risk of losing the pot worse than the risk of giving the free card.

People are just assuming that giving a free card is terrible, without comparing that to how terrible being bluffed out of the pot is.

[BigEndian]

Not true that he would have capped, it's heads-up.

Narrowing the range of hands he would bluff with narrows the number of times he would bluff...if you assume an equal distribution of the hands you cited.

I think the last part is a good point. If (a big if) he's a decent player, he's seeing the turn with AK or some kind of made hand. There's always the chance of course that he's not particularly good and is there with something he shouldn't be. So you're either way ahead or way behind between say AA-88 and AK/AQ/KQ/QJ most of the time.

So I think I agree with you now, though via a different path.

- Jim

[gaming_mouse]

[ QUOTE ]
Not true that he would have capped, it's heads-up.

[/ QUOTE ]

Maybe not, but I was assuming it for a TAG. I'll agree it's not for sure either way.

[ QUOTE ]
Narrowing the range of hands he would bluff with narrows the number of times he would bluff...if you assume an equal distribution of the hands you cited.

[/ QUOTE ]

Yes, but all I need to assume is that he is bluffing at least 10% of the time, or whatever it needs to be. Your point relates to estimating that 10% number in the first place. But I think without even doing any calculation, based on his AF of 6, we can assume that 10% is a minimum without even analyzing his hand range.

[ QUOTE ]
There's always the chance of course that he's not particularly good and is there with something he shouldn't be. So you're either way ahead or way behind between say AA-88 and AK/AQ/KQ/QJ most of the time.

So I think I agree with you now, though via a different path.

[/ QUOTE ]

Let me make sure I understand how you think the path is different. To clarify my point about this, I do think you were correct to point out that alot hinges on wheather or not he sees a turn with hands like AQ/KQ/QJ. Of course, I had no specific read on that, and I really don't know if most TAGs would here.

If he is seeing a turn with these hands, we want to check behind. But if he's not seeing a turn with these hands, the only ones (with the exception of AK) that he is seeing a turn with are probably ones that beat us anyway. So checking behind is still best.

Essentially, the difference in our paths is that your argument is based on the fact that his likely holdings beat us, whereas mine was based more on the liklihood that he was bluffing?

[AngryCola]

[ QUOTE ]
[ QUOTE ]
Not true that he would have capped, it's heads-up.

[/ QUOTE ]

Maybe not, but I was assuming it for a TAG. I'll agree it's not for sure either way.

[/ QUOTE ]


This is why I included QQ-JJ in my range of hands.
It sort of balances out that issue.

[BigEndian]

Pretty much, but my line also stipulates heavily on them being a reasonable TAG. You can still fold to the turn CR above imo. That's worth noting as well.

- Jim

[scott2130]

Just to throw my 2 cents in. Why not 3-bet the c/r? If he has the Q then he will cap and you can fold. If he doesn't have it and has AK instead he might fold right there.

Feel free to throw rocks.

Scott

[flair1239]

[ QUOTE ]
Just an extra thought on this situation.

If you plan on betting the turn and calling down if raised then consider 3-betting the turn and checking behind on the river (or folding to a cap). Crazy? Well, if you suspect villian is on a bluff he will likely fold to your 3-bet, thus relinquishing his 2-6 outs. If he has a legitimate hand then you will lose the same by calling down as you will by 3-betting/checking behind on the river. Plus, you might fold JJ or a weak queen (QTs, QJs, KQ) if he can make a tough laydown. Plus, you might spike a T on the river and get an extra bet.

Seems ballsy, but I don't think it's that risky when you are way ahead/way behind.

[/ QUOTE ]

I like this line.

[gaming_mouse]

[ QUOTE ]
Pretty much, but my line also stipulates heavily on them being a reasonable TAG. You can still fold to the turn CR above imo. That's worth noting as well.


[/ QUOTE ]

Yeah, that's fine. But the argument is that we should not bet since we plan to do this. This is separate issue, and I actually agree with you. But because I agree with you, and after all the analysis, I am convinced that checking behind is better here.

[Guruman]

I think that checking the turn is a mistake for a few reasons:

1)free card-the fact that he raised pre-flop screams overcard(s) the only question is which ones. If he had overs with no Q then you are ahead and do not want to give him a free shot at counterfeiting your pair. TAG or not, bet the turn to protect against the overcards.

2)value bet-If you are ahead, you're also losing money by not extracting bets on the turn.

3)information-Your turn bet has very specific possible consequences:
villain folds drawing hand or overcards,
villain calls overcards (still behind you),
villain calls overpairs or a Q (ahead but not sure of himself),
villain re-raises trips, a boat, a Q or overpairs (this is the info you're looking for)
villain re-raises as a bluff

I think he gave you all of the info you needed on the turn, but you would have never found out without the bet. This is an easy value/protection/information bet to me. A re-raise scares the hell out of me, but I have to admit that I'd have a hard time putting him on that six given his pre-flop play.

Overall, hell of a good hand by the villain post-flop - though I think he got pretty lucky when the first three cards came. /images/graemlins/wink.gif

[Guruman]

[ QUOTE ]
Also, I challenge anyone to come up with a line that loses more chips than mine.


[/ QUOTE ]

same line, only three-bet the turn and call a cap. That'll lose you an extra BB when he bets the river and you're tied to the pot. /images/graemlins/grin.gif

[Elizabeth]

[ QUOTE ]
[ QUOTE ]

Something is wrong -- the value of checking cannot be dependent on his bluff frequency because he's not getting a chance to bluff raise you.

[/ QUOTE ]

elizabeth,

you are right. but something is also wrong that this chance is NOT being factored into anyone else's calculations. the decision of wheather or not to check behind clearly must be based on this. 3-betting can also come into play.

i still cannot figure out the proper way to analyze this. i'll keep trying....

[/ QUOTE ]

It comes into play in comparing the EV in checking to the EV of betting. The Percentage the the other player will bluff is lowering your equity in the pot as it increases from zero to the optimal bluffing frequency, but only when you bet.

If he bluffs too much, then you are correct to call and further bluffs increase the EV of betting.

Whether or not the opponent will bluff raise infrequently enough so that hero can fold, and exactly how much this drops the EV of betting are calculations that you could make after making some reasonable assumptions about the range of hands and bluffing frequency.