Sushi vs Clarkmeister

[marchron]

I thought you were actually playing Clarkmeister, i.e. the person, in this hand, not debating whether or not to exercise his Theorem. As such, I feel let down.

As for the hand, there's really no good options here. The problem with Clarking it is that you're very rarely folding a better hand. Villain almost never has AA/KK here, and definitely doesn't have JJ/TT. That leaves AK. If one of them's a [img]/images/graemlins/spade.gif[/img], you're owned, and if he's [img]/images/graemlins/spade.gif[/img]-less, he won't call. (That said, if you bet it's a turbofold if he raises. A bluffraise here would be almost inconceivable.)

So your play is to check, but I don't like either of the options if Villain bets. Yes, he has huge odds to get a bluff to work, but is he more likely to just check behind AK UI, either hoping for a chop or figuring a bluff is worthless?

[MrWookie]

X,

Your math it a little off, but thanks for attempting this. Your percentages don't add up to 100%, I don't think. Here's how I would set it up:

Chance we're ahead * (11.5 * chance villain checks through + 12.5 * chance villain bluffs) + chance we're behind * (0 * chance villain checks through with a better hand + (-1) * chance villain bets)

This is, of course, assuming we always call. If we always fold to his bet, the math is somewhat different, but I'd like to see if you can set that case up and compute the EV in a similar manner.

I'm interested in the numerical EVs for the following cases:
Villain always bluffs and we always call.
Villain never bluffs and we always call.
Villain never bluffs and we always fold.
Villain bets at the game theory frequency, and we either call or fold (hint: it doesn't matter which we do).

[Shillx]

EV of betting:

(11.5 BB) * 0.486 + (-1 BB) * 0.514 = +5.075 BB

This is just .486 - .514 = -0.28 BB. If you bet and he folds AK [img]/images/graemlins/heart.gif[/img] you win nothing and not the pot. You would be correct if your options were to just open fold or bet.

If non flush KK folds to our bet, then we have:

11.5 BB * 0.514 -0.486 BB = 5.425 BB

This is 11.5 BB * .027 = +0.31 BB. If he has K [img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/diamond.gif[/img] and folds then we win the pot since we can't win by checking (unless we c/r) and the rest is a wash.

This is a really clear check. You are going to lose a bet either way when he has a flush but by checking you will sometimes get him to bluff at it. It isn't a situation where worse hands might call since stuff like A [img]/images/graemlins/heart.gif[/img] J [img]/images/graemlins/diamond.gif[/img] isn't in his range. The EV of betting will be the exact same as check/calling if he never bluffs (unless you fold KK or he decides to call with AK) and you win that extra bit when he takes a stab at it. The best play might be to check/fold but it is tough to say since we don't know his bluffing frequency.

Anyway a Clarkmeister is typcally wrong when you have the lead. It is a far better play when you have been check/calling and a 4th suited card hits on the river. The guy betting could have been bluffing/betting a weak hand and you can end up bluffing the bluffer. Or the guy might think you're bluffing and you can sneak in a value bet with a non-flush hand. A guy calling is much more likely to have a flush then a guy who is betting so you will run into a boss hand more when you try a Clark after betting all the way down.

[Sushiglutton]

[ QUOTE ]
I'll also assume AK never bluff raises, and we always fold to a raise.

[/ QUOTE ]

I accept the challenge but just got home from a long day teaching noobs linear algebra, so I check in later to complete the calculations. Anyway I think the assumption of zero bluff raising is pretty dangerous. The reason is that AKo ís really pure trash on this board. No way he can win with it. It's almost like 23. When a poker player finds himself with junk on the river in a big pot, I think almost everyone consider bluffing. And I don't thnk bet/fold on a four flush river is all that new to someone with his stats.

[Sushiglutton]

Ok let's have some fun with the numbers [img]/images/graemlins/grin.gif[/img]!

MrWookie has given villain the following (weighted) range before our action on the river:

9 AKo (no spade, in this analysis)
7 AK[img]/images/graemlins/spade.gif[/img]
0.5 KK [img]/images/graemlins/spade.gif[/img]
0.5 KKo (without a spade)
0.5 QQ
1 JJ

I think KK is a bit more unklikly than this given villains stat
and the fact he had two opps acting behind him on the flop and still didn't raise.
But whatever I think it's good enough. These calculations will be pretty rough anyway.

We want to calculate the EV of checking against 3 different types of opps:

1) Opp always bet
2) Opp bet when he think he is good
3) Opp bluffs acording to game theory


1) So we win the pot + 1 bet, 9 times, lose an extra bet 9.5.

-> EV1 = (9*12.5 + 9.5*(-1))/18.5 = 5.567



2) I think opp will think he is god with the following range:

7 AK[img]/images/graemlins/spade.gif[/img]
0.5 KK [img]/images/graemlins/spade.gif[/img]
0.5 QQ
0.5 JJ (he may check and he may bet)

So we lose 1 bet 8.5 times and lose 0, 1 time (when he holds JJ, KKo and doesn't bet)
and finally we win 11.5 bets the 9 times he holds AKo.

-> EV2 = (8.5*(-1) + 1*0 + 9*11.5)/18.5 = 5.135




3) So villain value bet the excact range he did in 2) but he also bluffs sometimes with AKo,
but never with KKo or the 0.5 JJ. How ofen should he bluff? After he has bet we get 12.5:1 pot odds.
Game theory suggests villain should bluff with a frequency so that our call is excactly break-even.
That way his strategy is unexploitable.
Let x be he number of times he bet AKo. We have that he value-bet 8.5 times. We get:

x/(x+8.5) = 1/13.5 -> 12.5x = 8.5 -> x = 0.68


So our EV is:

EV3 = (8.5*(-1) + 1*0 + 0.68*12.5 + 8.32*11.5)/18.5 = 5.172


Notice that we are better off if he plays according to game-theory than if he only bets when he thinks he is good.
That is because in 2) he is exploiting our 'misstake' to allways call.

So MrWookie calculated our EV of betting to be somewhere in the interval: <font color="green"> 5.075-5.425 BB </font> , depending on how often villain folds KKo.


Conclusions: If villain is hyper-aggro we should check. Against 2) and 3) the important factor is how show-down bound vilain is. If he never folds KKo we should check,
if he sometimes do i we should bet.



Accounting for bluffraising:
Let's just for experiment say that villain bluffraises 5% of the times he holds AKo
(we still don't get the odds to call the raise!). That means
0.05*9 = 0.45 times.

EV = (9.95*(-1) + 8.55*11.5)/18.5 = <font color="red"> 4.78 </font>


If he only bluffraises 5% of the times he holds AKo we would be better off checking.
I think this shows what an extremly dangerous line b/f is in this hand.


<font color="blue"> The correct line agaisnt a fairly unknown is c/c IMO. </font>

[neurotiq]

MrWookie:

[ QUOTE ]

I think I'm fighting a hopeless battle here. This is such horrible thinking that is costing you money.

[/ QUOTE ]

First, thanks for a great post right above mine. My post was not intended to be a slight to your well-thought out post, and I didn't even read it at the time that I posted. I always grunch. Always. So, I wasn't even aware that my post right behind yours was in disagreement. My apologies if you were offended by it.

As far as my "horrible thinking," I think I'd appreciate some more substantive thoughts on the matter. One thing that struck me about your post is that I'll never have the time to run all the calculations that you did when I only have 15 seconds to act. So, what are some good guidelines for refining the Clarkmeister "theorem"? I think that the reason why Clarkmeister has caught on so popularly with 2+2ers is because it generally does work. You're probably right that running the calculations you talk about would illuminate that it isn't always profitable, but in the absence of being able to run such calculations every time we have 15 seconds to make a decision, what would you advise that we do?

I'll freely confess that I still have my training wheels on in a lot of facets of my game, so I really do appreciate any thoughts you (or others) might have on how to refine Clarkmeister.

[MrWookie]

[ QUOTE ]
I think that the reason why Clarkmeister has caught on so popularly with 2+2ers is because it generally does work.

[/ QUOTE ]

No, the reason why it's caught on so much is that people don't realize when or why it doesn't. If you bet and he folds a worse hand than yours, many people take that as a positive result, because (a) you win the pot, which is a good thing, and (b), you can delude yourself into thinking he might have folded a better hand, which is also feels like a good thing.

Poker is pretty good about instructing people when choosing between +EV spots and -EV spots. That catches up with you pretty quickly. However, it can be difficult to get the proper positive or negative reinforcement for choosing an option that's +EV, but that has lower EV than another option. You get positively reinforced for choosing the wrong thing!

Edit: Also, the point of working out the math in all the nitty gritty detail is not so that you will work it all out at game time. The reasons you work out all the math are thus:

1. You might get a result that surprises you, and you learn something.
2. You hone your understanding of the situation. You're not allowed to gloss over details you don't understand, like you might do at game time.
3. You develop your intuition and estimation skills. It's easier to extrapolate from mathematical results you've calculated in the past to the new situation right now than it is to try and divine some sort of estimate from scratch.

[Xylocain]

ya, I noticed my calculations were off, I miscounted the number of bets. the reason it doesn't add to 100 is because some actions have 0 impact our EV in the formula (like vil checking behind with the best hand).

I'm at work now and I am not going to have time to do it today, I guess the calculation when Vil bluffs at game theory shouldn't be that hard given pot is laying 11.5:1. That should then also be the ratio between Vils valuebets and his bluffs (thus valuebet 56.4% (still assuming Wooks hand range) and bluff 4.9%) . Right?

If I'm in a good mood I'll do it this week unless someone beats me to it.

[neurotiq]

Thanks again for having this discussion with me, MrWookie. I think it will be helpful.

[ QUOTE ]
No, the reason why it's caught on so much is that people don't realize when or why [Clarkmeister] doesn't [work].

[/ QUOTE ]

You're probably very right here; I certainly have no idea when or why it doesn't work. Do you have any good guidelines for when it might not work? Or, if it would be easier, do you have any good guidelines for when it does work? I realize that my question lends itself to speaking in generalities and doesn't delve much into specifics, but generalities are really all I'm curious about for the time being. After understanding the generalities, I'll then worry myself about some more specific scenarios...

Thanks! [img]/images/graemlins/smile.gif[/img]

[MrWookie]

Have you read Theory of Poker? Look at the section on betting on the river OOP. Those guidelines apply to EVERY river situation OOP, not just the once when there are 4 spades on the board. Plus, it IS mathematically true.

Now, this doesn't mean I want you guys to check every river, either. Don't turn this into an anti-Clarkmeister nit revolution, checking every four flush river OOP because Wookie told you to. I want you to THINK, ANALYZE, and EVALUATE every single situation for the specifics of that hand, not blindly doing the same damn thing every damn time because some guy who doesn't even post here anymore said it was a good idea SOMETIMES.