From the Vault: Clarkmeister's Theorem Examined

[WVHillbilly]

This EV calculation will always be -EV as long as our equity is less than 50%.... I don't see how it has much to do with the statement that villain has to call with his entire range.

Right. Which is what I said originally. Unless we have greater than 50% equity we don't have a value bet.

I just said he calls with his entire range because I didn't want someone coming back with well what if he folds his weak hands or bluff raises. It was just there to make it as clear as possible. Clearly it doesn't matter. He could call with half his total range but we still need to be ahead of greater than 50% of the hands he calls with to have a profitable value bet.

 

[baudib1]

He could call with half his total range but we still need to be ahead of greater than 50% of the hands he calls with to have a profitable value bet.

But what if he only calls with 40% of hands we beat and folds 15% of hands that we don't beat?

I don't like this theorem at all. Any generalizations which completely ignore villains range should never be used as rules to use 100% of the time.

Clarkmeister is just a general rule, much like Baluga but not nearly as reliable, so surely it should not be used 100%

Deco, I have to agree with C9 here because I cannot see very many cases where villain's range on river is always going to be huge flushes when it's the fourth of a suit. To believe this you would basically be saying that people never get to the river on 3-flush boards with worse than a set.

Also there are plenty of people who will find a hero fold of a J-high/Q-high flush or worse and surely people who will fold worse.

The basic idea is this: There are plenty of hands where people have reasonably wide ranges and you get to a 4-flush river and the action goes check-check. A huge % of the time a bet by either party will take down the pot, it's an obvious spot where we should polarize our betting range.

 

[Deco]

Clarkmeister is just a general rule, much like Baluga but not nearly as reliable, so surely it should not be used 100%

Originally posted by Clarkmeister here
If you are -
1. Out of Position
2. Headsup
3. The 4th flush card comes *on the river*

You should bet out 100% of the time.

All 3 qualifications must be met.

Just going on what the rule says. I'm certainly bluffing these spots alot of the time but not 100% of the time which is exactly my problem with this theorem.

 

[Deco]

Throw out a scenario, because I can't say I agree. I find it pretty hard to conjure up a scenario where an opponent would have air and a nutted range when we're OOP.

We don't need air to bluff we just need non-flushes to bluff. Normally I think villains turning their hands into bluffs is very rare especially at SSNL and uSNL but 4flush boards are the one spot when you can catch anyone doing. Us checking to them on just about the scariest river card possible is bluffing 101 even if you do hold a nice pair.

If we have 4s5s flop a flush, bet/bet the river and turn and then the 4th flush card comes in we are not going to get value from betting if villain isn't a station or mad paranoid as non-flushes will fold and only better hands will call. Based on villain and his range we should check/call or check/fold.

5high is an extreme example, I rarely find value betting any 1card flush smaller than queen high vs non-fish on the river OOP. Bear in mind to get to this position we'll have likely fired two barrels already, we look strong, we repped a draw, the pot is big. This situation is further amplified if the board has paired.

The worst thing about this rule is that disregards all prior hand reading/ranges is it applies to the river, the street were we have the most information and the best read on villains range.

 

[c9h13no3]

we still need to be ahead of greater than 50% of the hands he calls with to have a profitable value bet.

This isn't true, because we still make money when he folds.

EV = F*P + W*(1-F)*(P+B) + (1-W)*(1-F)(-B)

Where P is the pot, B is what we're betting, F is the fraction he folds, and W is the fraction we win at showdown. That's why bluffs are profitable, because the first term in the EV equation is bigger than the EV when we're called terms. Your example doesn't account for this because he never folds, so you're neglecting the F*P contribution to your expected value.

I'll get to Deco after work.

 

[WVHillbilly]

If he has 100 combos on the river and folds 50 of them to a 1/2 pot bet, you need to be ahead of 26 of the ones he calls with for the bet to show profit.

 

[c9h13no3]

If he has 100 combos on the river and folds 50 of them to a 1/2 pot bet, you need to be ahead of 26 of the ones he calls with for the bet to show profit.

Assuming a pot of $100 because it makes the math easy. I'll also assume villain has 25 combos we beat and 25 we lose to, since it makes the math easy.


-When villain folds, we win $100. This happens half the time, so 0.5*100 is the first term in that equation.

-If we bet $50, and lose, we lose $50. This happens one quarter of the time. 0.25*(-50) is the next term in the EV equation.

-The other quarter of the time, we win $150. 0.25*150.

EV = 50 - 12.5 + 37.5 = $75

Am I missing something? Because this bet seems hugely +ev, not break even like you suggest...

Hell, just look at the EV chart Jurn posted. If you bet half pot, and get 33% folds, a bluff is profitable. Now, you're giving me 50% folds AND I win at showdown half the time! HUGE PROFIT!

 

[c9h13no3]

WV, Deco, or whoever. What's your WTSD when "saw river = true"? Run that filter for me if you could. And take out spots where you're all in on the turn.

I bet its pretty high, and thats prolly what the Clark theorem is getting at. "F" in the EV calculation is abnormally high, and thus most bets are profitable.

 

[WVHillbilly]

Assuming a pot of $100 because it makes the math easy. I'll also assume villain has 25 combos we beat and 25 we lose to, since it makes the math easy.


-When villain folds, we win $100. This happens half the time, so 0.5*100 is the first term in that equation.

-If we bet $50, and lose, we lose $50. This happens one quarter of the time. 0.25*(-50) is the next term in the EV equation.

-The other quarter of the time, we win $150. 0.25*150.

EV = 50 - 12.5 + 37.5 = $75

Am I missing something? Because this bet seems hugely +ev, not break even like you suggest...

Hell, just look at the EV chart Jurn posted. If you bet half pot, and get 33% folds, a bluff is profitable. Now, you're giving me 50% folds AND I win at showdown half the time! HUGE PROFIT!

Nope. $75 is exactly the same EV as checking since we beat 75% of his total range. The 50 combos he folds to the 1/2 pot bet + 25 he calls with that we beat.

 

[c9h13no3]

Nope. $75 is exactly the same EV as checking since we beat 75% of his total range. The 50 combos he folds to the 1/2 pot bet + 25 he calls with that we beat.

Assuming he never (list of many things most players do)

To me there's more assumptions to be made with check/calling than bet/folding. If we have sufficient fold equity (which on these rivers we almost always do) betting can never be -EV. However, check/calling has the potential to be a negative EV play, and check/folding is obviously always zero.

Anyways, I'll follow up with a graph(s) that I think will explain things better when I get to a real computer.

 

[WVHillbilly]

Let's just assume we're in position on the river and this guy checks to us (the 100/50/25 combos guy). The EV of any bet (again assuming he never folds more/less) is exactly the same as checking behind.

Also my initial comment was not really related to the OP. Just a little comment on the chart Jake posted which is 100% correct when we're bluffing but not when we're betting for value.

 

[c9h13no3]

Let's just assume we're in position on the river and this guy checks to us (the 100/50/25 combos guy). The EV of any bet (again assuming he never folds more/less) is exactly the same as checking behind.

Also my initial comment was not really related to the OP. Just a little comment on the chart Jake posted which is 100% correct when we're bluffing but not when we're betting for value.

Well, you just said "profitably". Which I thought you meant negative EV, but you just meant less EV than checking.

I agree, in position, checking behind is the same EV as betting in the 100/50/25 case. This is the case because you don't have any decisions after you check or bet (if you're bet/folding). But checking OOP leaves us with another tricky decision that can put us in a -EV spot. However betting OOP is pretty much the same decision tree as betting IP: you bet/fold unless you're holding nuts or near nuts.

 

[Hrrmnhrrm]

This is right for bluff bets but remember to have a value bet you need at least 1/2 of his worse hands to call regardless of your bet size.

This is in-position, though. OOP you don't need 50%.