Worth a read - the EV of checking (aka "merging yur range" and "take the free card&qu

opr

http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=10297503&page=12&fpart=all&vc=1

After writing this post, I've decided to come back to the beginning and add a disclaimer: normally folding is considered to be 0 EV, and the EV of all other actions are based around that. Here, I have based my EV calcs upon your pot equity - that is, I've defined 0 EV to be what would happen if no more betting were to take place and both hands were shown down. This helped me to explain things better, although it is nonstandard. With the way I have written things, folding would be a -EV decision which costs you your entire equity in the pot. Everything here could be rewritten using EV in its traditional sense, but I prefer to leave it alone.

A lot of analysis that I see posted in these forums is flawed because the author simply assumes that the checking is a neutral EV action. It is not. Sometimes checking can be very +EV and sometimes it can be very -EV. Our goal is to maximize EV on every decision. Just because one action is +EV doesn't mean that it is the best action, and just because one action is -EV doesn't mean it is wrong.

I will start with a very simple example. You are HU on the river, first to act. There is $1000 in the pot and you have $1000 left. The betting from previous streets tells you that your opponent has a very strong hand and he is convinced that he holds the winner. He never holds any sort of busted draw or air. Your hand is also very strong, but you estimate that you can only beat 40% of his range. Thus, you have $400 of equity (if the hands were shown down with no more betting, you would get $400 from the pot on average). If you check, he will go all-in with his entire range. Since you only need to be good 1/3 of the time to call this bet, you must call. The pot is now $3000 and you win it 40% of the time, which averages out to a $1200 value. It costs you $1000 to get there, which leaves you $200 profit from your call. Clearly calling is better than folding... but your expectation from the hand is now only $200 rather than the $400 that it was prior to facing his bet. What happened here is that you lost money while calling the bet, but the money that you lost came from your equity in the pot, not from your remaining chips. You have more money now than you would have if you had folded, but less than you would have had if the bet had never taken place.

On the other hand, you could have bet the river instead of checking. Your opponent will call with his entire range, which beats you 60% of the time. Your bet is not a bluff, because your opponent never folds, and it is not for value, because you lose the majority of the times that you are called. However, you cannot say that betting here is a mistake, because the end result is identical to checking - either way, all of your money goes into the pot every single time. Betting costs you $200 (as compared to your pot equity vs his range) and checking also costs you $200.

In reality, people rarely have identical betting and calling ranges. If you play around with various scenarios, it will be easy to see that there are times when it is correct to make a -EV river bet because the EV of checking is even worse.

Another reason that checking can be -EV is because it can give your opponent a free card to beat you. Suppose you have an overpair on the turn, and only one pot-sized bet left. In many cases it is correct to just shove the rest of your money in, even if you don't expect to get called very often by worse hands. Making your opponent fold a 5-9 outer (sometimes even more) in a big pot has immediate value, so if you are pretty sure you are ahead, this value can overcome the fact that when you get called you are way behind. Also, checking allows a solid opponent to bluff you with a frequency that eats away at your EV, similar to the previous example.

In theory, you could construct a scenario where it is correct to bet your entire range of hands - your weakest hands as a bluff (your opponent folds >50% of the time), your strongest hands for value (usually ahead when called) and for protection, and your marginal hands simply because betting is better than checking (protecting vs draws, and protecting vs potential bluffs). This would be the epitome of merging your ranges.

So far I've only discussed spots where checking is -EV, but there are many times when checking is +EV. Anytime that you have a draw and are last to act, checking is +EV. Again, assuming $1000 in the pot and $1000 left on the turn. If we have a draw that hits 20% of the time, then we have $200 pot equity. If our opponent will play the river perfectly against us, then checking is worth $200 to us. If our opponent will pay off the river half the time when we hit (and we never bluff when we miss), then we figure to earn an extra $1000 10% of the time, which is worth $100. In this case, checking is worth $300. I almost never see anyone attempt to calculate the value of checking in these spots, instead people merely try to calculate whether semi-bluffing is profitable. There are certainly going to be spots where semi-bluffing is profitable, but checking is more profitable. (Obviously though, checking is not nearly as valuable when OOP because you are likely to face a bet.)

Checking can also be profitable for other reasons, which generally relate in some manner to getting more money in the pot on future streets with a big edge, whether it be from inducing bluffs, or underrepresenting your hand to induce light calls.

So cliff's notes = think about the EV of checking, don't just assume it is a neutral factor.

After having added the disclaimer at the beginning, I'd like to add an observation at the end: thinking about EV in this fashion can really help to illustrate what is going on in hands - it is easy to get to the river and call a bet while saying "I'm good here often enough to make a +EV call" without ever really considering that despite making a correct call, you have actually lost a lot of sklansky bucks over the course of the hand - you want the value of your river call to cover your entire investment for the hand, not just one street of it. If you are facing a bet and getting exactly the right odds for a breakeven call, then you have lost your entire equity in the pot - the only way that your call is breakeven is because you are using up all of your previous investment in the pot to help "pay" for the call. This is what implied odds and reverse implied odds are all about. If you are making calls with less than 50% pot equity, then you've stuck yourself in a reverse implied odds spot. There's some food for thought.

Opr

pumpkinpints

excellent, well thought out post.

Hitman Actual

opr wrote:

If you are facing a bet and getting exactly the right odds for a breakeven call, then you have lost your entire equity in the pot - the only way that your call is breakeven is because you are using up all of your previous investment in the pot to help "pay" for the call. This is what implied odds and reverse implied odds are all about. If you are making calls with less than 50% pot equity, then you've stuck yourself in a reverse implied odds spot. There's some food for thought.

A little help here, anyone? I've a feeling this part is really obvious, but I just can't 'see' the meaning. Specifically I can't see why you need to have more than 50% pot equity when making a call, otherwise you're in reverse implied odds territory. Am I dumb? Surely there are situations where you can have less than 50% equity, and still be covering yourself over the whole hand?

Good link anyway, opr.

Ste05

Nice link,

Question for everyone, in aejones's reply, what is he talking about when he is talking about shania??

"based on the fact that there is a "correct" way to play a hand, since shania has little to effect on tournament play,"

and

"Basically, that is shania vs optimalness. i mean, a year ago or whatever shania was everyone's favorite freakin thing. everyone was so in tune with pleasing shania, they forgot that a.... "

At first I presumed he was talking about Shana Hiatt, and thinking about your exiting from a tournament and making sure you went out making a "correct move".... but now I'm not sure, anyone??

EDIT: LOL I read on like 5 posts and saw the exact same question and the reply was "metagame"?? Now I'm even more confused...

phantom_lord

shania is balance isn't it?

mrflash

ok this is math poker, and sometimes its correct and sometimes its incorrect, a river value bet which might be a -ev is sometimes a very strong move, either as a bluffing move or as an enticer with the stone cold nuts. you cannot rely on this sort of betting all the time as it simply will not work against the better opponents. betting a regular amount is a good way of disguising hands, working on an ev situation fulltime is not a realistic way of playing poker.

opr

aejones wrote:

"Basically, that is shania vs optimalness. i mean, a year ago or whatever shania was everyone's favorite freakin thing. everyone was so in tune with pleasing shania, they forgot that a TON of times they were jamming draws vs people that they didn't need to jam draws against. they were raising the flop and firing again on the turn with just K high but a flush draw becuase they thought "this increases my FE, i would not be checing 2p+ here and opponent knows that, etc." i have to please shania the beautiful goddess that sings country music or w/e. anyways, i think more recently, people have become adept with playing closer to optimal and worrying abotu shania less. basic stuff like checking behind draws at certain times, just basic plays that are perhaps more obvious but still the highest EV. now, i think g-p is the only person still in love with shania, and rest of us just sort of like her. "

I love this paragraph.

In poker terms its Metagame. I think what he is talking about relates to the fact that people for a long time now are making plays based more on metagame considerations rather than what was the optimal play in certain situations.
This is maybe around the time that more and more players started to learn about FE and how to play draws more aggressive , what this does for your image and how it helps to get paid on your big hands if you widen your range to include draws in these situations. (Metagame)

Basically as "FoxwoodsFiend" says metagame considerations might dictate a bet in a case where it's -EV and we all used to be so mad into metagame considerations that we bet without thinking but people now have become adept with playing closer to optimal and worrying less about Meta-game.

Opr

Hectorjelly

Does anyone else think MrFlash may just be the product of our collective subconsciousness

NickyOD

Hectorjelly wrote:

Does anyone else think MrFlash may just be the product of our collective subconsciousness

Why? Is the whole forum stoned?

opr

lenny_leonard wrote:

A little help here, anyone? I've a feeling this part is really obvious, but I just can't 'see' the meaning. Specifically I can't see why you need to have more than 50% pot equity when making a call, otherwise you're in reverse implied odds territory. Am I dumb? Surely there are situations where you can have less than 50% equity, and still be covering yourself over the whole hand?

We make a call on the river for a pot of 800 dollars and have 45% equity in the pot and are making a break even call thus the value of the call is 360 but if the pot was heads up we have invested 400 meaning we lose 40 sklansky bucks by calling.

I have no idea if this is correct but its what i took when reading it. Anyone else please shed some light on what is meant ?

Opr

LuckyLloyd

This post has been deleted.

jimmii

opr wrote:

We make a call on the river for a pot of 800 dollars and have 45% equity in the pot and are making a break even call thus the value of the call is 360 but if the pot was heads up we have invested 400 meaning we lose 40 sklansky bucks by calling.

I have no idea if this is correct but its what i took when reading it. Anyone else please shed some light on what is meant ?

Opr

If you are getting 2/1 on a call on the river and feel that you beat 33% of your OPs range then you are not getting the correct odds on the whole hand and that while its a neutral EV call on that street its -EV on the overall hand. In a HU pot a 2/1 call is actually an Evens call on value against not playing the hand at all as you are only "winning" the money the OP has put into the pot. Or something like that!

Hitman Actual

Hmm. I'm still not sure. The only way I can make sense of the whole last paragraph, regarding (reverse) implied odds and 50% pot equity, is as follows (using one of the examples earlier in the post):

Say the hand has been HU all the way, we get to the river, there is $1000 in the pot and we have $1000 left each. So I've invested $500 to get there (well, we both have). He's first to act and pushes, giving me 2/1 to call (33% BE).

If I beat 40% of his range, I call obviously, ending up with $1200 on average. That's $200 profit on the river call, but it took me $500 to get to the river (before the bet).

Now say I beat 55% of his range. This time when I call I end up with $1650, or a profit of $650 on the river call. This is better than the $500 it took to get me to the situation.

So the first case (<50% Pot Equity) indicates reverse implied odds (i.e. bad) throughout the hand, and the second case (>50% PE) indicates implied odds (i.e good) throughout the hand.

(M)Any loopholes?

jimmii

Thats pretty much it. Its basically pointing out that a +EV call on one street is a -EV play overall and probably loses players a good bit of money in the long run.

pumpkinpints

LuckyLloyd wrote:

BOOM

lol, yesh