Exploiting your opponents errors.

Stu_Ungar

Stu_Ungar

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I decided to write this because I was reading something from Harrington which was based on the old idea of Sklansky bucks and it really made sense to me.
Harrington said that when two skilled players play, neither really does anything particularly special. Its not that the winner does something that the other is not capable of, but rather that the loser makes more errors than the winner.
It may seem obvious, but its meaning is slightly subtler. The winner doesn’t really make that many great decisions, rather the loser makes more bad decisions.
So that got me thinking.. where in my game can I force my opponent to make errors?

I thought about a simple drawing scenario and the results were surprising.
The simple modle is that I raise in middle position with AhJc , the button calls, the blinds fold.
I know the button plays a lot of drawing hands, he likes to play flushes and would usually have rereised with hands like AA- JJ

The flop comes Jd 6d 3c

I figure that my TPTK is good and that he will usually fold to a c-bet, if he does not then he is most likely on a flush draw.

So how do I proceed?

We all know that charging draws is a good idea… so I charge the draw.. but how much?

Well some people say ½ pot so lets charge him 1/2pot.

Preflop I raise 3BB, he calls, the blinds fold. So the pot is 7.5 BB
A half pot raise from me is 4BB giving him an 11.5 : 4 decision (about 2.9 : 1) he needs pot odds of 4:1 to call (actually 4.22 : 1) so he has made a mistake.. I am happy he is a donkey etc etc.
But how big is his mistake?
Well to justify calling 4BB, the pot needed to be about 16 BB ( this would give him his 4 : 1 odds needed )
The pot was 11.5BB and he needed 16BB to justify the call so his mistake was 4.5BB (16 – 11.5).
So calling is a mistake, it has a negative equity but its not that big of a mistake, its 4.5BB
If he folds then his EV is -3BB (the amount he has put in the pot so far)
So whilst his mistake of calling is bigger than that of folding, in real terms its not that much of a mistake. His net error is only 1.5BB more than the cost of folding


The Turn comes 2h and so I decide to charge him another ½ pot. The pot is now 15.5BB as he called preflop.

Now I bet 8BB. He is faced with a 23.5 : 8 call (2.9 : 1).

He would need a pot of 32BB to justify a call of 8BB so his error is 8.5BB (32 – 23.5). When we compare this figure to his investment in the pot so far, which is 7BB, we see that his error is again only 1.5BB.
Folding is the better option, but in reality its only marginally better than calling.

So lets go back to the flop and try a 2/3 pot bet.. lets see how much of an error that causes.

Preflop, the pot is 7.5BB and so now ill bet 6BB (2BB more than previously)
Now he is offered a 13.5 : 6 call (2.25 :1)
To call call a bet of 6BB he would need a pot of 24 to give him 4 : 1 odds. Here his mistake is 10.5. He has already invested 3BB so his net error becomes 7.5BB.
So when we bet ½ pot we paid 4bb and got a net error of 1.5BB, when we bet 2/3 pot we paid 6BB and caused a net error of 7.5BB…. that’s a lot more bang for your buck.

Lets now bet ¾ pot on the turn

Now the pot is 19.5BB (he calls 6BB for the pot of 13.5BB)
We bet 2/3 pot .. say 15BB. He is offered a 34.5 : 15 call (2.3: 1)
He needed a 60BB pot to give him his required 4 : 1 odds so his mistake is 25 .5BB!!! (60 – 34.5). He has put 9BB in the pot so his net error is 16.5BB.

So ½ pot ½ pot caused a net total error of 3BB and cost us 12BB
The ¾ pot ¾ pot caused a total net error of 24 BB and cost us 21BB

Is there a better way?

What about we bet only ½ pot and the ¾ pot on the turn?

Well from before, the half pot flop bet 4BB and causes him to make a 1.5BB net error, but it also swells the pot a little so now our ¾ pot bet will be bigger that a ¾ pot bet made on the flop.

Now on the turn the pot is 15.5BB.
He faces a ¾ pot bet of 12BB giving him a 27.5:12 call.
He needs a pot of 48 BB to justify his call so his error is 20.5BB!!! His investment in the pot so far has been 7BB, so his net error here is 13.5BB!!
His total net error is 15BB and we have spent 16BB inducing it.

Now this might seem like we get less of an error out of him than when we bet ¾ pot ¾ pot and that is true, but we have actually beaten him in a subtler way.

¾ pot ¾ pot builds a total pot on the river of 49.5 BB

½ pot ¾ pot builds a pot of 39.5 BB.

By betting a smaller amount on the flop, we aren’t really charging him much for his draw, but at the same time we are setting up a turn bet which will charge him heavily plus we are reducing the size of the total pot. Our hand is small, its TPTK.. but if he makes his, its a flush.
Not only do we charge him on the turn for his draw, but we also ensure that we don’t build a pot big enough to justify playing his hand in the first place (in essence we kick him in the nuts!!)
In fact we can take the idea a bit further.. we can actually offer him good odds on the flop, say betting 1/3 pot. (2.5BB) he gets his correct 4:1 odds so makes no mistake by calling.. but errors made on the flop are relatively small to those made on the turn. So we set him up for a big error on the turn and build a pot of 30.5BB by the river.. that’s a nice sized pot for our hand but a nasty one for his.. even if he wins, its not much to win with a flush.

So by betting 1/3 pot on the flop, we make a small error.. but in return we get to cheaply force our opponent to make a bigger error on the turn and build a pot that he wont be happy with.

Now remember back to the start of my ramblings.. the loser is the opponent who makes more errors. By adopting this kind of thinking and questioning not only what and why we do things, but also how big of an impact does it have on our opponent, we can think about coming up with better strategies to force bigger errors from our opponents.
 
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Steveg1976

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Nice post Stu and clearly explained.
 
zachvac

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Note that before the river though he's not making as big a mistake as you think. Say he calls with the flush draw then turn goes ch/ch and he bets half pot on river with 3 diamonds on board. You really folding?

Also I don't really understand what you mean by pot big enough for the hand. If we can force him to make as big an error as we can on the flop and then a still bigger error on the turn, why not do that? If we are reasonably sure we are ahead and he is drawing it doesn't matter what a good sized pot for a typical flush or a typical TPTK hand is. Hell if he'll call with a flush draw top pair is a great hand to get all-in with.

edit: also you talk of the "cost" of inducing a mistake. Remember that his mistake includes the fact that he sometimes wins our money (the reason he needs odds), thus there is no cost associated with us inducing the mistake, unless I'm misreading or misunderstanding what you're talking about.
 
Infamous1020

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Note that before the river though he's not making as big a mistake as you think. Say he calls with the flush draw then turn goes ch/ch and he bets half pot on river with 3 diamonds on board. You really folding?

Also I don't really understand what you mean by pot big enough for the hand. If we can force him to make as big an error as we can on the flop and then a still bigger error on the turn, why not do that? If we are reasonably sure we are ahead and he is drawing it doesn't matter what a good sized pot for a typical flush or a typical TPTK hand is. Hell if he'll call with a flush draw top pair is a great hand to get all-in with.

edit: also you talk of the "cost" of inducing a mistake. Remember that his mistake includes the fact that he sometimes wins our money (the reason he needs odds), thus there is no cost associated with us inducing the mistake, unless I'm misreading or misunderstanding what you're talking about.

Yes.
 
Infamous1020

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Oh btw OP--

does this apply to chess too?
 
Stu_Ungar

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Also I don't really understand what you mean by pot big enough for the hand. If we can force him to make as big an error as we can on the flop and then a still bigger error on the turn, why not do that? If we are reasonably sure we are ahead and he is drawing it doesn't matter what a good sized pot for a typical flush or a typical TPTK hand is. Hell if he'll call with a flush draw top pair is a great hand to get all-in with.

Well our hand is TPTK.. what if he picks up 2 pair along the way, what if we get it wrong and he is playing a set? This time he isnt drawing, but keeping the pot down prevents us routinely paying off sets whilst charging draws. I think by building a large pot with a TPTK type hand we enhance our own errors (when we make them... and we will)

edit: also you talk of the "cost" of inducing a mistake. Remember that his mistake includes the fact that he sometimes wins our money (the reason he needs odds), thus there is no cost associated with us inducing the mistake, unless I'm misreading or misunderstanding what you're talking about.

Obviously betting 3/4 pot 3/4 pot causes him to make the biggest mistake.. but the trade off he gets is that when he does win, its a pot worthy of playing a flush. In effect he plays badly but gets a correct payoff. what im advocating is that by keeping the payoff small we cause him to make an error.. the error being playing us in pots which we dont build big enough to justify playing flushes against us.

Many of the times he calls with SC in position he will not hit the flop, so when he does hit a flop, by keeping the pot size down we dont give him the payoff needed to justify playing the cards in the first place.


What I got from the whole 'people loose because of the errors they make' is that we tend to view winning in a results orientated way.. we see charging draws as the entire goal. By looking at it in a different way we see that his mistakes are bigger on later streets so by allowing him to make a smaller error on the flop.. or even to make the correct decision on the flop, allows us to force him to make a bigger error on the turn whilst not over-inflating the pot.
 
Steveg1976

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Well our hand is TPTK.. what if he picks up 2 pair along the way, what if we get it wrong and he is playing a set? This time he isnt drawing, but keeping the pot down prevents us routinely paying off sets whilst charging draws. I think by building a large pot with a TPTK type hand we enhance our own errors (when we make them... and we will)



Obviously betting 3/4 pot 3/4 pot causes him to make the biggest mistake.. but the trade off he gets is that when he does win, its a pot worthy of playing a flush. In effect he plays badly but gets a correct payoff. what im advocating is that by keeping the payoff small we cause him to make an error.. the error being playing us in pots which we dont build big enough to justify playing flushes against us.

Many of the times he calls with SC in position he will not hit the flop, so when he does hit a flop, by keeping the pot size down we dont give him the payoff needed to justify playing the cards in the first place.


What I got from the whole 'people loose because of the errors they make' is that we tend to view winning in a results orientated way.. we see charging draws as the entire goal. By looking at it in a different way we see that his mistakes are bigger on later streets so by allowing him to make a smaller error on the flop.. or even to make the correct decision on the flop, allows us to force him to make a bigger error on the turn whilst not over-inflating the pot.

Correct me if I am wrong but I took your post to be not only about inducing mistakes in your opponent but also reducing your own. By betting the manner you suggest 1/2 then 3/4 rather than the more aggressive 3/4 3/4 with a TPTK you are trying to not only extract as much value as you can, you opponents mistake, but also limit your loss when you are wrong or he makes his hand which is just as important.

Obviously the better you are or the better your read is the more aggressively you can play the hand with greater confidence of being correct.

as usual I could be completely wrong too :)
 
Stu_Ungar

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Correct me if I am wrong but I took your post to be not only about inducing mistakes in your opponent but also reducing your own. By betting the manner you suggest 1/2 then 3/4 rather than the more aggressive 3/4 3/4 with a TPTK you are trying to not only extract as much value as you can, you opponents mistake, but also limit your loss when you are wrong or he makes his hand which is just as important.

Yes.. this is exactly what I was trying to get at. The traditional bet bet (extract maximum value) stratagy is setting us up for a bigger error when we are wrong.

By sacrificing some of that equity we force our opponent into a situation where he is always making more errors that we do.

By giving him an easier time on the flop (an error made by us) we are able to punish him on the turn at less cost to ourselves. We also avoid tougher decisions on the river etc etc.
 
StormRaven

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Yes.. this is exactly what I was trying to get at. The traditional bet bet (extract maximum value) stratagy is setting us up for a bigger error when we are wrong.

By sacrificing some of that equity we force our opponent into a situation where he is always making more errors that we do.

By giving him an easier time on the flop (an error made by us) we are able to punish him on the turn at less cost to ourselves. We also avoid tougher decisions on the river etc etc.

Great article Stu, looks like a lot of time and thought went into this. I love what you have to say here, I've recently been playing around with this type of betting a bit more.

In past if I put my opp on a draw on the flop I haven't been betting 3/4 or whole pot as much, they seem to pot commit themselves this way. I've started betting about 1/2 the pot, if they don't hit on the turn then I'm betting 3/4 - whole pot to take away odds.

If they do hit turn then I haven't invested so much that I can't get away from the hand.

Obviously the factors vary and hands do but hopefully my meaning is understood.
 
zachvac

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Sorry but our goal should be to maximize our opponents' mistakes. I think you're getting too much into the pot size for each hand. Sure it's a good starting guideline, but I think people in general are thinking too much about that and misapplying the logic. The reason we want to build different-sized pots with different hands is simply what the opponent is likely to have and likely to pay us off with. Most opponents don't stack with 2nd pair, so trying to get all our chips in with top pair no kicker is usually a losing play. This is why in general we want to bet bigger on drawy boards. There is a lot more that calls us so let him make the bigger mistake.

But the biggest logical error I think you are making is discussing what we lose when he hits. Sure what we lose when we're wrong is totally relevant to the discussion, but think for a minute what you are doing when you calculate odds. You are calculating how much he will win when he hits and lose when he misses. Then you're counting what it costs us when he hits again? The size of the pot compared to our absolute hand strength is irrelevant. We want to think about the pot size according to relative hand strength. So it is not a "mistake" when we build a big pot with TPTK and are beating our opponent's range. Sure once in a while we're wrong, but if he calls with worse enough without odds, that's how we profit. We don't profit when we build a perfectly-sized pot with TPTK or cause him to build what we arbitrarily decide is too small a pot for a flush. It simply doesn't work like that, we need to think about comparative strength. Also note though that on such a drawy board that he is likely to raise sets, therefore we can get a lot more value out of our TPTK because when he calls he almost always has worse or a draw. So as long as we don't give him odds (including implied, we can't say we've denied him good odds then pay him off when he hits) we want to induce the largest mistake period. You said it yourself in the OP, our money comes from opponent mistakes. Our money doesn't come from building perfectly-sized pots with different hands. So if we can induce a bigger mistake, not doing it is simply burning money. It's that simple.
 
Steveg1976

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But the biggest logical error I think you are making is discussing what we lose when he hits

Agreed but I don't think this was the most important point Stu was trying to make

. Sure what we lose when we're wrong is totally relevant to the discussion

This is the most important point he was trying to highlight I think...

, but think for a minute what you are doing when you calculate odds. You are calculating how much he will win when he hits and lose when he misses. Then you're counting what it costs us when he hits again? The size of the pot compared to our absolute hand strength is irrelevant. We want to think about the pot size according to relative hand strength. So it is not a "mistake" when we build a big pot with TPTK and are beating our opponent's range. Sure once in a while we're wrong, but if he calls with worse enough without odds, that's how we profit. We don't profit when we build a perfectly-sized pot with TPTK or cause him to build what we arbitrarily decide is too small a pot for a flush. It simply doesn't work like that, we need to think about comparative strength. Also note though that on such a drawy board that he is likely to raise sets, therefore we can get a lot more value out of our TPTK because when he calls he almost always has worse or a draw.

No description of the villian aggressiveness were given in the example so this is an assumption you are making based on your experience and we both know that there are villians so bad/passive this is not always true.

So as long as we don't give him odds (including implied, we can't say we've denied him good odds then pay him off when he hits) we want to induce the largest mistake period. You said it yourself in the OP, our money comes from opponent mistakes.

True but also by not making our own. I am not a very good player so I would estimate that my margin for error is possibly as high as 30-35% Total guess or even higher. When I add that into the equation there are times where I benefit more from taking a slightly less aggressive line more that I do by trying to induce a bigger mistake from my opponent and instead making that mistake myself. Obviosly this is villian dependant but something players need to be aware of.

Our money doesn't come from building perfectly-sized pots with different hands. So if we can induce a bigger mistake, not doing it is simply burning money. It's that simple.

My thoughts are above fwiw.
 
Steveg1976

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I should add that I am trying to put words in Stu's mouth, this is just what I took away from the post, right or wrong as I might be.
 
Stu_Ungar

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I should add that I am trying to put words in Stu's mouth, this is just what I took away from the post, right or wrong as I might be.

No you seem to be thinking about it in the same way that I was.

I can see why Zach advocates bet bet bet.. the equity error that our opponent makes is larger when we are correct. But we increase our own errors the times that we are wrong (and no poker player is ever 100% right).

If we are correct often then bet bet bet will cause him to make larger errors more quickly so our payoff is bigger. But at the same time, if our opponent is making these errors far more often than we are, then is there really a need to risk more chips on a single hand in order to exploit him? Surely if we can put him in a situation where just about every choice he makes is wrong, and we can do that often, then we reduce our own variance by sacrificing some equity.

As a side note, by betting big on each round, we do give him at least one correct and easy choice.. that being to fold!!!

Part of what I was trying to do was to put some figure on our chips to the size of his error. What this showed was that the only bet that was really causing him to make a large error was the 3/4 pot bet. The half pot bet gave him incorrect odds, but didnt induce much of an error. The error is also bigger on later streets as the pot is bigger, so by sacrificing a smaller error on the flop, we induced a larger error on the turn at a lower cost (chips) to ourselves. I supose you could say that it reduces varience!
 
widowmaker89

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Sorry but our goal should be to maximize our opponents' mistakes. I think you're getting too much into the pot size for each hand. Sure it's a good starting guideline, but I think people in general are thinking too much about that and misapplying the logic.

This.

Are we assuming that he is only on a flushdraw here? If so we want to charge him as much as he will call. I will gladly stack A high here if I knew he is on a flush draw, the strength of the hand doesnt matter at all. Like zach said, its a good guideline but it is not being applied correctly. The whole TPTK in general not being good to stack is because it doesnt play well on most boards against good opponants to raises and reraises. You are below the range(especially the players harrington is talking about) of the nits who are playing. It does not mean you should bet less so you lose less when they hit. What happens when the flush fills it goes ch/ch then they bet on river they have KJ? Im assuming you are folding or you are not taking everything into account.
 
Stu_Ungar

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It does not mean you should bet less so you lose less when they hit

This just isnt the point I'm trying to make. If you have read it fully and take away that point, then I am sorry.. I have just written the post really badly.
 
zachvac

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If we are correct often then bet bet bet will cause him to make larger errors more quickly so our payoff is bigger. But at the same time, if our opponent is making these errors far more often than we are, then is there really a need to risk more chips on a single hand in order to exploit him? Surely if we can put him in a situation where just about every choice he makes is wrong, and we can do that often, then we reduce our own variance by sacrificing some equity.
See this is the thing. In the long run variance evens out. So I'd rather take the higher equity higher variance route every single time.

As a side note, by betting big on each round, we do give him at least one correct and easy choice.. that being to fold!!!
Well obviously if we think he'll fold to a 3/4 pot bet or w/e we shouldn't make it. We want to bet as big as we think he'll call. If he'll call a pot bet we can make that. If we think he'll fold to a pot bet only 3/4 pot or w/e we think he'll call.

Part of what I was trying to do was to put some figure on our chips to the size of his error. What this showed was that the only bet that was really causing him to make a large error was the 3/4 pot bet. The half pot bet gave him incorrect odds, but didnt induce much of an error. The error is also bigger on later streets as the pot is bigger, so by sacrificing a smaller error on the flop, we induced a larger error on the turn at a lower cost (chips) to ourselves. I supose you could say that it reduces varience!

Right, it decreases variance, but that's what poker's about. We could just not play poker at all and have 0 variance, but then we would have no equity. Poker's about pushing edges and taking the variance along the way. Sure there are some spots where you may want to sacrifice your tiny edge for a huge variance play, especially when taking shots, but in general we should be maximizing our equity and ignoring the variance.
 
Stu_Ungar

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I can certainly see what you are saying.

Going a bit off topic.

How do we factor in the variance of our read being completely wrong?

Say we have TPTK, the board is a flush draw board so we start charging that. At the same time we are paying into a set.

Usually variance is meant when a miracle card comes, but I suppose it can also be used when our read is off (assuming that our read is good to begin with).

So how would that be factored into the decision?

Infact, should it be factored into the decision?
 
cardplayer52

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if you bet 1/3 of the pot it's still a mistake for a flush draw to call. the draw is getting 4 to 1 odds and needs 4.2 to 1 odds. as i understand sklanky its known as a battle of mistakes. it's not always who makes more mistakes but how big the mistakes are can factor into it. the key to it all is to make there mistakes more costly to them. if betting 1/3 the flop on a drawing board will get them to call a bigger turn bet do it. but IMO this is wrong. as they may call the flop bet for a little mistake but fold to the turn bet as the odds are no where close to good. this big turn bet helps them to play there hand correctly and not to make a mistake. i would think betting 1/2 to 2/3 the pot on the turn would still induce them to make a mistake. and as another poster points out you got to shut down if the flush happens to come out.
 
zachvac

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I can certainly see what you are saying.

Going a bit off topic.

How do we factor in the variance of our read being completely wrong?

Say we have TPTK, the board is a flush draw board so we start charging that. At the same time we are paying into a set.

Usually variance is meant when a miracle card comes, but I suppose it can also be used when our read is off (assuming that our read is good to begin with).

So how would that be factored into the decision?

Infact, should it be factored into the decision?

Well we want to use his range, and since we're never 100% sure he has a flush draw we need to consider part of his range flush draws, part of it better than us, part of it worse than us. So yes it should be factored in.
 
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Sorry to get into this late but I believe there is a crital error In the orginal post. please correct me if I am totally wrong. The caluation take into consideration the amount if funds in the pot. I believe this is wrong. How much does this change your error numbers?
 
Stu_Ungar

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Sorry to get into this late but I believe there is a crital error In the orginal post. please correct me if I am totally wrong. The caluation take into consideration the amount if funds in the pot. I believe this is wrong. How much does this change your error numbers?


Yes it does.

At any point the -EV of folding is the money put into the pot. There are some situations where both calling and folding are -EV plays but calling is yields a smaller -EV than folding.

If you were given two choices.. one had a LR EV of - 50 and the other - 25. Both are loosing plays but one looses less money that the other and therefore is the better choice.

The reason I compared the error to the money in the pot was to show that although calling a half pot raise was an error, it was only fractionally worse than the EV of folding. When the raise became 3/4 pot the error of calling was significantly bigger than the cost of folding.

Calling in either case is a greater error than folding, yet with 1/2 pot raises the error is very small (in the region of 1.5BB.. which is less than a standard preflop raise.)

So in this case it isnt wrong to look at the money already put in the pot, I needed something to actually compare ther error of calling with
 
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Thanks for the response. I understand why you did the comparison the way you did. It took me several lawn mowings of thought to find that i agree with you and your methodology. Buy yourself a beer . thanks.
 
widowmaker89

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There are some situations where both calling and folding are -EV plays but calling is yields a smaller -EV than folding.

Um... Folding is always zero EV. Each decision you start over. You might lose money on a hand but when you are deciding what to do on a flop or whenever if you fold the EV is obviously zero. Its more of an actual value of zero, but its what we compare any EV to.
 
Stu_Ungar

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Um... Folding is always zero EV. Each decision you start over. You might lose money on a hand but when you are deciding what to do on a flop or whenever if you fold the EV is obviously zero. Its more of an actual value of zero, but its what we compare any EV to.

No it isn't. Folding has an - EV its just usually significantly worse than calling
 
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