Equity and value betting
 

Hey,

For simplicity's sake, let's assume you're on the riever, in position with a deep stack left. You have a decent hand and it's checked to you.

How does your equity vs. the vil's range affect your decisions regarding value betting? At what equity does value-betting make sense? 30-40% and up?

Thanks.

Re: Equity and value betting
 

Ummm.. I'll take a stab.... I think the basic thought here would be to answer this question: Given by read on the vil and his range, how likely am I to get called by a hand that I can beat? Taken to the extreme, if I am only going to get called by a hand that beats me, then you have no additional equity in the hand by betting and hence you check it down (UNLESS, OF COURSE, YOU DON'T WANT YOUR HOLE CARDS SEEN - IF, FOR EXAMPLE, YOU WERE RAISING WITH SOME ODD COMBO FROM EARLY POSITION OR SOMETHING WHICH WAS IN CONTRAST TO YOUR TABLE IMAGE, IN WHICH CASE, IT WOULD PAY TO MAKE THE BET AND HOPE TO WIN THE HAND WITHOUT EXPOSING YOUR CARDS). On the other extreme - if you KNOW you are going to get called on the river by a substandard hand that you surely have beaten, then, by all means, you would try to extract every $$ possible by betting.

As far as the math - you really don't need much fold equity at all to make it a positive EV play on the river - I mean, if you have a hand thats gonna be a loser 2 out of 3 times on showdown, and your opponent is going to call 70% of the time, you still have a 53% EV position and, if you arent risking much of your stack percentage wise, it's clear that you should make the bet, unless there is a possiblity that your opponent could be check-raising 5th street. But if your read on him is right and you don't think he will, then by all means make the value bet. The question becomes, "how much to bet so that I maintain what little fold equity (30%, lets say) that I have. If there is 1000 in the pot, and you bet 200, your opponent is getting 6/1 pot odds (200 to call to win 1200) and might make the call just figuring he can lose this 80% of the time and still make money. So your river bet must be large enough to maintain the "fold equity" that you require depending on your assessment of your hands chances on showdown.

If you feel that your hand has a higher chance to prevail on showdown adjust accordingly and feel free to offer what seem to be better pot odds for the call.

not sure if this helps

Re: Equity and value betting
 

[ QUOTE ]
Ummm.. I'll take a stab.... I think the basic thought here would be to answer this question: Given by read on the vil and his range, how likely am I to get called by a hand that I can beat? Taken to the extreme, if I am only going to get called by a hand that beats me, then you have no additional equity in the hand by betting and hence you check it down (UNLESS, OF COURSE, YOU DON'T WANT YOUR HOLE CARDS SEEN - IF, FOR EXAMPLE, YOU WERE RAISING WITH SOME ODD COMBO FROM EARLY POSITION OR SOMETHING WHICH WAS IN CONTRAST TO YOUR TABLE IMAGE, IN WHICH CASE, IT WOULD PAY TO MAKE THE BET AND HOPE TO WIN THE HAND WITHOUT EXPOSING YOUR CARDS). On the other extreme - if you KNOW you are going to get called on the river by a substandard hand that you surely have beaten, then, by all means, you would try to extract every $$ possible by betting.

As far as the math - you really don't need much fold equity at all to make it a positive EV play on the river - I mean, if you have a hand thats gonna be a loser 2 out of 3 times on showdown, and your opponent is going to call 70% of the time, you still have a 53% EV position and, if you arent risking much of your stack percentage wise, it's clear that you should make the bet, unless there is a possiblity that your opponent could be check-raising 5th street. But if your read on him is right and you don't think he will, then by all means make the value bet. The question becomes, "how much to bet so that I maintain what little fold equity (30%, lets say) that I have. If there is 1000 in the pot, and you bet 200, your opponent is getting 6/1 pot odds (200 to call to win 1200) and might make the call just figuring he can lose this 80% of the time and still make money. So your river bet must be large enough to maintain the "fold equity" that you require depending on your assessment of your hands chances on showdown.

If you feel that your hand has a higher chance to prevail on showdown adjust accordingly and feel free to offer what seem to be better pot odds for the call.

not sure if this helps

[/ QUOTE ]

That makes sense, thanks. I guess the simplicity is to compare the fold equity and chance that he holds and will call with weaker hands to the size of your bet and the pot.

Theoretically, a $50 river bet into a $100 pot would need at least 50% equity outlined above, right?

Re: Equity and value betting
 

That's good that you think about stuff like this. One of the best ways I've improved is breaking down even the simplest concepts.

However, fold equity has nothing to do with deciding whether or not you should value bet. Also, try not to think about it in terms of Equity %'s either.

Here is a hint: When you bet what needs to happen in order to show a profit (think of it in the long run)?

Re: Equity and value betting
 

[ QUOTE ]
That's good that you think about stuff like this. One of the best ways I've improved is breaking down even the simplest concepts.

However, fold equity has nothing to do with deciding whether or not you should value bet. Also, try not to think about it in terms of Equity %'s either.

Here is a hint: When you bet what needs to happen in order to show a profit (think of it in the long run)?

[/ QUOTE ]

Im not sure I agree with you here Craig on the matter of fold equity... after all, the original question was what to do with a MEDIOCRE HAND on the river. If the question was, "I have a pretty damned good hand (not the nuts) which I am pretty damned sure is ahead here (although not 100%), then you are correct - fold equity wouldn't be part of it because, you really don't want the person to fold.

But the question here was specifically a mediocre hand which, I take to mean as one which could pretty much be a loser as often as it's a winner on showdown. With that type of hand, the river bet truly isn't a "value bet" in the true sense of the word, and I think fold equity should be at least PART of your thinking and I think EV and pot odds offered are definitely part of it as well.

Re: Equity and value betting
 

Pot equity is not the main point. As PhlegmWad said, you have to think about the chance of being called by a hand that you can beat. You also have to know what you will do to an all-in reraise.

It's the texture of board that matters, along with the betting to date and style of the other player. You almost never want to bet into a hand that might be sure it has you beat. You also almost never want to bet if you have the weakest likely hand given your betting so far (and if you do bet, it's a pure bluff). You almost always want to put in a sizeable bet if it's a wide-open hand such that the other player is not likely to have nuts, and you have something signficantly better than your weakest possibility. You can't really figure out the EV in that situation, but you can force a hard choice on the other player. When you can't do something right yourself, give someone else a chance to do something wrong.

Re: Equity and value betting
 

[ QUOTE ]
Ummm.. I'll take a stab.... I think the basic thought here would be to answer this question: Given by read on the vil and his range, how likely am I to get called by a hand that I can beat? Taken to the extreme, if I am only going to get called by a hand that beats me, then you have no additional equity in the hand by betting and hence you check it down (UNLESS, OF COURSE, YOU DON'T WANT YOUR HOLE CARDS SEEN - IF, FOR EXAMPLE, YOU WERE RAISING WITH SOME ODD COMBO FROM EARLY POSITION OR SOMETHING WHICH WAS IN CONTRAST TO YOUR TABLE IMAGE, IN WHICH CASE, IT WOULD PAY TO MAKE THE BET AND HOPE TO WIN THE HAND WITHOUT EXPOSING YOUR CARDS). On the other extreme - if you KNOW you are going to get called on the river by a substandard hand that you surely have beaten, then, by all means, you would try to extract every $$ possible by betting.

As far as the math - you really don't need much fold equity at all to make it a positive EV play on the river - I mean, if you have a hand thats gonna be a loser 2 out of 3 times on showdown, and your opponent is going to call 70% of the time, you still have a 53% EV position and, if you arent risking much of your stack percentage wise, it's clear that you should make the bet, unless there is a possiblity that your opponent could be check-raising 5th street. But if your read on him is right and you don't think he will, then by all means make the value bet. The question becomes, "how much to bet so that I maintain what little fold equity (30%, lets say) that I have. If there is 1000 in the pot, and you bet 200, your opponent is getting 6/1 pot odds (200 to call to win 1200) and might make the call just figuring he can lose this 80% of the time and still make money. So your river bet must be large enough to maintain the "fold equity" that you require depending on your assessment of your hands chances on showdown.

If you feel that your hand has a higher chance to prevail on showdown adjust accordingly and feel free to offer what seem to be better pot odds for the call.

not sure if this helps

[/ QUOTE ]
You need to factor in that your mediocre hand will sometimes win if you check. Saying "if I bet $X and he fold Y% of the time, I profit, therefore I should bet" is correct only when your hand has no chance of winning the showdown. It will often appear that you stole the pot when the pot was yours. Remember, you can't bluff with the best hand.

Re: Equity and value betting
 

Ok here is what goes through my mind when deciding to value bet:

First, I kind of visualize what I think his range is. Then I think of all the hands that he calls my bet with, how many I am beating and how many I am losing to. A value bet must be called by more hands that you beat then are beating you. If he calls with 20 hands and I beat 12 of them, then it will be a profitable bet.

It doesn't matter how much the guy folds, if he calls with more hands that beat you then you beat, you should not bet. The only time FE comes into play is when you are deciding to bluff..

Edit: If when the guy calls and he has more hands that beat you and it is still more profitable to bet then check, then you are technically bluffing not value betting

Re: Equity and value betting
 

[ QUOTE ]
Pot equity is not the main point. As PhlegmWad said, you have to think about the chance of being called by a hand that you can beat. You also have to know what you will do to an all-in reraise.

It's the texture of board that matters, along with the betting to date and style of the other player. You almost never want to bet into a hand that might be sure it has you beat. You also almost never want to bet if you have the weakest likely hand given your betting so far (and if you do bet, it's a pure bluff). You almost always want to put in a sizeable bet if it's a wide-open hand such that the other player is not likely to have nuts, and you have something signficantly better than your weakest possibility. You can't really figure out the EV in that situation, but you can force a hard choice on the other player. When you can't do something right yourself, give someone else a chance to do something wrong.

[/ QUOTE ]

Very excellently said Aaron. Perfectly and simply described - I liked the last sentence - as poker is all about making better decisions then your opponents, and they can't make bad decisions if they have no decision to make in the first place! [img]/images/graemlins/smirk.gif[/img]

Also excellent to stress the "all-in reraise" angle. Alot of that has to do with your read on the Vil and your table image, and how we got to the point where you are faced with a possible river bet with a medium-stregnth hand.

For example, what if you raised with some suited ace, say A5h and got called preflop by someone who you have position on - say the SB and are heads up. The flop comes 5 K 10 with 2 hearts, Vil checks, you bet out half the pot and get called. Say turn is a blank 2, and Vil check-calls after you bet half the pot again with bottom pair and nut-flush draw. Say river comes another blank.. say a off suit 7 (5 K 10 2 7) and now the Vil checks again. In this case your table image and read on the other player is critical. Could this person have been paying to see with JQ? Against that type of player, a bet on the river will get you nothing. Maybe they were calling you down with a non-nut flush draw and missed. Same thing.

Maybe they have a "decent" or "mediocre" hand here too, like A-10 or J-10? Strangely enough, this is <u>the type of player</u> against whom IN GENERAL, you probably would consider making a nice healthy river bet against with a medium strength hand (even though they have you beat in this case) because they are more likely to call with a hand that you have beat and <u>a reraise is highly unlikely</u>.

But maybe they have a set of 2's or they flopped 2 pair and didn't repop. Are they the "sneaky" type of player who could sit there and just let you fire away, hoping you'll fire a 3rd bullet on the river? Against that type of player, you want to check it down. If its the type of player who bets their hands more forwardly, then you have to think "if he had a set or 2 pair I would have heard about it on 4th street" so you are less likely to face the big reraise out of the blue.

Needless to say, the situation would be completely different if you raise with suited A5, the BB called. Flop, check/check, turn, check/check, river, check and its up to you.

Poker situations aren't static. We aren't plopped down in a situation where we have a "decent" hand on the river, what do we do? <u>How we got to that point is everything.</u>

Re: Equity and value betting
 

[ QUOTE ]
You need to factor in that your mediocre hand will sometimes win if you check. Saying "if I bet $X and he fold Y% of the time, I profit, therefore I should bet" is correct only when your hand has no chance of winning the showdown. It will often appear that you stole the pot when the pot was yours. Remember, you can't bluff with the best hand.

[/ QUOTE ]

Good point. That is factored in, however. Like I say, for example, if you figure you have a hand that is ahead of 60% of his hands (60% chance to win on showdown) and there is a 30% chance that he will fold - when you put these two TOGETHER, you are in a 72% situation. So, in a world without reraises (hahaha), if the only decision on the river is bet/no bet, followed by call/fold you really only need to have a hand that wins 1/3 of the time combined with a 30% chance of folding in order to bring the entire transaction up to a positive EV at 53%. (this is more akin to shove/fold strategy, though it can be applied on the river as well where the chance of reraise is significantly close to zero)

Re: Equity and value betting
 

[ QUOTE ]
Pot equity is not the main point. As PhlegmWad said, you have to think about the chance of being called by a hand that you can beat. You also have to know what you will do to an all-in reraise.

It's the texture of board that matters, along with the betting to date and style of the other player. You almost never want to bet into a hand that might be sure it has you beat. You also almost never want to bet if you have the weakest likely hand given your betting so far (and if you do bet, it's a pure bluff). You almost always want to put in a sizeable bet if it's a wide-open hand such that the other player is not likely to have nuts, and you have something signficantly better than your weakest possibility. You can't really figure out the EV in that situation, but you can force a hard choice on the other player. When you can't do something right yourself, give someone else a chance to do something wrong.

[/ QUOTE ]

Well put, and I agree. I guess my original question is better understood in context of how it came about. I was watching one of Townsend's videos and on the turn of one of his hands, he remarked how he still had a lot of equity against his opponent's range, and that he could've pushed instead of calling (he was analyzing a hand in PT).

I was just curious how he concluded that. I guess he was looking at his equity versus this vil's range and also the probability of the vil calling his shove with an underdog hand.

BTW, what did you mean by a "wide-open hand"?

Re: Equity and value betting
 

[ QUOTE ]
That's good that you think about stuff like this. One of the best ways I've improved is breaking down even the simplest concepts.

However, fold equity has nothing to do with deciding whether or not you should value bet. Also, try not to think about it in terms of Equity %'s either.

Here is a hint: When you bet what needs to happen in order to show a profit (think of it in the long run)?

[/ QUOTE ]

Well, as Phlegm was saying, I'm looking at marginal situations where you may or may not have to best hand (kicker wars or something), but you feel you have too much equity vs. the vil's range to simply check. Folding equity, I feel, has a little to do with it as the vil may fold the better hand.

Re: Equity and value betting
 

[ QUOTE ]
[ QUOTE ]
Ummm.. I'll take a stab.... I think the basic thought here would be to answer this question: Given by read on the vil and his range, how likely am I to get called by a hand that I can beat? Taken to the extreme, if I am only going to get called by a hand that beats me, then you have no additional equity in the hand by betting and hence you check it down (UNLESS, OF COURSE, YOU DON'T WANT YOUR HOLE CARDS SEEN - IF, FOR EXAMPLE, YOU WERE RAISING WITH SOME ODD COMBO FROM EARLY POSITION OR SOMETHING WHICH WAS IN CONTRAST TO YOUR TABLE IMAGE, IN WHICH CASE, IT WOULD PAY TO MAKE THE BET AND HOPE TO WIN THE HAND WITHOUT EXPOSING YOUR CARDS). On the other extreme - if you KNOW you are going to get called on the river by a substandard hand that you surely have beaten, then, by all means, you would try to extract every $$ possible by betting.

As far as the math - you really don't need much fold equity at all to make it a positive EV play on the river - I mean, if you have a hand thats gonna be a loser 2 out of 3 times on showdown, and your opponent is going to call 70% of the time, you still have a 53% EV position and, if you arent risking much of your stack percentage wise, it's clear that you should make the bet, unless there is a possiblity that your opponent could be check-raising 5th street. But if your read on him is right and you don't think he will, then by all means make the value bet. The question becomes, "how much to bet so that I maintain what little fold equity (30%, lets say) that I have. If there is 1000 in the pot, and you bet 200, your opponent is getting 6/1 pot odds (200 to call to win 1200) and might make the call just figuring he can lose this 80% of the time and still make money. So your river bet must be large enough to maintain the "fold equity" that you require depending on your assessment of your hands chances on showdown.

If you feel that your hand has a higher chance to prevail on showdown adjust accordingly and feel free to offer what seem to be better pot odds for the call.

not sure if this helps

[/ QUOTE ]
You need to factor in that your mediocre hand will sometimes win if you check. Saying "if I bet $X and he fold Y% of the time, I profit, therefore I should bet" is correct only when your hand has no chance of winning the showdown. It will often appear that you stole the pot when the pot was yours. Remember, you can't bluff with the best hand.

[/ QUOTE ]

Good point. I was just thinking with the occasional hand where, by the river, you feel you have too much equity to simply check as the vil's range includes a fair amount of hands that he will call with and lose. In that case, a check-check is most likely lower EV than check-value bet. I'm going to play around in Excel on this and see what I come up with.

Re: Equity and value betting
 

[ QUOTE ]
Ok here is what goes through my mind when deciding to value bet:

First, I kind of visualize what I think his range is. Then I think of all the hands that he calls my bet with, how many I am beating and how many I am losing to. A value bet must be called by more hands that you beat then are beating you. If he calls with 20 hands and I beat 12 of them, then it will be a profitable bet.

It doesn't matter how much the guy folds, if he calls with more hands that beat you then you beat, you should not bet. The only time FE comes into play is when you are deciding to bluff..

Edit: If when the guy calls and he has more hands that beat you and it is still more profitable to bet then check, then you are technically bluffing not value betting

[/ QUOTE ]

This is good, but it doesn't take into the account the probabilities of each holding in his range. You don't want to weight each holding equally, unless you truly feel each is equally likely.

When working EV calculations, this is easy, but it's tough to do at the table. I've created EV "drills" that I do, which is helping a lot. At the tables it helps my feel for situations as I'll remember drilling a similar situation before.

Re: Equity and value betting
 

[ QUOTE ]
[ QUOTE ]
That's good that you think about stuff like this. One of the best ways I've improved is breaking down even the simplest concepts.

However, fold equity has nothing to do with deciding whether or not you should value bet. Also, try not to think about it in terms of Equity %'s either.

Here is a hint: When you bet what needs to happen in order to show a profit (think of it in the long run)?

[/ QUOTE ]

Well, as Phlegm was saying, I'm looking at marginal situations where you may or may not have to best hand (kicker wars or something), but you feel you have too much equity vs. the vil's range to simply check. Folding equity, I feel, has a little to do with it as the vil may fold the better hand.

[/ QUOTE ]
If villain is folding better hands then how is he calling with many worse hands? This would be a bluffing situation.

Re: Equity and value betting
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
That's good that you think about stuff like this. One of the best ways I've improved is breaking down even the simplest concepts.

However, fold equity has nothing to do with deciding whether or not you should value bet. Also, try not to think about it in terms of Equity %'s either.

Here is a hint: When you bet what needs to happen in order to show a profit (think of it in the long run)?

[/ QUOTE ]

Well, as Phlegm was saying, I'm looking at marginal situations where you may or may not have to best hand (kicker wars or something), but you feel you have too much equity vs. the vil's range to simply check. Folding equity, I feel, has a little to do with it as the vil may fold the better hand.

[/ QUOTE ]
If villain is folding better hands then how is he calling with many worse hands? This would be a bluffing situation.

[/ QUOTE ]

Well, I don't consider it bluffing unless you know you have the worst hand. If your vil's range includes several likely holdings that are weaker than yours, it's not a complete bluff.

Re: Equity and value betting
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
That's good that you think about stuff like this. One of the best ways I've improved is breaking down even the simplest concepts.

However, fold equity has nothing to do with deciding whether or not you should value bet. Also, try not to think about it in terms of Equity %'s either.

Here is a hint: When you bet what needs to happen in order to show a profit (think of it in the long run)?

[/ QUOTE ]

Well, as Phlegm was saying, I'm looking at marginal situations where you may or may not have to best hand (kicker wars or something), but you feel you have too much equity vs. the vil's range to simply check. Folding equity, I feel, has a little to do with it as the vil may fold the better hand.

[/ QUOTE ]
If villain is folding better hands then how is he calling with many worse hands? This would be a bluffing situation.

[/ QUOTE ]

Well, I don't consider it bluffing unless you know you have the worst hand. If your vil's range includes several likely holdings that are weaker than yours, it's not a complete bluff.

[/ QUOTE ]
The best thing to do is to open up pokerstove and make up a hypothetical situation with a marginal hand and divide up villains range into calling and folding. Then run the math and you'll see what I mean.

Edit: Basically, what I'm saying is that if you think there is a situation where you're bluffing and he's calling you with worse hands, you'll see that checking is actually better. And if there is a situation when you're value betting and he is folding better hands, you'll also see that checking is better. There won't be a villain where you can consider FE when value betting and value from worse hands when bluffing..

Re: Equity and value betting
 

[ QUOTE ]
Theoretically, a $50 river bet into a $100 pot would need at least 50% equity outlined above, right?

[/ QUOTE ]

Well, if you were CALLING $50 to win $100, you are correct, you would have to win half the time to be even. But you aren't calling here.. you are betting, <u>and so you must consider what decision you are placing on the lap of your opponent</u> Once you make a $50 bet into the $100 pot on the river, assuming he is not reraising, he has to ask himself "I need $50 to call the $150 in the pot... I have to be right better then 1/3 of the time"... again, we have no idea how you got to this point, but if they think there is any realistic shot that they have the best hand, and they are deep stacked relative to the pot (as you said), then 1/2 the pot might not be a difficult decision for them to screw up given that they can be wrong twice as often as right and still be "whole" on the decision...they are gonna call and your hand will have to prevail on its own merits (thus the trouble with betting "medium" strength hands).. if you have a "strong" hand, then offering them 3/1 might be just the ticket to get them to make a mistake calling with a hand that they are going to lose with a much higher % of the time than that. Remember the choice you are giving your opponent and don't give them a decision that they can't screw up!

Re: Equity and value betting
 

This has been solved for the uniform [0,1] game.
Using low values as best. One bet only. Only
you may bet, opp(onent) may call or fold.
Pot size is two chips. Bet size is one chip.

You should bet =&lt; 0.3 and bluff &gt;= 0.9.
Opp should call =&lt; 0.6.

Now to apply this to a real game was left as
an exercise for the reader.

Re: Equity and value betting
 

[ QUOTE ]
There won't be a villain where you can consider FE when value betting and value from worse hands when bluffing..

[/ QUOTE ]

Either we are saying the same thing 2 different ways, or I'm not sure I agree or I'm confused on your definition of bluffing?? ..after all, what are the only 2 reasons you would bet on the river? Either (1)if you can get a better hand to fold, or (2) you can get called by a worse hand. So therefore, fold equity is a consideration when you are facing a hand that "could" be ahead of yours - so with any "medium" hand, its a consideration as it reduces the % of times your hand has to prevail on its own merits when called. Theoretically, the only time when fold equity can be completely ignored is when you hold the nuts. Although for sufficiently strong hands, it may be considered small de-minimus and, thus, ignored.

Re: Equity and value betting
 

[ QUOTE ]
So therefore, fold equity is a consideration when you are facing a hand that "could" be ahead of yours - so with any "medium" hand, its a consideration as it reduces the % of times your hand has to prevail on its own merits when called.

[/ QUOTE ]
There won't be a situation like this where you can consider FE because the bet will be -EV and checking will be better. The reason for this is because no villain will call with enough worse hands while still folding better.

You have to do it yourself to understand. If you still think I am wrong, then all you have to do is make up a hypothetical situation and show me the math.

Re: Equity and value betting
 

[ QUOTE ]
Good point. That is factored in, however. Like I say, for example, if you figure you have a hand that is ahead of 60% of his hands (60% chance to win on showdown) and there is a 30% chance that he will fold - when you put these two TOGETHER, you are in a 72% situation. So, in a world without reraises (hahaha), if the only decision on the river is bet/no bet, followed by call/fold you really only need to have a hand that wins 1/3 of the time combined with a 30% chance of folding in order to bring the entire transaction up to a positive EV at 53%. (this is more akin to shove/fold strategy, though it can be applied on the river as well where the chance of reraise is significantly close to zero)

[/ QUOTE ]
I think I just found the source of confusion. The part in bold is wrong. You are assuming that the hand he holds is independant of whether or not he'll call.

Let event A be your opponent calling on the river
Let event B be your opponent having the best hand

P(A &amp; B) != P(A)*P(B)

P(A &amp; B) = P(A|B)*P(B)

Keep in mind much of your equity is a result of your opponent having a busted draw or another "nothing" hand that will never call the river.

Your opponent should have some line for quality of hand he calls with; if his hand is above this line he'll call, if his hand is below it he'll fold. If this "line" happens to be set at the same level as your hand, you should never bet (because he'll call with all his better hands and fold all his worse hands). If your opponent's "line" is well below your hand you should bet for value. If your opponent's "line" is well above your hand you should bet as a bluff. As a general rule, the further your hand is from this "line" the more likely you should be to bet. This line will usually be set in the marginal range. When your hand is marginal you're close to his line and should check. If you have reason to believe the line is lower than it should be make more value bets.

This line exsists in a quantum state. (You don't know exactly what he'll fold and what he'll call with and have no way of knowing it.) With certain conditions you might be able to make a 2-way bet (this is a bet where you may get called by a worse hand and may fold out a better hand), but this virtually never happens on the river. An example of a 2-way bet would be betting on a draw heavy board with A-high; your opponent would likely fold a small pair, but would call with a flush or straight draw.

Edit: also, I think the term "fold equity" is being misused. It's not the size of the pot*probabiity of him folding. It's the equity you gain when he folds, this is equal to his equity*size of the pot. If your opponent has a worse hand on the river he has 0% equity. 0*size of the pot = 0 = your fold equity.

Re: Equity and value betting
 

[ QUOTE ]
With certain conditions you might be able to make a 2-way bet (this is a bet where you may get called by a worse hand and may fold out a better hand), but this virtually never happens on the river.

[/ QUOTE ]

Ok .. we are just focusing in on different aspects of this. I disagree with the quoted part above in NO LIMIT. In NL, it's much easier to do these 2 things. In limit poker, I think you are more on target.

As for the math, in the binary 2-step process (bet/no bet) followed by (fold/call), your chances of winning a hand after betting are:

F + (1-F)(W)

where F is the chance that your opponent will fold; and
W is the chance that your hand will prevail upon turning the cards up (or the number of hands that your hand beats)

so, if I bet, and there is a 30% chance that my opponent will fold and my hand, if showed down will only win 33% of the time, then my combined chance is

.3 + (.7)(.33) = .531

If we wanted to put $$ on this, we would have to define the stakes, such as S1 =initial pot, S2 = inital pot + (2*river bet). This would give us an equity in $$ of betting option. So, if the inital pot were $100, and my bet is $50, then my $ expected value of the bet would be:


(.3 * 100) + (.7)(.33)(200) = $76
for making a $50 bet at a $100 pot with a 30% chance of winning by default (fold %) and a 70% chance that the hand will show down with me losing 2/3 of the time.

Re: Equity and value betting
 

[ QUOTE ]
[ QUOTE ]
With certain conditions you might be able to make a 2-way bet (this is a bet where you may get called by a worse hand and may fold out a better hand), but this virtually never happens on the river.

[/ QUOTE ]

Ok .. we are just focusing in on different aspects of this. I disagree with the quoted part above in NO LIMIT. In NL, it's much easier to do these 2 things. In limit poker, I think you are more on target.

[/ QUOTE ]
I agree that NL does give one an opportunity to turn a marginal hand into a bluff, an opportunity that you'll never have in FL (in a HU pot anyway), but I don't see how that makes it a 2-way bet.

Re: Equity and value betting
 

[ QUOTE ]
(.3 * 100) + (.7)(.33)(200) = $76
for making a $50 bet at a $100 pot with a 30% chance of winning by default (fold %) and a 70% chance that the hand will show down with me losing 2/3 of the time.

[/ QUOTE ]
^ This is well off. Here is what the math is for that situation:
EV of bet= 1/3(+50) + 2/3(-50)
= -$16.6
This is assuming that no better hands fold.

You have to look at it logically. You can't think a $50 bet is going to yield you a $76 profit.

Re: Equity and value betting
 

[ QUOTE ]
I don't see how that makes it a 2-way bet.

[/ QUOTE ]

a) what's a 2-way bet?
b) how is this related to the initial question?

Re: Equity and value betting
 

[ QUOTE ]
a) what's a 2-way bet?

[/ QUOTE ]
[ QUOTE ]
...a 2-way bet (this is a bet where you may get called by a worse hand and may fold out a better hand), but this virtually never happens on the river.

[/ QUOTE ]

[ QUOTE ]
b) how is this related to the initial question?


[/ QUOTE ]
In your calculations you use both value and fold equity when dealing with the same bet. A bet that has both value and fold equity is a 2-way bet.

Re: Equity and value betting
 

[ QUOTE ]
In your calculations you use both value and fold equity when dealing with the same bet. A bet that has both value and fold equity is a 2-way bet.

[/ QUOTE ]

I would agree that there are very few cases where you feel that you are value betting but are really bluffing. Typically, in NL these only happen when you catch a big river card that gives you like 2nd or 3rd nuts and run into the nuts. And when this is the case, certainly, you are always making the river bet hoping for a call (even when you are beat) so it's not 2-way.

The flip side, however, happens quite frequently with aggressive players in NL tourneys -- that being a situation where you are bluffing with the best hand. That is, you have a medium-strength hand but are representing more and get to the river and decide to fire away with what you suppose might be the worst hand (but the only way you are gonna win the pot is by betting) but, as it turns out, you actually have the best hand. This happens frequently with aggressive players who are playing draws or who know each others games well.

Good discusion!

Re: Equity and value betting
 

[ QUOTE ]
[ QUOTE ]
(.3 * 100) + (.7)(.33)(200) = $76
for making a $50 bet at a $100 pot with a 30% chance of winning by default (fold %) and a 70% chance that the hand will show down with me losing 2/3 of the time.

[/ QUOTE ]
^ This is well off. Here is what the math is for that situation:
EV of bet= 1/3(+50) + 2/3(-50)
= -$16.6
This is assuming that no better hands fold.

You have to look at it logically. You can't think a $50 bet is going to yield you a $76 profit.

[/ QUOTE ]

Appolgy.. my 76 was a combination typo/ommission. I understand. Humor me and take it apart step by step. Let's say there is $200 already in a pot that you are proposing a potention $50 river bet. 30% chance of opponent folding, 1/3 chance of prevailing on showdown.. step by step, wouldnt the math be the sum of the following 2 steps?:

step 1 - the first thing that can happen - I bet, they fold. $200 in the pot. We will assume that this happens 30% of the time. So, 30% of the time I win the $200 that is already in the pot....so my expected value of this outcome is .3*$200 = 60


step 2 - 70% of the time, my opponent does not fold, and my hand must win or lose on its own merits. If the pot is $200, I bet $50, opponent calls for $50, there is now $300 in the pot. If my hand wins 1/3 and loses 2/3, thats a net loss of 1/3 of the new pot ($300) or -$100*.7 = -$70

Add step one and two: 60-70 gives us a -$10 expectation on this new scenario?

Re: Equity and value betting
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
(.3 * 100) + (.7)(.33)(200) = $76
for making a $50 bet at a $100 pot with a 30% chance of winning by default (fold %) and a 70% chance that the hand will show down with me losing 2/3 of the time.

[/ QUOTE ]
^ This is well off. Here is what the math is for that situation:
EV of bet= 1/3(+50) + 2/3(-50)
= -$16.6
This is assuming that no better hands fold.

You have to look at it logically. You can't think a $50 bet is going to yield you a $76 profit.

[/ QUOTE ]

Appolgy.. my 76 was a combination typo/ommission. I understand. Humor me and take it apart step by step. Let's say there is $200 already in a pot that you are proposing a potention $50 river bet. 30% chance of opponent folding, 1/3 chance of prevailing on showdown.. step by step, wouldnt the math be the sum of the following 2 steps?:

step 1 - the first thing that can happen - I bet, they fold. $200 in the pot. We will assume that this happens 30% of the time. So, 30% of the time I win the $200 that is already in the pot....so my expected value of this outcome is .3*$200 = 60


step 2 - 70% of the time, my opponent does not fold, and my hand must win or lose on its own merits. If the pot is $200, I bet $50, opponent calls for $50, there is now $300 in the pot. If my hand wins 1/3 and loses 2/3, thats a net loss of 1/3 of the new pot ($300) or -$100*.7 = -$70

Add step one and two: 60-70 gives us a -$10 expectation on this new scenario?

[/ QUOTE ]

$100 pot and $50 river bet. I think the math goes like this:

(.3*100)+(.7((.33*150)+(.66*-50)))

30% of the time we'll win the $100 because he'll fold.

70% of the time he'll call, and 33% of the time we'll win the $100 in the pot plus the $50 he just added (our $50 bet isn't figured into this--you don't add your money wagered).

66% of the time we'll get called and we'll lose our $50.

Re: Equity and value betting
 

[ QUOTE ]
As for the math, in the binary 2-step process (bet/no bet) followed by (fold/call), your chances of winning a hand after betting are:

F + (1-F)(W)

where F is the chance that your opponent will fold; and
W is the chance that your hand will prevail upon turning the cards up (or the number of hands that your hand beats)

so, if I bet, and there is a 30% chance that my opponent will fold and my hand, if showed down will only win 33% of the time, then my combined chance is

.3 + (.7)(.33) = .531


[/ QUOTE ]
You're still assuming independance, which is not even close to correct. To give you an idea of how incorrect it is, it would be correct if your opponent's memory of his cards was erased after the turn and he was not allowed to look at his cards. If you don't understand why assuming independance is wrong you should think about it for a while. If that doesn't work you should learn about Bayes' Theorem. Every calculation you've done so far has been wrong for this reason.

If your equity is 33% and your opponent will fold 30% of the time you'll rarely win the showdown when you bet. Your hand is equal to the 33rd percentile of your opponent's range. If you bet he'll fold all but the top 70% of his range, and you only beat (3/70) of the top 70% of his range. If you check you'll win 33% of the time. If you bet you'll win (3/70)*(0.7) + 0.3 = 33% (this is an application of Bayes' theorem).

Notice how betting didn't improve your chances at winning. This is because your hand is too good to bluff with; you have no fold equity. For a bluff to be successful you have to be able to make a better hand fold. And the worse your hand is the easier it is to make a better hand fold.

His line is at 30% and your hand is at 33%. Because your hand is above your opponent's "line" you're value betting, not bluffing. And value betting when your hand has less than 50% equity vs. your oppoenent's calling range is -EV. This is a great example of when not to bet.

Re: Equity and value betting
 

[ QUOTE ]
Hey,

For simplicity's sake, let's assume you're on the riever, in position with a deep stack left. You have a decent hand and it's checked to you.

How does your equity vs. the vil's range affect your decisions regarding value betting? At what equity does value-betting make sense? 30-40% and up?

Thanks.

[/ QUOTE ]
To answer this you need to know what he'll call with. If you have 99% equity, but he'll only call with the top 1% of his hands you should check. Instead of thinking about your equity vs. his range think about your equity vs. his calling range.

If your equity vs. his calling range is less than 50% you cannot consider value betting. If the answer is well above 50% you should bet. If it's slightly above 50% you need to consider how you'll respond to a check-raise. If your decision vs. a check-raise will be easy you should bet. (An example of an easy decision would playing against a player who would never check-raise the river with a hand worse than yours. Against him you'd have an easy fold. Against a player who check-raised the river way too much, you'd have an easy call.) Against a player who check-raised the river with the correct frequency you'd have a very tough decision. They'll usually have the goods, but they'll be bluffing often enough to worry about it. When your equity vs. your opponent's calling range is in the 50-65% range evaluate how easy the decision will be if you get check raised. If it will be an easy decision, bet. If not, check.

On the river you should bet the top X% of your range for value, bet the bottom Y% of your range as a bluff and check everything in between.

Re: Equity and value betting
 

[ QUOTE ]
[ QUOTE ]
Hey,

For simplicity's sake, let's assume you're on the riever, in position with a deep stack left. You have a decent hand and it's checked to you.

How does your equity vs. the vil's range affect your decisions regarding value betting? At what equity does value-betting make sense? 30-40% and up?

Thanks.

[/ QUOTE ]
To answer this you need to know what he'll call with. If you have 99% equity, but he'll only call with the top 1% of his hands you should check. Instead of thinking about your equity vs. his range think about your equity vs. his calling range.

If your equity vs. his calling range is less than 50% you cannot consider value betting. If the answer is well above 50% you should bet. If it's slightly above 50% you need to consider how you'll respond to a check-raise. If your decision vs. a check-raise will be easy you should bet. (An example of an easy decision would playing against a player who would never check-raise the river with a hand worse than yours. Against him you'd have an easy fold. Against a player who check-raised the river way too much, you'd have an easy call.) Against a player who check-raised the river with the correct frequency you'd have a very tough decision. They'll usually have the goods, but they'll be bluffing often enough to worry about it. When your equity vs. your opponent's calling range is in the 50-65% range evaluate how easy the decision will be if you get check raised. If it will be an easy decision, bet. If not, check.

On the river you should bet the top X% of your range for value, bet the bottom Y% of your range as a bluff and check everything in between.

[/ QUOTE ]

I like that reasoning, thanks. Why 50% equity against his calling range to consider value betting, though?

Where can I read more on this? I'm in the middle of NLHE T&amp;P right now and was planning on reading Chen's Math of Poker next.

Re: Equity and value betting
 

if you are ahead more than 50% it is a valuebet because you will win (0.5+e) the opponents bet and (0.5-e) lose your bet.
where e is your edge...

you don't have to consider the pot because you have the opportunity to check, where you will gain the pot anyway if you are ahead...

valuebetting means that you get called by worse hand and therfore win an additional amount added to the pot.

its a valuebet even if you lose sometimes as long as you win more than 50%...

Re: Equity and value betting
 

[ QUOTE ]
if you are ahead more than 50% it is a valuebet because you will win (0.5+e) the opponents bet and (0.5-e) lose your bet.
where e is your edge...

you don't have to consider the pot because you have the opportunity to check, where you will gain the pot anyway if you are ahead...

valuebetting means that you get called by worse hand and therfore win an additional amount added to the pot.

its a valuebet even if you lose sometimes as long as you win more than 50%...

[/ QUOTE ]

I see. I guess then you tailor your bet size to ensure his calling range includes enough for your equity to be over 50%, right?

Re: Equity and value betting
 

[ QUOTE ]


$100 pot and $50 river bet. I think the math goes like this:

(.3*100)+(.7((.33*150)+(.66*-50)))

30% of the time we'll win the $100 because he'll fold.

70% of the time he'll call, and 33% of the time we'll win the $100 in the pot plus the $50 he just added (our $50 bet isn't figured into this--you don't add your money wagered).

66% of the time we'll get called and we'll lose our $50.

[/ QUOTE ]

Doesn't work that way. You must bluff else he need not call.
You're only betting you best 30% of hands. Why should he ever call with 30 to 70% of the best hands? Those calls will never win. He will instead call with only his best 22.5% of his hands.

But if you occasionally bluff. He must call with worst hands else you'll steal him blind. The recommended amount is 10% of your worst hands.
He does best by calling 60% of his hands. This is solved by differential calculus. You need to determine the proper equations for the relationship between betting, checking, bluffing, calling and folding. Or just put it all in an excel file and use trial and error.

Re: Equity and value betting
 

Like Pax said you have to look at the EV of betting vs. the EV of checking; not the EV of betting vs. the EV of mucking. You have 2 options; check or bet, not muck or bet. If your equity in the pot is 70%, the pot is $100, you can bet $50 and your oppoenent will call with the top 50% of his hands:

EV_checking = 0.7*$100 = $70

If his hand is in the range (0, 50) he'll fold to your bet and you'll win. If his hand is in the range (50,70) he'll call and you'll win, if it's in the range (70, 100) he'll call and you'll lose. 20% of the time he'll call and you'll win. 30% of the time he'll call and you'll lose.

EV_betting = 0.5*$100 + 0.2*$150 + 0.3*(-$50) = $65

EV_mucking = $0

Betting is better than mucking, but worse than checking. (Also, this does not take into consideration the possibility of being check-raised, which would make betting worse.)

Re: Equity and value betting
 

[ QUOTE ]
[ QUOTE ]


$100 pot and $50 river bet. I think the math goes like this:

(.3*100)+(.7((.33*150)+(.66*-50)))

30% of the time we'll win the $100 because he'll fold.

70% of the time he'll call, and 33% of the time we'll win the $100 in the pot plus the $50 he just added (our $50 bet isn't figured into this--you don't add your money wagered).

66% of the time we'll get called and we'll lose our $50.

[/ QUOTE ]

Doesn't work that way. You must bluff else he need not call.
You're only betting you best 30% of hands. Why should he ever call with 30 to 70% of the best hands? Those calls will never win. He will instead call with only his best 22.5% of his hands.

But if you occasionally bluff. He must call with worst hands else you'll steal him blind. The recommended amount is 10% of your worst hands.
He does best by calling 60% of his hands. This is solved by differential calculus. You need to determine the proper equations for the relationship between betting, checking, bluffing, calling and folding. Or just put it all in an excel file and use trial and error.

[/ QUOTE ]

That makes sense. Where can I read more about these concepts?

Re: Equity and value betting
 

[ QUOTE ]
Like Pax said you have to look at the EV of betting vs. the EV of checking; not the EV of betting vs. the EV of mucking. You have 2 options; check or bet, not muck or bet. If your equity in the pot is 70%, the pot is $100, you can bet $50 and your oppoenent will call with the top 50% of his hands:

EV_checking = 0.7*$100 = $70

If his hand is in the range (0, 50) he'll fold to your bet and you'll win. If his hand is in the range (50,70) he'll call and you'll win, if it's in the range (70, 100) he'll call and you'll lose. 20% of the time he'll call and you'll win. 30% of the time he'll call and you'll lose.

EV_betting = 0.5*$100 + 0.2*$150 + 0.3*(-$50) = $65

EV_mucking = $0

Betting is better than mucking, but worse than checking. (Also, this does not take into consideration the possibility of being check-raised, which would make betting worse.)

[/ QUOTE ]

That makes sense. I really need to read more about these concepts and then drill them. Where can I read about them?

Re: Equity and value betting
 

[ QUOTE ]
That makes sense. I really need to read more about these concepts and then drill them. Where can I read about them?

[/ QUOTE ]
What we've done here is create a probability density function (PDF) for both betting and checking then calculate the mean of each of them. This isn't so much a poker idea as it is a statistics idea with a poker application. Calculating the mean of a distribution is not difficult.

The tough part is quickly creating a PDF that accurately reflects the situation. This an exercise in logic more than anything else. Experience is helpful too.

It's a two step process:
1) Make good assumptions
2) Use assumptions to make a decision

Step 1 is the hard part.