Equity and value betting

[craig1120]

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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.

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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.

[DrVanNostrin]

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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)

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

P(A & 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.

[PhlegmWad]

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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.

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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.

[DrVanNostrin]

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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.

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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.

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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.

[craig1120]

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(.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.

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^ 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.

[PhlegmWad]

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

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

[DrVanNostrin]

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a) what's a 2-way bet?

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...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.

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b) how is this related to the initial question?


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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.

[PhlegmWad]

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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.

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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!

[PhlegmWad]

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(.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.

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^ 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.

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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?

[SeanC]

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(.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.

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^ 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.

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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?

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$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.