Fundamentals- Value Betting Rivers

For my 500th post I thought I would give a little back to this great community that has helped me so much in my poker endeavors, and write about something that every poker player needs to understand in order to improve as a player ---> Value Betting Rivers

What does it mean to "value bet" on the river?

(Specifically, it is assumed that we are heads-up, in position, the river card has just fallen, and our opponent has just checked to us)

Many of the definitions I found from various online sources were inadequate and stated something like:

A) " You should value bet the river when you think worse hands will call"

or

B) " You shouldn't value bet the river if you think better hands will call"

or

C) " Value betting is the act of extracting value from your hand when you have the best hand"

My problem with these examples is that they don't explain the concept mathematically, and are hardly specific enough to be of any real use.

Take example "A" for instance. Obviously when we hold the nuts on the river our course of action is clear, since EVERY hand our opponent could have is a worse hand (excluding chops) we should choose to bet the highest amount that we think will be called in order to maximize profit since there is no chance we are beat. Even if we are relatively certain our bet won't get called we still bet because there is value in it the small % of the time we do get called (Not to bet the nuts on the river is a poker sin, whatever your reasoning. Don't be a Darvin Moon! ---> YouTube - Checking The Nuts)

However, holding the nuts on the river is a rare event, so we're likely going to be against some hands that beat us and some hands that don't, which clearly makes example "C" seem worthless (If our opponent could have better and worse hands than us, how are we supposed to know if we have the best hand this time if we can`t see his hole cards?)

So referring back to example "A", when we hold the non-nuts should we always bet when we think worse hands will call? Conversely, referring to example "B", should we always check behind when we think better hands will call? It may be surprising to many of you that the answer to both of these is no!

***In order for value betting to be correct on the river, we want the number of hands that our opponent is calling a river bet with which are worse than ours to be greater than the number of hands which are better than ours which are also calling a bet***

(Notice that in both cases our opponent is simply 'calling' our river bet. Discussions regarding whether our opponent may c/r for value or as a bluff are beyond the scope of this post)

Hopefully you can inherently see why this is true. The higher % of the time we have the best hand versus our opponent's river calling range, the more money we shall make. You should also see why it is not reason enough for us to value bet simply because worse hands will call. If there are more better hands in our opponent's river calling range than there are worse hands, we will (on average) lose $$$ by betting.

How do we explain this mathematically? Actually it's quite simple:

"If we have greater than 50% equity versus our opponent's calling range on the river, we should bet for value"

What this means is that if we rate to hold the best hand over 50% of the time, we should bet. Why 50%? Because if we hold the best hand over half the time we stand to gain (on average) any money going into the pot.

How do we know if we have the best hand over 50% of the time? This actually takes a lot of work, since there are many factors that go into coming to a right conclusion.

1) You need to practice forming hand ranges for your opponent on every street so you can have a base from which to form his river calling range. These hand ranges need to be as specific as possible and based upon observations/data/player-tendencies/reads you have while at the table.

2) You need to practice putting these ranges into pokerstove and comparing them with your hand(s) in order to get a feel for what your equity versus their calling range could be. Ex-If you're opponent is a calling station, you'll need to add a lot of weaker hands to his calling range and subsequently should be adding more hands to your river value betting range. Conversely, if your opponent has a tight preflop range and is passive postflop, you should generally avoid value betting mediocre hands on the river since his range is so strong.

3) You need to consider board texture and be aware of your relative hand strength in order to determine if value betting is correct. (ie should you be value betting AA on a 4T5Q7 board if it is likely your opponent will be calling with any decent diamond and they are in his range?)

When putting all these factors together you should be able to determine whether a bet for value is correct.

Let`s try an example. Let`s say we hold Q J on the button vs an opponent in the cutoff who we`ve isolated after he limped, and the board runs out Q3845 after he`s check-called two continuation bets by us, and he again checks the river.

Let`s say that we have some history with this opponent and that we know the hand range for him getting to the river this way is KQs,Q9s+,KQo,Q9o+, and we also know he`s planning on just calling any bet we make. Should we value bet?

Once we plug his hand range into pokerstove we get:




Which shows we have 63% equity versus his calling range, and thus we should value bet.

Now let`s say we are in the exact same situation, with our opponent having the same calling range, and this time we hold Q10, should we still value bet?

Plugging into pokerstove we now get:



Now we only have ~37% equity versus his calling range, and should check behind.

I encourage you to mess around with pokerstove so you can begin to learn which river situations demand a value bet, and hopefully with practice you will become more adept at this fundamental of poker.

1rd...good post, spoon has some post somewhere that is similar to this and comes to the same conclusion. either way it was well thought out and easy to follow, ty caddie congrats on your 500th post

Wouldn't we need less than 50 win% depending on our bet size? Also the threat of being check raised plays a huge role in deciding if we can value bet imo

Originally Posted by JKDS

Wouldn't we need less than 50 win% depending on our bet size?

No.

Originally Posted by JKDS

Also the threat of being check raised plays a huge role in deciding if we can value bet imo

Only if we're getting raised off of our hand against a hand we beat.

Originally Posted by spoonitnow

No.

Nvm, i still make the same mistake i used to. You're right

Edit again: To clarify for others, i made the mistake of finding the EV of a bet...but didnt compare it to the EV of a check. By doing so, you see that betting is only better if we win more than half the time.

Originally Posted by JKDS

Nvm, i still make the same mistake i used to. You're right

Edit again: To clarify for others, i made the mistake of finding the EV of a bet...but didnt compare it to the EV of a check. By doing so, you see that betting is only better if we win more than half the time.

ldo, when we bet for value we aren't winning any moar of the pot thats already out there than when we check (unless we fold better, but thats not value betting); so we're taking like 1:1, even though villain is taking better odds b/c of the money that was already out there

Originally Posted by Imthenewfish

ldo, when we bet for value we aren't winning any moar of the pot thats already out there than when we check (unless we fold better, but thats not value betting); so we're taking like 1:1, even though villain is taking better odds b/c of the money that was already out there

Well, slightly worse than 1:1 because of the rake, but yeah.

ummm.. can't we get away with less than 50% in some cases?

Eg. If we know that we have 40% equity vs villains calling range but we also know he is going to c/f 90% of the time on the river then the extra dead money in the pot compensates for the fact that we may not be ahead of his range, no?

I mean, clearly in this example it would be a huge mistake to not bet the river just because we're not ahead of his calling range. We're picking up what's already in the pot so often we can sacrifice some equity and still make a +EV bet.


This could also be called a "thin" value bet imo. We know that there are some worse hands that are going to call us, we know there are some better hands that are going to call us, and we think that better hands are going to call more often, but betting still works.

nice post caddie. thanks for this.

Originally Posted by kfaess

ummm.. can't we get away with less than 50% in some cases?

Eg. If we know that we have 40% equity vs villains calling range but we also know he is going to c/f 90% of the time on the river then the extra dead money in the pot compensates for the fact that we may not be ahead of his range, no?

I mean, clearly in this example it would be a huge mistake to not bet the river just because we're not ahead of his calling range. We're picking up what's already in the pot so often we can sacrifice some equity and still make a +EV bet.


This could also be called a "thin" value bet imo. We know that there are some worse hands that are going to call us, we know there are some better hands that are going to call us, and we think that better hands are going to call more often, but betting still works.

No.

lol ok after lengthy discussion in irc I now see I was wrong.

Originally Posted by spoonitnow

No.

ok what about in this example,

Board is Kh 2c 2d 9s 7d

Ok lets say some how we know Villains range when we get to river is AK, KQs, KK, 99, 22, dont ask how we know that we just do.



Fact- when we check to villain, he is going to shove everything except KQ which he will check behind.

Fact- If we shove he is going to call 100% of his range

Fact- Pot odds are such that when we check and he shoves, we are getting the pot odds to call with our 27% equity

We hold AsKs.

Against range with KQs we have 38.5% equity
against range without it we have 27% equity
Can we not value shove to get value from the KQ that we will otherwise miss. even though we have less than 50% equity against either range?

Cheers caddie I enjoyed reading this.

Thanks for your 500th.

Clarity, absolute.




EDIT: your Avatar looks ugly now ,re:divorce etc

Originally Posted by philly and the phanatics

ok what about in this example,

Board is Kh 2c 2d 9s 7d

Ok lets say some how we know Villains range when we get to river is AK, KQs, KK, 99, 22, dont ask how we know that we just do.



Fact- when we check to villain, he is going to shove everything except KQ which he will check behind.

Fact- If we shove he is going to call 100% of his range

Fact- Pot odds are such that when we check and he shoves, we are getting the pot odds to call with our 27% equity

We hold AsKs.

Against range with KQs we have 38.5% equity
against range without it we have 27% equity
Can we not value shove to get value from the KQ that we will otherwise miss. even though we have less than 50% equity against either range?

No.

I'm going to try to use an example to explain this with an example in the most straight-forward way I know possible.

Suppose you're on the river, heads-up, in position in a $10 pot with $10 remaining in the effective stacks. Your opponent checks to you with 15 combinations, 5 of which beat you. Suppose he folds x number of combinations if you bet, and that he never folds a hand that beats you.

The EV of checking is (5/15)(0) + (10/15)(10) = $6.67.

The EV of betting is (5/15)(-10) + (x/15)(10) + ((10-x)/15)(20). Let's quickly simplify the betting equation:

(5/15)(-10) + (x/15)(10) + ((10-x)/15)(20)
-3.33 + (2/3)x + 13.33 - (4/3)x
10 - (2/3)x

So when is the EV of checking greater than the EV of betting?

6.67 > 10 - (2/3)x
-3.33 > -(2/3)x
5 < x

Checking is better than betting whenever he folds more than 5 combinations. If he folds more than 5 combinations, that means he's calling with less than 10 combinations. Since 5 combinations beat us, if he's calling with less than 10 combinations, then our equity against his calling range is less than 50%.

Therefore, checking is better than betting when we have less than 50% equity against our opponent's calling range.

nh spoon

Perfect explanation imo spoon, way to jack Caddie's glory...lol

Caddie, great op, I don't think this is something most people put much thought into, including myself.

Very nice post caddie. And spoon example really simplified them. B4 i can implement this, i need to put opp on ranges. So i need some enlightment. I usually put opp on strong made hand / weak made hand / draw. And i base my play on that. I try to put opp on ranges but feel like i need forever to do it. Lol. Not to mention to calculate no of combos. So need some explanation on how to do that fast, any shortcuts? Or practice make perfect thing? Btw i play 6 max 5nl, 4 - 6 tbls now. I have been playing 50nl too and properly br... At that time and now on 5nl due to br requirement, dun ask what happened (lmao, learned the hardway). And alot of the seniors here are 12-16 tbling, i feel like wtf going on in their brain to figure all that thing? Lol. Regards Andy

@ andyw: First off I think it's good advice to start to lower the amount of tables you play so you can really start to observe the other players at your table ie- what their opening ranges are from which positions, how often they're c-betting/raising and with what. This will greatly help you when forming hand ranges, and you won't feel overwhelmed like you would when trying to do this with 6+ tables.

Keep in mind most of the work done for poker is done away from the table. Ideally you should be studying as much as you play, but I realize it's not that realistic for most ppl. I suggest that when you play some sessions to minimize the amount of tables you play and really try to think out every decision based on range estimation. During the sessions mentally note some hands that you were wondering about, and either post them here for clarification or do some study yourself using pokerstove. There are lots of great links in the beginners digest showing you how to do this.

Remember that we do the studying so we can become familiar with common situations that occur as well as to improve our thought processes while at the table. Remember that to be successful at this game it takes a lot of work, but if you're willing to do it you will definitely have an edge over most of your opponents.

Added to the digest. Thanks caddie.

Originally Posted by spoonitnow

Added to the digest. Thanks caddie.

np thanks for the step by step maths breakdown, really punches the point home

great informative post. but your avatar is a little disturbing =P

Originally Posted by spoonitnow

I'm going to try to use an example to explain this with an example in the most straight-forward way I know possible.

Suppose you're on the river, heads-up, in position in a $10 pot with $10 remaining in the effective stacks. Your opponent checks to you with 15 combinations, 5 of which beat you. Suppose he folds x number of combinations if you bet, and that he never folds a hand that beats you.

The EV of checking is (5/15)(0) + (10/15)(10) = $6.67.

The EV of betting is (5/15)(-10) + (x/15)(10) + ((10-x)/15)(20). Let's quickly simplify the betting equation:

(5/15)(-10) + (x/15)(10) + ((10-x)/15)(20)
-3.33 + (2/3)x + 13.33 - (4/3)x
10 - (2/3)x

So when is the EV of checking greater than the EV of betting?

6.67 > 10 - (2/3)x
-3.33 > -(2/3)x
5 < x

Checking is better than betting whenever he folds more than 5 combinations. If he folds more than 5 combinations, that means he's calling with less than 10 combinations. Since 5 combinations beat us, if he's calling with less than 10 combinations, then our equity against his calling range is less than 50%.

Therefore, checking is better than betting when we have less than 50% equity against our opponent's calling range.

Hi guys, thanks for this very informative post. Just for the sake for answering my own question, I tried the following calculations:

Scenario 1: if we bet smaller on the river (Let’s go for the extreme, $1), wouldn’t we need to hv less equity against his range to be a better play than checking?

EV of checking remains the same as Spoonitnow’s calculation: 6.67

EV of betting: (5/15)(-1) + (x/15)(10) + ((10-x)/15)(11)
= (-5 + 10x + 110 – 11x)(1/15)
=(1/15)(105 – x)

For betting to be better than checking:

(1/15)(105 – x) > 6.67
105 – x > 100
5 > x

Hence villain has to fold less than 5 combos. Let’s say he folds 4. Hence he’s calling with 11 combos, out of which 5 beats us. Hence we have 6/11 equity against his rang. To conclude, our equity against his calling range has to be greater than 50% for our bet to be better than our check. Hence, whatever amount u bet on the river, u still need to be stronger than his calling range 50% of the time to make it a better EV play than checking! (Duh… Why would I think otherwise in the first place…..?)

This is where I had another question. The above scenario is based on the assumption that he’ll never fold a hand that is better than our range. What if we bet the pot and he folds, let’s say, 1 or 2 of his 5 combo that beats us?

Scenario 2, if we bet pot: $10, and he folds 1 combo that beats us:

EV of checking remains the same: 6.67

(Assume he folds y hands out of the 5 that beats us)

EV of betting = ((5 – y)/15)(-10) + ((10 + y)/15)(10)
=(2/3)(5 + 2y)

For EV of betting to be great than EV of checking:

(2/3)(5 + 2y) > 6.67
5 + 2y > 10
y > 1/2


Hence, for our bet on the river to work as a semi-bluff, we have to make him fold more than half of his hands which are beating us.

So basically now we’re turning the hand into a bluff. I've done calculations assuming opponent's range beating us 10/15 of the times, and the results are the same. We still hv to make him fold 50% to make the bluff profitable.

So... I guess the conclusion here is... u hv to make villian folds more than half of his beating us range to make ur bluff on the river to be profitable.

Someone please discuss about this.

Taking a few mins to rethink about the whole thing. Basically when it's checked to us ip on river. We should first consider his entire range.

If we're ahead of more than half, we consider if we bet, can we beat half of his calling range.

If we're behind more than half of his range, we consider that if we bet, would he only call with less than half the range that is currently beating us.

Ok, that's my new conclusion lol

Please discuss.

Just saw this get bumped and wanted to throw this out there.

Some of your really close value bets should be checked behind if there's any chance of being check-raised off of your hand by a worse hand.