Equity Value Betting: Getting the Best Return on Your Money

[SixForty]

(Sorry in advance for the long theory post!)

There's a topic that I have thought about and researched for a long time that has really helped my poker game, and I want to share it with others in a clear light. It's a topic that, once I fully understood the ramifications of it, it really took my Small Stakes poker playing to a new level.

That topic is when to bet and raise for value when you have an equity edge.

Now, let me start by saying that I am by no means an expert poker player. There are still a number of concepts that I struggle with. But I will tell you that I do make my sole source of income from playing poker at this time, and I know that a large part of my profits come from the types of situations that I am going to describe to you. So I feel I know enough about this topic to explain the concepts below. But let's start with some housekeeping.

First, I apologize for some of the math in this article. I know - we all hate math! But I was a math guy in university, so I tend to delve into it a little bit more. I promise to try and keep the math to a minimum!

Second, I'm going to assume that everyone knows about pot odds, and understands how to use them. That is, if the odds of you winning are 4-1, and the odds you are getting on a call are 6-1, you make the call. If the odds you are getting on the call are 2-1, it's better to fold. If the odds you are getting to call are 20-1, you call really quickly!

Third, I am going to consider only one reason to bet or raise in this article - Value betting or raising when you have an equity edge. There are many reasons to bet or raise - you know you have the best hand (ie, you're holding the nuts), you want to get a freecard on the next round, you think you can induce someone to fold. All of these are good reasons to bet or raise, and all of these can often combine together to cause you to bet or raise. But for the purposes of this article, I'm going to ignore them all. Not because they aren't important, but just because it makes it easier to focus on the main thing we are looking at - equity edges.

And Fourth, I'm going to assume that everyone has at least a basic understanding of how to figure out your pot equity and determine whether or not you have an edge. Many authors discuss this in some detail (I personally find the info in Small Stakes Hold 'Em by Ed Miller and The Complete Book of Hold 'Em Poker by Gary Carson to be fantastic at explaining this concept) But a lot of these authors don't really give examples that show the true power of how these edges can work in your favour. The true eye opening experiences that I hope some of the following examples will show.

So, you're in a nice good poker game. You're playing, having fun, making a bit of money. You get dealt a good starting hand on the Button, so you see the flop. The actual hand you have doesn't matter. As soon as the flop comes, you can instantly tell that you have a 30% chance of winning the pot. Someone in front of you makes a bet. What do you do?

Well, right now, I haven't given you enough information. The answer of whether or not to continue with the hand depends on the odds you are getting. It depends on the size of the pot and the number of people in. So let's say that 4 people saw the flop - BB, UTG, CO and you - with no preflop raising. Now UTG has bet and the CO called. You are getting 6.5-1 on your call, and you are 70-30, or 2.3-1, to win. So you want to continue with the hand. What if it was just you and the BB? When he bets the flop, you are getting 3.5-1 on your call, so you still want to continue.

Once you've decided to continue with a hand, since you are getting the proper odds, the question then is whether to call or raise. Again, we're going to ignore things like raising for a free card or because we may have fold equity. We're only going to look at whether or not calling or raising has a positive expectation in regards to the pot equity that we have.

So let's get back to the hand. If it's heads up, and BB bets, we have 30% equity. But we are putting in 50% of the money on the flop, since it's heads up. We put in 50% of the money, but we only get 30% back. We put in 1 bet for our call, but we only get 0.6 bets worth of that back from the money going in on the flop. So we actually lose money on the flop - 0.4 bets worth. That's okay though, since we more than make up for this from the money already in the pot. That's why we called in the first place - the pot was giving us proper pot odds. But that 0.4 bets worth is what we lost on the flop. This is because we have an equity deficit on the flop. We are contributing more money on this betting round than we are getting out of this betting round.

Another way to look at it is we are contributing 50% of the money, but only getting 30% of it back. The difference is our equity deficit. When we compare this 20% difference to the money that we are putting in (namely the 50%) we get a ratio of 20/50 - or 0.4. That's the 0.4 bets that we saw before. We can also refer to this ratio in percentage terms as a 40% equity deficit. That is, for every bet that we put in on the flop, we lose 40% of that bet. Again, this is no big deal, since the existing money already in the pot from before the flop more than covers it - that's what the pot odds told us.

Now, let's say that this hand was 3 handed. BB bets the flop, UTG calls, and it's up to us. We know that the pot odds will tell us to call. Let's look at our equity. Now we are only putting in 33.33% of the money. And we still have our 30% equity, so we get 30% of that money back. We put in 33.33% - we get back 30%. Using the same ratio as before, we can subtract the difference (33.33-30=3.33) and divide that by what we contribute (3.33/33.33=0.1) and we end up with 10%. So now, for every bet that goes in on the flop, we only lose 10% of our money. This is a much better situation than heads up, where we lost 40% of what we put in.

To see how good of an improvement this is, let's pretend that BB and UTG get into a raising war here, with you stuck in the middle, and the betting ends up getting capped. You've put in 4 bets. And we've determined that you are losing 10% of what you put in here. 10% of 4 bets is 0.4 bets. You are losing 0.4 bets on this flop. This is actually the exact same as what you lost on the flop when it was heads up. Back there you lost 0.4 bets on the flop when only one bet went in.

This is really the first important thing we've discovered here - the lower your equity deficit is, the more action your hand can withstand.

I'm actually no more upset about the second hand where these idiots capped it and I had to call 4 bets, than I am about the fact that the BB bet in the first hand and I had to call 1 bet!

Now, let's have a look at what happens when it's 4 handed. BB bets, UTG calls, CO calls, and now it's up to you. Again, pot odds will tell you that you can't fold, so you are going to continue. Let's look at our equity. Now we are only putting in 25% of the money, but we are still getting back 30%. So now we are actually making money on a bet. Now we have an equity edge. Using the same ratio as previously we can determine that edge - 5/25=0.2, which is 20%. So now we are actually making 20% return on our money. For every bet that we put in, we'll be getting 1.2 bets back. This is fantastic. Not only are we making money from the pot odds that we were already getting from all the preflop money in there, but we make money from every single bet that goes in on the flop. If we put in 1 bet on the flop, we get back 1.2 bets. If we put in two bets on the flop, we get back 2.4 bets. If the betting gets capped with all four of us still in there, we get back 4.8 bets. That's great for us!

Now let's take it one step further, and look at a 5 handed pot. We're putting in 20% of the money, but getting back 30%. The equity ratio that we've been using leads us to determine that we now have a 50% equity edge on our money. So for every bet we put in, we make 50% profit. That's fantastic! If I could find investments out in the real world where I'd get a 50% return on my money, I'd jump at the chance! Especially if that 50% return is going to be handed to me in less than one minute from now! [img]/images/graemlins/smile.gif[/img]

So going from 4 handed to 5 handed, we see that our profit margin jumps quite a bit. If you keep doing the calculations for more and more people in the pot, you'll see that the profit margin goes up at a steady rate. Here's the numbers for everything from a 2-handed pot to a 10-handed pot when you have 30% equity on the flop:

2-handed - 40% equity deficit
3-handed - 10% equity deficit
4-handed - 20% equity edge
5-handed - 50% equity edge
6-handed - 80% equity edge
7-handed - 110% equity edge
8-handed - 140% equity edge
9-handed - 170% equity edge
10-handed - 200% equity edge

Basically, whenever you have an equity edge - the more people in the pot, the more profit you make on your money. You're happy to have lots of bets going into the pot. And you're happy to be the one doing the betting or raising to make this happen.

Now, we're going to start looking at this from a different angle. Now we're going to fix the number of opponents so that it stays the same, and we're going to change the amount of equity that we have in the pot, and see how it changes our equity edge (or deficit)

So, let's use 4 players total. You and 3 opponents. This means that you will be putting in 25% of the money. We already showed that with 30% equity in the pot, you have a 20% equity edge. You make 20% for every bet that goes in. Now let's say that your hand only has 25% pot equity. You are putting in 25% and getting back 25%. You're equity edge is zero - it's totally neutral. In a situation like this, it doesn't matter to you how many bets go in on the flop. You are neither making nor losing money on any of those bets. If the flop gets checked through, it doesn't matter. If those maniacs you are playing against cap the flop 4 ways, again, it doesn't matter. For every bet you put it, you will get one bet back on average. You gain or lose nothing.

Now, what if you had 35% pot equity. Now you have an equity edge of 40%, so you make 40% profit for every bet that goes into the pot. In a situation like this, you love it when the pot gets capped 4 ways on the flop. You are making a great profit!

Let's look at a table of how various changes to your pot equity can affect your equity edge:

4-handed, 20% pot equity = 20% equity deficit
4-handed, 25% pot equity = neutral
4-handed, 30% pot equity = 20% equity edge
4-handed, 35% pot equity = 40% equity edge
4-handed, 40% pot equity = 60% equity edge
4-handed, 45% pot equity = 80% equity edge

So again, for every little bit of pot equity that your hand increases, your equity edge increases as well.

Now let's take a look at what happens when we do the same calculations 5-handed. Putting in only 20% of the money, if we have 20% pot equity we are again in that neutral situation. If we have 25% pot equity, we actually have a 25% equity edge. With 30% pot equity, we have a 50% equity edge. The table will look like this:

5-handed, 20% pot equity = neutral
5-handed, 25% pot equity = 25% equity edge
5-handed, 30% pot equity = 50% equity edge
5-handed, 35% pot equity = 75% equity edge
5-handed, 40% pot equity = 100% equity edge
5-handed, 45% pot equity = 125% equity edge

So, what does this show us? With more people in the hand, our equity edge increases at a faster rate for similar values of pot equity.

Now, what does this mean in terms of real poker?

Well, we know that there is a direct relationship between our pot equity and the number of outs that we have. If we have a 9 out flush draw, we have approximately 35% pot equity. But if our flush draw happens to be A high, and we are against only hands that have one pair and no Ace kicker, then hitting an Ace will win, and our 3 Aces are outs. So we actually have 12 outs, and 45% pot equity.

If we are 4 handed, those extra 3 outs change a hand that had a 40% equity edge into a hand that has an 80% equity edge. So we are adding an extra 40% profit off every bet that goes in on the flop.

But if we are 5 handed, those extra 3 outs will change a hand that had a 75% equity edge into a hand that has a 125% equity edge. Now we are adding an extra 50% profit.

So the more players in a hand, the bigger of an impact each additional out makes. This can be very important. Extremely important. And I hope the following examples prove just how important this can be.

We're going to look at two different hands on the flop, and see how adding a backdoor flush draw changes each of these hands.

For the first hand, you have T[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/club.gif[/img] on the button. A player in MP limps in, you call, the small blind folds, the big blind raises, and both MP and you call. Now, the flop comes down 8[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 2[img]/images/graemlins/heart.gif[/img]. This gives you an open-ended straight draw to the nuts. With 6.5 bets in the pot already, you will be seeing this hand to the river. Now, because I'm such a nice guy, I'm going to tell you exactly what the other two players have. BB has K[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/heart.gif[/img], and MP has A[img]/images/graemlins/diamond.gif[/img] 8[img]/images/graemlins/diamond.gif[/img]. Given this information we can determine your pot equity. If we plug these numbers into PokerStove, we get:

Flop: 8[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 2[img]/images/graemlins/heart.gif[/img]
BB: K[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/heart.gif[/img] - 44.740%
MP: A[img]/images/graemlins/diamond.gif[/img] 8[img]/images/graemlins/diamond.gif[/img] - 21.484%
You: T[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/club.gif[/img] - 33.776%

So, from this we can see that you currently have neutral equity - you have neither an equity edge nor an equity deficit (you actually have about a 1% equity edge, but that is small enough that I'm going to ignore it). So whether you call here or raise doesn't change how much money you spend on the flop. You effectively neither spend nor lose money for every bet that goes in. If the other two get in a raising war - no worries, it costs you nothing. If BB bets and MP calls, you can raise. It's not costing you anything to do so in terms of value. (Notice, in fact, that even if BB 3-bets, MP is still getting correct odds to call two more cold there.) With neutral equity there, you don't need to fear a raise, thinking it's costing you money.

Now, let's examine the exact same hand, except instead of the 2[img]/images/graemlins/heart.gif[/img] on the flop, it's actually the 2[img]/images/graemlins/club.gif[/img]. This gives you a backdoor flush draw to go with it. If we plug this back into PokerStove, we get:

Flop: 8[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 2[img]/images/graemlins/club.gif[/img]
BB: K[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/heart.gif[/img] - 43.079%
MP: A[img]/images/graemlins/diamond.gif[/img] 8[img]/images/graemlins/diamond.gif[/img] - 20.487%
You: T[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/club.gif[/img] - 36.434%

This bumps up your equity by a few percent. If we use the ratio we learned above, we discover that we now have a 9.3% equity edge. Now we earn 9.3% for every bet that we put in on the flop. So now, I'm happy if the other two start a raising war! It makes me money! Now, if it goes BB bets, MP calls, I'm happy to throw in a raise! I'm making money off that raise! Now, it's true that 9.3% return on my money isn't huge, but it's good! I like extra money in my hands! Basically, any potential downsides of raising (ie, maybe there is some chance that MP might fold) can now be quantifiably balanced out by the fact that there is value to our raise.

Now, let's look at a different hand.

You have K[img]/images/graemlins/club.gif[/img] Q[img]/images/graemlins/club.gif[/img] on the Button. UTG limps in, a player in MP calls, the CO calls, you raise it, the SB calls, the BB calls, and everybody else calls. You've got a nice 12 small bet pot in a 6-player hand, with a beautiful hand and position on everybody. Now the flop comes down: A[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/spade.gif[/img]. Ugh!!! That's not too nice. You've got yourself a measly little gutshot here, and your hopes of winning are dwindling. Now, SB leads out with a bet, BB calls, UTG calls, MP calls, CO calls, and it's up to you. Everybody seems to have something they want to see the turn with. Now, the interesting thing here is that there are now 17 small bets (or 8.5 big bets) in the pot. This is almost enough right now to ensure that you will be seeing the river with your gutshot. The pot is big enough to call here, and will almost definitely be big enough to call on the turn.

Now again, since I'm a nice guy, I'm going to show you exactly what everybody else has:

SB: A[img]/images/graemlins/diamond.gif[/img] 7[img]/images/graemlins/diamond.gif[/img]
BB: K[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/heart.gif[/img]
UTG: 8[img]/images/graemlins/spade.gif[/img] 8[img]/images/graemlins/diamond.gif[/img]
MP: T[img]/images/graemlins/spade.gif[/img] 9[img]/images/graemlins/spade.gif[/img]
CO: 5[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/heart.gif[/img]

So let's have a look at your equity. Back to PokerStove:

Flop: A[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/spade.gif[/img]
SB: A[img]/images/graemlins/diamond.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] - 33.033%
BB: K[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/heart.gif[/img] - 12.538%
UTG: 8[img]/images/graemlins/spade.gif[/img] 8[img]/images/graemlins/diamond.gif[/img] - 8.559%
MP: T[img]/images/graemlins/spade.gif[/img] 9[img]/images/graemlins/spade.gif[/img] - 13.063%
CO: 5[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/heart.gif[/img] - 15.165%
You: K[img]/images/graemlins/club.gif[/img] Q[img]/images/graemlins/club.gif[/img] - 17.643%

So, you happen to have a very slight equity edge here - somewhere in the vicinity of 5.9%. So you do make a slight bit of money for each bet that goes into the pot. So you can feel free to raise, and know that it's not actually costing you money (as long as everybody calls, which it looks like they probably will - big pot!) Now, again, we're going to throw in a backdoor flush draw for you and see how that changes things. Let's change the A[img]/images/graemlins/heart.gif[/img] on the flop to the A[img]/images/graemlins/club.gif[/img] and see what that gives us in PokerStove:

Flop: A[img]/images/graemlins/club.gif[/img] T[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/spade.gif[/img]
SB: A[img]/images/graemlins/diamond.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] - 33.483%
BB: K[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/heart.gif[/img] - 7.808%
UTG: 8[img]/images/graemlins/spade.gif[/img] 8[img]/images/graemlins/diamond.gif[/img] - 8.559%
MP: T[img]/images/graemlins/spade.gif[/img] 9[img]/images/graemlins/spade.gif[/img] - 13.063%
CO: 5[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/heart.gif[/img] - 13.814%
You: K[img]/images/graemlins/club.gif[/img] Q[img]/images/graemlins/club.gif[/img] - 23.273%

So again, this backdoor flush bumps your equity by a few percent. But look what it does to your equity edge - it's now at 39.6%!!! That's a pretty big profit margin there! Now when SB bets and everybody calls, you absolutely must raise! It's too big of an edge to give up! A 39.6% return on your money is golden, and you should push it every chance that you get.

Interesting hand examples here. We've seen that, when we were 3-handed, adding a backdoor flush draw took a hand with a neutral equity edge and gave it a 9.3% equity edge. That's a good increase. But when we were 6 handed, that same backdoor flush draw took a hand with a 5.9% equity edge and bumped it all the way up to 39.6%! That's huge! It just can't be overstated - that's HUGE!

So you say that you don't feel comfortable raising with your gutshot plus backdoor flush? You're not convinced that a 39.6% equity edge is all that it's cracked up to be? Well, think about this.

Let's say you're in the Big Blind. The player to your left, who is UTG, decides to have some fun. Before even getting his cards, he yells "Blind Raise!" and throws out a raise. Everybody else at the table is too timid, and it folds all the way around to you. You look down at AK offsuit. Now, you know that your hand is better than his random garbage, so you reraise. (At least, I hope that everybody here reraises! [img]/images/graemlins/smile.gif[/img] ) But actually how much better than his random hand is your AKo here? Well, AKo has about 65.320% pot equity against a random hand. If we calculate the equity edge, it works out to about 30.6%. So raising with that gutshot plus backdoor flush from earlier is actually more profitable than reraising here with your AKo!

Another example. Everybody folds to the Button. He looks at only one card and says "I have a King, I raise!" The small blind then looks at only one of his cards and says "I have that beat, I have an Ace! I call!" You look down in the big blind and see pocket Jacks. So you do the smart thing and 3-bet. Why? Because you know that against any random Ace-anything hand and any random King-anything hand, your JJ will win more than its fair share. It's a value raise, pure and simple. But how much value is there in it? Well, if you run it through PokerStove, you'll find that in this situation, JJ has about 45.784% pot equity, which leaves you with an equity edge here of 37.4% when 3-handed here. Even this comes up shy of the profit margin of that gutshot plus backdoor flush!

Okay - one last example for fun. You're in the big blind. A tight UTG player raises. You know from playing with this player that his range here is relatively small. He's only ever going to raise the following hands from UTG:

AA, KK, QQ, JJ, TT, 99
AKs, AQs, AJs, ATs
AKo, AQo, AJo
KQs

Now, everybody folds around to you, and you have pocket Kings in the big blind. Of course you 3-bet him! But what is the true value that you are getting when you 3-bet him? What is your equity edge? Plug his range into PokerStove, and we can see that your KK will have about 69.687% pot equity, for an equity edge of 39.4%. Wow - look at that! 3-betting with pocket Kings when heads up preflop STILL isn't even as profitable as raising that gutshot plus backdoor flush draw when the flop is 6-handed.

Unbelievable!

So - when we get right down to it, and after all this babbling by me, what is the point of it all?

Understand your equity edges!

When you have an equity deficit, the size of that deficit is the true measure of how much a bet or raise is costing you. If your equity deficit is 50%, then you don't want to be betting or raising if you don't have to. But if your equity deficit is only 5%, then a bet or a raise isn't really costing you that much. If there are other benefits to that bet or raise (ie, fold equity or freecards) then don't be afraid to do it.

When you have an equity edge, push it! If it's small, it's not going to make you huge money. But there is still value in it. And if there are other benefits to the bet or raise (ie, again, fold equity or freecards) then go ahead a push it. If your equity edge is large, then you absolutely must push it. Giving up a raise in a spot where you have a 25% equity edge (and can make a 25% profit on that extra bet) is not maximizing your EV. Any chance you have to get a 25% profit on your money, you should take it.

And finally, know how to count your outs. If the pot is many handed, that one or two extra outs can turn a neutral call into a very profitable raise. Don't forget to count a backdoor flush. Don't forget about backdoor straights. If you have JTo on an 873 rainbow board, you have a gutshot. But if you have JTs on a 973 rainbow board with one of your suit, don't forget to add the backdoor flush outs, and even the half an out for a runner-runner KQ backdoor straight. If you are heads up, it may not make much of a difference. But if the pot is 5-handed, it's a huge difference that you just can't miss out on.

And don't forget about counting overcards. Sure, overcards outs are often VERY dirty in a multi-way pot. But if you think that they are worth even 1 out total, well, we've seen what something as small as a backdoor flush can add! That 1 out that you give your overcards only strengthens the case for sometimes raising when you may otherwise only call.

That's all - sorry I took up so much of your time! I hope this helped at least one person! Now go out there and start pushing your equity edges!!!