Disclaimer: The first few paragraphs might be a little dry, but I’m going to get into some interactive game at the end, so I hope it's not tldr.

I often read two statements on the board that are used as rational for making a play, “If you do X, then you’ll be exploitable” or “You do not need to be balanced”. Both the statements could apply to the same hand and both could be correct. The purpose of this post is to begin to untangle the implications of Exploitative vs Balanced Strategies and hopefully begin to provide a framework upon which you can build a theoretical understanding of how poker works.

DEFINITIONS

Before we go on, let’s try and define the 3 main concepts:

Expected Value:
is an analysis which tells us what we can expect to gain or lose from an action. The goal of poker is to maximize our EV. With that in mind, let’s briefly look at the possible action of 3 poker actions. The relative EV of folding is 0. So if a call is –EV, then you would maximize your EV by choosing to fold instead. And if a call is +EV, then you would make a better choice by calling than folding. It’s also important to remember that just because one action is +EV does not mean it’s the best, since another action might be higher EV.

Exploitative Strategy:
is a strategy which will maximize our EV by making the action which has the highest EV based on the assumptions we make about the opponents ranges and tendencies. The goal is to exploit leaks in our opponents game to the maximum effect. For example, if we are in position on the river and we assume that our opponent will fold 100% of his range to a bet, then we maximize our EV by betting and bluffing 100% of the time on the river. On other hand, if we’re on the same river, but we assume that our opponent will call a river bet 100% of the time, then we maximize our EV by never bluffing and betting all hands which have more than 50% equity against the opponents calling range. We are able to exploit our opponents leak because she has an unbalance of either folding too much or calling too much.

Balanced Strategy:
is a defensive strategy designed to keep our Opponents from exploiting us. You design your ranges to be balanced so the Villain cannot increase his EV by using an exploitative strategy. For example, a balanced betting range has an optimal mix of value and bluff hands, so the Villain is indifferent to calling with the bottom of his bluff catching range. A balanced calling range defends enough so the Villain cannot bet 100% of his bluffs profitably. If the Villain is not playing a balanced strategy as well, then he could improve his EV by switching from an exploitative strategy to a balanced strategy. However, if we are employing a balanced strategy, we only maximize our EV if our opponent is playing a balanced strategy as well.

ABSTRACT

Balanced Strategy and Exploitative Strategy are two different sides of the same coin. You cannot employ an Exploitative Strategy to beat a Balanced Strategy. And a Balanced Strategy does not maximize EV against an opponent who is using an Exploitative Strategy. So I propose that the best approach is to use our knowledge of balanced ranges to find leaks in our opponent's game which we can use an Exploitative Strategy to maximize our EV.

Ok. Are you bored or confused yet?

ROSHAMBO

It’s a lot easier to understand the relationship of these two concepts in context of simpler games. So I’d like to look at them in context of the game Roshambo (rock, paper, scissors), and then extract the principles we learn from it and apply them to poker scenarios.

If you don’t know the game Roshambo, then climb out from under your rock or go here: http://en.wikipedia.org/wiki/Rock-paper-scissors

Now let’s assume that we’re in this juicy Roshambo game against a player called Geo. Now Geo is a geologist so he can’t help but employ the following strategy:

50% rock, 25% paper, 25% scissors

Not only does he use that strategy, but he won’t ever change it – regardless of how we play. What is the best counter strategy for us to employ? Describe your strategy in the same terms. So something like…

25% rock, 50% paper, 25% scissors

Do you have it? See the correct answer in the spoiler.



Let’s look at this a little closer. Geo plays an unbalanced strategy where he plays rock too much. The best way to maximize our EV against his strategy is to goto an extreme and play paper 100% of the time. Even though, we’ll lose the 25% of the time that he has scissors. The approach we took to maximize our EV was an exploitative approach.

Let’s figure out the EV of playing against Geo.

EV of playing paper 100% against Geo:
< Hero plays paper, Villain plays rock, hero wins > = .50 * 1 = .5
< Hero plays paper, Villain plays paper, hero ties > = .25 * 0 = 0
< Hero plays paper, Villain plays scissors, hero loses > = .25 * -1 = -.25

< TOTAL EV OF STRATEGY PLAY PAPER 100% > = .5 + 0 + -.25 = .25

So we can expect to win .25 points every round of we play against Geo.


Ok… but now a new opponent sits down at our table of Roshambo, and it’s no other than the Phil Rivey – the Phil Ivey of Roshambo. So you’ll only play against one person at a time, but you need to go back and forth from playing with Phil Rivey to playing against Geo, and you can’t sit out against Phil Rivey. The game is too juicy to leave, but there’s just no way you’re going to be able to out play Phil Rivey. So what strategy should we use when we play Phil Rivey (I just like typing that name, is it tilting you yet?). Well we can’t expect to beat him, so we should just come up with a strategy to minimize our losses.

I think everyone has an intuitive sense that we should play the following strategy:

33% rock, 33% paper, 33% scissors

This is a perfectly balanced strategy. So regardless of how Phil Rivey plays, he cannot exploit us. Let’s look at the EV for Phil Rivey depending on different actions he chooses:

EV PHIL RIVEY
< EV Phil Rivey plays Rock > = (.33 * 0) + (.33 * -1) + (.33 * 1) = 0
< EV Phil Rivey plays Paper > = (.33 * 1) + (.33 * 0 ) + (.33 * -1) = 0
< EV Phil Rivery plays Scissors > (.33 * -1) + (.33 * 1) + (.33 * 0 ) = 0
< TOTAL EV for ALL STRATEGIES PHIL IVREY USES > = 0 + 0 + 0 = 0

In other words, Phil Ivrey might as well just sit out when he plays us because he’s not going to make any money and neither are we. The EV for both of us is 0. So by using a balanced strategy, we were able to keep the greatest roshambo player in the world from making any money from us.

FROM ROSHAMBO TO POKER

Now you might be asking yourself, how is this helpful for us when it comes to poker because frankly, you don’t play against brain dead geologists or Phil Ivey at poker. Or do we?

Have you never played against a Geo at a poker table? There are quite a few players at the micros who will let you pound on them with 3-bets and never adjust or won’t adjust correctly. For example, let’s say that you’re at a table in the BB and when ever it folds to the SB, he’ll raise it up to 3 bb, and when you raise to 10 bb, he’ll fold 80% of the time. Is this SB unbalanced? Does he not defend his open enough? Can we exploit him by 3-betting? Let’s look.

When we bet 10 bb, we are risking 9bb to win 4 bb. So we need our bluff to work this frequently in order for us to be able to bluff any two cards:

Bluff Must Work = 9 / (9 + 4)
Bluff Must Work = 9 / 13
Bluff Must Work = .692
Bluff Must Work = ~70% of the time

So if the Villain folds more than 70% of the time, when we 3-bet him to 10 bb, then we are making automatic profit by 3-betting any two cards. Therefore, what exploitative strategy maximizes our EV? We should 3-bet here with 100% of our range. This is the exact same scenario in the Roshambo, where Geo played rock too much, it’s just now this guy folds too much.

You might ask yourself, but what if this guy notices that we’re 3-betting him 100%? Well do you really think this guy that has been folding a ton is going to start 4-betting you light? Or do you think he might be the type that will start calling you lighter with hands like 87 which he plans on check-folding when he misses on the flop? And if you think he’s more likely to adjust by calling and folding the flop 66% of the time, is this such a bad thing? Or can we exploit a postflop unbalance of his then?

But let’s say that Geo at the poker world is sick of getting powned by you, so he calls up his uncle Phil Ivey and acts for some team viewer help. And you know that Phil Ivey is across from you, and he just 4-bet you to 22 bb. What do you do? Do you open fold AA? Nope. You do some math and figure out what is a balanced range for 5-betting in this scenario and you play that range. Just like we knew that the proper adjustment at Roshambo was to play 33% of each choice. This way, you might not pown Phil Ivey, but you know that we won’t pown you.

FROM POKER BACK TO ROSHAMBO

So hopefully, you might start to see that looking at some simpler game examples, can provide insight into poker. You might think that you have a good sense of what balanced ranges look like in poker, but the chances are that you’re wrong. So let’s turn our attention back to Roshambo. Now you might think that you have that game completely figured out but we’re going to take it up a notch.

So the rules of the game are going to stay exactly the same. But Geo was getting pissed that we was losing, so he wanted a bonus for winning with Rock. So the pay out for winning with Rock is going to be 3 points now instead of 1. Losing with rock (ie. Winning with paper will still be 1 point. Winning with scissors over paper will still be 1 point). What now is the correct balanced strategy if you were playing Phil Rivey? Seriously take a moment and come up with it?



Is this what you guessed? Did you think that we should be playing more rock because we got more points for winning with it? It’s important to remember that a balanced strategy in essence is a defensive strategy. We’re not trying to exploit our opponents, we just don’t want them to exploit us. So in this example, we play paper 3 times more than rock in order to neutralize the bonus that rock has from winning.


VILLAIN'S STRATEGY CAUSES ONE OF OUR ACTIONS TO BE -EV
Ok. Let's say that Phil Rivey has picked up that we're playing paper 60% of the time. And he decides that he's going to start to pound on us. He's going to play Scissors 100% of the time.

What is the Hero's EV of Paper against Phil Rivery's Strategy:
< Hero has Paper, Phil has Scissors, Hero Loses > = (.60 * 1 * -1) = -.6

So within our overall strategy, we are losing -.6 points on avg with the times we choose paper. In other words, Phil is pounding us by choosing Scissors every time, so it's -EV for us to choose to throw paper. Is Phil Rivery exploiting us?

Phil Rivey is not exploiting us. By using a balanced strategy he can't exploit us. It is completely fine that the times we throw paper, we lose points because we make it up with our other actions.

Let's look at our EV with our other actions, when Phil is choosing only scissors:

< Hero has Paper, Phil has Scissors, Hero Loses > = (.60 * 1 * -1) = -.6
< Hero has Scissors, Phil has Scissors, Tie > = (.25 * 1 * 0 ) = 0
< Hero has Rock, Phil has Scissors, Hero wins > = (.20 * 1 * +3) = .6
HERO'S TOTAL EV = -6 + 0 + .6 = 0

I think this is important to remember because I see this mistake made a lot in the forums. You need to think of your different ranges as different actions of roshambo. So think of your value betting range as playing rocks. Your bluffing range as being scissors. And your calling range as being paper. If you are using balanced range, and then Villain tries to take advantage of one set of your ranges, he is lowering his EV because you'll make more money with your other ranges. Just like in the Roshambo example. Let's look at this in context of poker.

We know that our balanced pre flop 5-bet shove range against a Villain includes some bluffs. But let's say that we're starting to get the feeling that the Villain is only 4-betting us with the nuts because every time we 5-bet shove, we're always getting called. He's never folding to our 5-bets. So isn't the Villain exploiting us by only 4-betting with the nuts, since we keep 5-bet bluffing and getting picked off? The answer is no. Because since the Villain is not 4-bet bluffing, it means that he's folding too much and our 3-bet bluffs are making more EV. And since poker, unlike Roshambo, is an un-symettrical game the Villain would maximize his EV by using a balanced 4-bet range which would include bluffs. You can't exploit a balanced strategy, and the best way to play against a balanced strategy is to play a balanced strategy yourself.

So the major takeaway of the article is that by knowing proper balanced ranges, we can find our opponents leaks and play exploitative poker to maximize our EV.

I Know that He Knows that I Know... Wait Where was I?

However, let’s say that you’re playing against a regular that you feel has some unbalances but you think he’s good enough to adjust to your exploitative strategies. Than if you can stay one step ahead of your opponent, then you can exploit them, trying to exploit you. This is slightly different than our original definition of an exploitative strategy. Our original strategy assumed that we could make fixed assumptions about our Villain’s play. If those assumptions were always in flux, then our strategies for exploiting them should adjust as well. Let’s look at Roshambo again with this new idea of leveling our opponent.

You can play Roshambo against a computer which will be utilizing an exploitative strategy. So the computer is going to try to exploit your unbalances. So you have two options, be a wimp and play a balanced strategy of 33% rock, paper, and scissors. Or man up and show that computer who is boss, since if he’s using an exploitative strategy that he’s open for exploitation also.

Here’s the link to the interactive Roshambo game:
http://www.nytimes.com/interactive/s...-scissors.html

How did you do? Did you represent the human race well? If you lost, the reason most likely is that you ran into variance or you might need to work on your leveling game. Let’s look at different levels of poker thought:

Level 1:
Only playing your cards. This is the Geo of the Roshambo world. He’s always going to play his fixed static strategy of 50% rock, 25% paper, 25% scissors.

Level 2:
Play the other player. This is the level that the computer is working on. He looks at your last 5 hands, and since you’re not an original snowflat but predictable like the rest of us, he uses an algorithm to guess what you’re next pick will be.

Level 3:
Don’t play your strategy… but play against the strategy that the Villain is going to think you’re playing. So if the Villain thinks your going to play paper, then he’s going to play scissors, therefore you should actually play rock.

If you use Level 3 thinking then you can beat the computer. And after you’ve done that for awhile and you think that you’re the man, then try and do it quickly like if you were playing 24 tables. ☺

But as I suggested before, it’s often hard to know how your opponents are going to adjust at the micros. People usually just play the same game with the same leaks for a long time. If they try and adjust to you, they often adjust the wrong way. So I wouldn’t worry too much about trying to out level your opponents. Instead I would focus on learning what balanced ranges look like in different situations, so you can identify and exploit leaks in your opponents.

Wow, gonna have to spend a lot of time reading this, but surely the title needs a "COTW..." before it!

kind of CoTW or PoohBah post? Great work RainbowBright. Thank you very much for nice post!

Thanks RB! Fantastic reading so far. This might be one to print out and read with my ovaltine at bedtime!

+1. This should get stickied for a while.

Started reading, but got confused in 5mins with all the numbers and other mathematical signs... Rainbow this is like explaining what exploitative and balanced strategies are? or was the message a bit different?
And of course very nice post as always from you : )

I apologize for it being confusing. I tried to go through every step of the math stuff at least once at the beginning so you could repeat it yourself.

If you let me know, where you got confused, I'd be happy to help. I get confused often myself and maybe you found a mistake I made.

It is explaining what the difference is. But even more so, it's explaining how you can use one to do the other better. So if you learned what balanced ranges looked like, then you could be better at finding leaks in your opponents play.

Maybe I should have explained that I think a leak is an unbalance in your game which someone else is exploiting. And if you don't know what a balanced range looks like then it's hard to identify those leaks. Once you find a leak in your opponents game, then you should use an exploitative strategy to maximize your EV. But you can only find those leaks if you know what a balanced range looks like. And balanced ranges aren't always what you think they might be.

And you don't necessarily need to seek out an opponent's leak. You'll notice tendencies for the regs at your level. For one thing, facing a 3bet preflop to a non-steal. Probably for anyone who is reading this, a 3bet is going to be insanely strong and you can exploit by folding almost everything. At the micros, this is how you should treat a 3bet until you have a specific read that he is 3betting light. It's often useful to use stake tendencies due to the large number of opponents you'll be facing.

havent read anything but the preface, but this has potential to be one of the best posts in ufr in months.

clicking on the big spoiler square was kind of a disappointment. Not because of the content, but I'm used to seeing something else in big spoiler squares.

agreed and done.

One minor thing that you didn't address but I think is relevant. You mentioned the option of maximally exploiting them then re-adjusting but let's say you think someone is a very good player when they think things through yet have some leaks you want to exploit elsewhere. Say they hand read pretty well but for whatever reason they fold to 80% of 3-bets. That's obviously exploitable but if you 3b them with 100% of hands it will lead them to think about it and adjust to a closer to balanced strategy. What if alternatively we start 3-betting them 15%? In roshambo terms this would be similar to say guy is going rock 50% paper and scissors 25% each so instead of 100% paper we now go to 40% paper 30% rock 30% scissors. It'll probably take a very long time to realize aren't actually going a third each and we might make more long-term doing this than the obvious 100% paper. That said in poker there are other players and it's highly possible another reg will alert him of his leak earlier and thus taking the long-term approach hurts your ev. But it's also possible he'll just adjust to that one guy. Just something to think about that I think ties in with the topic pretty well.

And we intuitively know this. If someone folds too much to 3bets, no one will ever suggest 3betting him 100% of the time.

Another difference is that playing a perfectly balanced roshambo game will always be a breakeven strategy, no matter how the opponent plays. A perfectly balanced poker strategy is only break even only against other perfectly balanced players and is profitable against anyone with leaks, even if it isn't necessarily the most profitable strategy. But it is a good way to play against someone you aren't sure how to approach.

agreed