Whats in a Range

[MLG]

Perhaps the most fundamental thing we do on this board is put opponents on ranges. When faced with a decision we try and figure out what they might have and make a decision based on how our hand fares against that range. Now, in some situations in order to make a decision we must consider what range our opponents put us on. For example on the river with a good but not great made hand we need to decide whether or not to value bet when first to act. So, the first thing we think about is what hands can our opponent have. The next thing we think about is, well which of those hands will our opponent call us with. Well, what defines what our opponent call us with is the range of hands he puts us on. This isn't really earth shattering. However, many people will say its pointless because Joe Internet doesn't understand ranges. Thats wrong. If Joe Internet calls to much its because he always thinks, hey he might be bluffing, so the range he puts you on is quite quite wide with a high bkuffing percentage. Knowingly or not, all opponents put you on a range, just as you put all your opponents on a range.

So, how do we exploit this situation. How do we make opponents who are putting us on a range make a mistake? When we bet on the river there are 4 possible outcomes (ignoring raising for the time being).

1. We have a better hand than villain and villain folds.
2. We have a better hand than villain and villain calls.
3. We have a worse hand than villain and villain folds.
4. We have a worse hand than villain and villain calls.

2 and 3 are obviously good for us, while 1 and 4 are obviously bad.

Simple. So, lets take an extreme example. A villain who will never ever ever call a reasonable (1/2 pot) bet on the river unless he has the mortal nuts. When you bet on the river he always puts you on the nuts. Likewise, if you check he will never bet anything short of the nuts. How do we deal with this situation? Seems simple, bluff a lot, but don't value bet medium strength hands right? Wrong. Every bet you make is a bluff, and they all have a very high chance of working. You should bet every hand on the river except for the 2nd nuts (because that is the only hand that cannot get a better hand to fold). Clearly Mr. Tighty McNuts is easy to exploit, thats not the point, the point is understanding why. He is easy to exploit, because the range he puts us on is so comically tight that he allows us to have a positive outcome for us (3) a rediculously high percentage of the time. Notice that it doesnt matter that the second highest outcome is (1) which is technically a bad outcome for us because we gain so much equity the times he folds. Also notice, that just because its absolutely correct to bet all of our hands doesnt mean we win every hand when we bet (we still lose the times he has the nuts).

Still, nothing ive said is earthshattering untill we begin to generalize away from the comic extreme. Why do we make money, because our range is extremely wide, while Tighty McNuts thinks its extremely tight. On the other extreme a villain who calls with any 2 hands will also be exploitable by value betting with a wider variety of hands than normal because he will call with worse hands, but never bluffing. Even though betting hands like 3rd pair will increase the instances of outcome 4 the increase in outcome 2 more than makes up for it.

The Actual Point
If an opponent can figure out your specific range when you bet, he can call with perfect frequency to maximize his positive outcomes. Tighty McNuts would be profitable if you only bet the 2nd Nuts and the Nuts. It is not his action that makes him bad, but his action in light of your range. So, if a villain think your range is tight in a spot (lets say he thinks you will never bluff) but in fact you are bluffing 5% of the time you are exploiting him even if those bluffs are never called, and you never show them because he is folding too much (or more accurately too large a % of his hands). The key is not what hands get shown down but what range of hands you will bet compared to what range of hands your opponent thinks you will bet. This gets much much much more complex as you add in more and more variables. Even this oversimplified post is pretty muddled, but its the beginnings of game theory. Use at your own peril.

[Lloyd]

I just saw this post. Don't have time to respond right now but think a bump is appropriate.

[MeanGreenTT]

[ QUOTE ]
Perhaps the most fundamental thing we do on this board is put opponents on ranges. .......Even this oversimplified post is pretty muddled, but its the beginnings of game theory. Use at your own peril.

[/ QUOTE ]

I've been thinking about these very things over the last couple of days, THANK YOU for for the post!!!

What I hear the better players talk about when making decisions, has got to be applied game theory.

Put them on a range, where do we fare against that range, what price am I getting, throw in a read and make the decision....

[Exitonly]

wow how did this get lost for a month?

nice post.

[Lloyd]

[ QUOTE ]
wow how did this get lost for a month?

nice post.

[/ QUOTE ]
The answer . . . . noise!!!!!!!!!!!!

Thankfully Foucault included this in his digest. I'm hoping that with me looking at every post these days for inclusion in the 3-day digest we won't be missing too many good posts.

[Sam T.]

[ QUOTE ]
The key is not what hands get shown down but what range of hands you will bet compared to what range of hands your opponent thinks you will bet.

[/ QUOTE ]

Trying to figure this out. It seems important, but my brain hurts. Little help?

[Lloyd]

Like MLG said, this is an initial post that will need further discussion to make it worthwhile. After reading this twice I know I need to read it a couple of more times. But I think this post has the potential to be very valuable to most of the forum. Not yet, but with ample discussion perhaps.

[MLG]

[ QUOTE ]
Like MLG said, this is an initial post that will need further discussion to make it worthwhile. After reading this twice I know I need to read it a couple of more times. But I think this post has the potential to be very valuable to most of the forum. Not yet, but with ample discussion perhaps.

[/ QUOTE ]

I usually pride myself on writing clearly. This post was/is fairly garbled and not particularly clear, which is why i didnt bump it. So yes, this post is gonna need some help to get its ppoint across.

[Lloyd]

I don't think it's a clarity thing but more of an incomplete thought. Seems like you slowly move from A-L and then all of a sudden where at Z and done. But I do think a theorem can be extracted with more examples. And who should be the first to expand but you yourself!!!

[Foucault]

I actually had "most underappreciated post of the month" in parentheses after this one in the digest, but chose to delete it because I wanted to be the one to revive it! Oh well, at least it is back. Here's what I was going to say:

I've been thinking about how ranges relate to the Fundamental Theorem of Poker. Sklansky says that we make money any time an opponent plays his hand in a way other than he would if he could see our cards, and conversely that we lose money any time we play our hand in a way other than we would if we could see our opponent's cards.

At least where online poker is concerned, I feel like this is results oriented, in some sense. Suppose Villain raises to 150, I push for 1000, and he calls with 22. If I have AK, then by the FTP, Villain's call is +EV. But I don't really 'have' AK, I 'have' TT-AA, AK. The fact that I turned over AK doesn't change the fact that calling with 22 was bad. Moreover, if Villain were to play like this against me in this same situation 1000 times, he would be in the red at the end of the session, because I'm turning over a dominating hand more often than not.

Now if we're playing live, maybe Villain notes that I always bet with my left hand when I have AK and my right when I have a big pair, and so he confidently and correctly calls. Over 1000 games, Villain could fold when I bet with my right hand, call when I bet with my left, and finish in the black. This tell helps him to determine which hand in my range I have this time I push. But absent such a tell, which is much harder to come by online, calling with 22 in this spot is not profitable for Villain.

I guess this is all pretty elementary so far, but I think it has some interesting implications for what deception means. It's not good enough to fool Villain about which hand I am holding right now; I have to fool him about the range of hands I could be holding when I play in a certain way. If I always and only check-raise sets and flush draws, then Villain is not really making a mistake when he calls with top pair and I have a set, since I will have a flush draw much more often.

This is why changing gears and being aware of table dynamics is important against thinking players. If you had a flush draw the last time you check-raised Villain, you may need to lead out with it the next time.

Often, however, you won't have enough history with a particular Villain to set up this kind of play. So where else can you get information about what range Villain will assign to you? For one thing, you can watch how he plays his hands. If he never raises a draw, he probably won't put you on a draw when you raise. If he slow-plays his sets, he won't expect you to have a set when you push.

The chat box can be helpful, too. Table coaches, in particular, reveal a lot about how they expect you to play through their berating of others. "All in with a draw? Donkey." The semi-bluff has got to be a substantial portion of your pushing range against this guy.

Finally, you can show uncalled hands if you intend to play differently in the future and you think Villain is alert enough for this to matter.

Sorry if this is a bit rambling, it's just what re-reading MLG's post got me thinking about. The bottom line is that you profit by deceiving your opponents about the range of hands you could have at any time, not just by playing the hand you are holding as though it were something else.