When you assign someone to a range, for example.
AA-22
AK-A7

Do you have to believe that your opponent has the same chance of having a hand in the lower end of his range as the higher end of his range?

So you know he would definately raise with AA-TT but maybe raise with 99-22.

Should there be different equities calculated because of this? High end v Low end of a range?

So pocket nines has completely different equities against his whole range compared to the top and bottom ends

Yeah of course there are different probabilities of different hands in the range. A real equity calculation of a large-ish range would be extremely tedious if done correctly.

The ProPokerTools equity calculator allows you to set weighted ranges very easily.

Say you have JJ and you put villain on any pocket pair:



Now suppose you think villain has all his AA-TT pairs, but only half his 99-22 pairs.

You could specify that for those lower pairs he has to hold the club card (which has the effect of halving the number of combos for those pairs):



Which is fine, but it's not so easy when you want something more complicated than a simple half of some sub-range. Which is where weighted ranges come into play.

So here we specify 100% of his bigger pairs, and only 50% of the smaller ones:



giving us the same result as before, but as you can see, this way of doing things is way more powerful.

Thank you

Thats pretty cool

I would imagine this an example between very good players and good players. Going that one step further.

There is another program called Combonator which lets you group a range as well

That's nice, but the real problem is that the range isn't linear. It might not even be possible to render it with a single equation even if it's curved. Maybe the guy has a bias toward pocket 3s for some strange reason, and he counts all pairs 99-66 as exactly the same. I'm not trying to get too far out there, I'm just saying these things are very much approximations.

Yes you are right spike

But that's the point of doing it, we try to approximate a reasonable range (or if you like to think about it that way, we're trying to make an educated guess)

And sometimes villain will deviate from it in one way or another, but if he deviates too much from optimal play he'll lose money so we can always approximate kind of optimal ranges and if he deviates from them we're actually winning money,

like for example we assign unknown with 2.6%a 3bet a reasonable 3bet range of QQ+/AKs and play accordingly, he might 3bet TJs because it's his favourite hand but if we play reasonably against a AKs+/QQ+ range he'll lose money if he deviates from that range(if he still keeps similar stats because he prefers TJs over QQ for example) if you get what I mean

That's why it doesn't matter if he prefers 33 over something else and our approximated ranges are useful

As soon as you put a guy on a range, you're entering the world of approximation.

That'll never change.

The question is whether there's any merit in trying to get more accurate approximations. (Would more accuracy change our decision? If not, we're wasting our time. If yes, we just found a way of making more $$$).

$0.02