Considering Weighted Ranges

Question

When reading about range analysis in books and looking at range analysis tools online it always seems that the ranges are not weighted, is there some reason for this?

What I mean here is that say someone opened from UTG, we could say he has a narrow range. In a book they would then say that his range is something like: 99+ KQs+. If we then do an equity calculation against this range we are calculating our equity against these hands and saying that they are all equally likely.

Why do we not consider a weighted range, so we would multiply the equity against each of these hands by the chance that they are playing that hand this way, this would seem to me to give a much better result?

Thanks for any help

Answer 1

I like this question. In contrast to Bogdan, I think weighted ranges do make sense. To stay with this example (and for the moment, forgetting about the difference between checking and betting), the UTG player surely would play any AA hand he is dealt. On the other hand, he typically would sometimes play marginal hands (like in this position say 99) and sometimes fold them. So in his range, 99 is not represented with the full relative probability of this hand, but only with the fraction of it corresponding to his playing rate.

Probably this is often neglected because

1. It adds the additional difficulty about guessing the folding frequencies of the marginal hands, while
2. it shouldn't make a big difference in most situations.

Answer 2

I think there are four reasons why people often stick to unweighted ranges, only a couple of which are theoretically interesting.

Optimal play often requires ranges with weights of 100%.

Deception is important to poker, but deception can often be achieved without playing the same hand in different ways in a situation. See The Mathematics of Poker for many examples of this in toy games.

Assuming unweighted ranges greatly simplifies calculation.

A common heuristic technique is: figure out the correct answer for some idealization/approximation of the question and then adjust that answer in light of the ways you expect the idealization to be wrong. Assuming unweighted ranges is one way we idealize, and it saves a lot of calculation.

When we want to consider weighted ranges, we are often "counting combos" instead of "narrowing ranges."

Of course, this is not interesting--it's just a terminological distinction we make that goes along with a slightly different method for calculating. But you very often will see people taking weighted ranges into account when they say, for example, that they're counting 3 of the 6 combos of QQ as possible because the opponent might have raised the turn with QQ half the time.

Answer 3

In a theoretically optimal sense you are correct.

The problem is in application. Although poker is becoming more and more of an exact science it is still a pretty broad one. In order for books to explain a point they have to be able to portray the example. If the book started analyzing weighted ranges it would have to start talking about playing styles and it would have to address each and every play style individually. Obviously that's unrealistic and highly inefficient.

That's why books would rather use 'Joe opens this from here and Bob calls with this' type of examples.

Answer 4

Weighted ranges is the theoretically correct method. Equal-weighted ranges is the "lazy" way that is considered "good enough" under most circumstances.

If you have a pocket calculator that can do this, using weight ranges is a good way to play online poker. More to the point, the practice that some people will get from such play may enable them to "do the math" in their heads in a "live" game, where calculators might not be allowed.

Answer 5

I don't understand much of your question, but you are missing a few points here.

The first point you're missing is that equity calculation against an UTG opening range has nothing to do with the fact that these hands are equally likely to be dealt. Equity calculation means the percentage of the time you'll win, likeliness is about probabilities and the fact that the cards have no memory.

The second point you're missing is that there is a thing in being dealt a hand and there is another thing in playing a hand. If I am dealt pocket aces, I have three options: raise, call or fold. Nobody is stopping me to fold pocket aces. So, what's your equity there? I folded my 85% equity against your hand, but your 15% equity brought you, in the best case, the blinds.

Your idea of "weighted ranges" is impossible to apply in practice, because there are many ways to play a certain hand and because you cannot tell for sure that the opening range of a player, in a certain position, will be fixed at all times. Nits play KK+, fishes play ATC. And this is only the preflop... you have three more streets to play and to compute.

I hope it helps.

Good luck!