Finding out where my hand stands in my range
Posted by midori
Posted by
midori
posted in
Low Stakes
Finding out where my hand stands in my range
I have a fairly simple PPT question.
Q. How can I find out where my hand stands in my range?
For example, I opened BTN with 9h9d5s4d and get called by BB. Flop comes Th7h2d and I am wondering where my hand stands in my range, i.e. top 50%, bottom 20%, etc.
I could do this with PQL interpreter like this:
select count(equity(myrange, flop) > equity(myhand, flop)) as frac
from game="omahahi", p1="50%6h", p2="9h9d5s4d", board="Th7h2d"
But is there a quicker/easier way of doing this? On the river I can just launch an equity calculation for 50%6h vs. 9h9d5s4d, for example, and get pretty much a reasonable result (because the river equity is final), but this is not the case on earlier streets. Could someone help me? :)
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Not aware of anything simpler.
I think it makes good sense to use equity as a metric. Postflop hand rankings aren't well-defined anyway, if hand value is what were really after. And hand value depends on how we play the hand, so I don't see any unique and totally correct way to rank postflop hands in a vacuum.
Equity is a meaningful measure. There are things it doesn't account for, like equity realization and future betting, but it's a simple measure and easy to interpret. Whatever postflop ranking we use, making it simple is probably more useful than complex-but-still-inaccurate models.
I think that taking equity as a measure is reasonable, but not optimal. For instance the equity of a hand like AsJcJh9c on JsTh8s3s might be lower than 5s5h6s6h versus your own range, but the EV should be higher since you block the nuts and can improve to a full house.
Also, calculating the equity of your actual hand versus your own range has its complications. For instance when your 4-bet range is AA!AAA, the flop comes AhJhTh, and you get raised with significant money behind. You cannot compare the equity of AsAcJs3d versus your own range since your hand blocks your entire range. In fact, any hand from your range blocks your entire range.
It makes more sense to compare the river equity of your hand against your opponents range with the equity of your entire range against your opponents range.
GameTheory
It makes more sense to compare the river equity of your hand against your opponents range with the equity of your entire range against your opponents range.
This is a neat idea. Well-defined and it intuitively seems useful.
I totally agree with the last paragraph. Unfortunately, this approach cannot be applied to earlier streets :(
As for my hand blocking my range, shouldn't this a problem only when blocker effects are significant, i.e. our range is narrow? For example, we might not be able to apply this when we flop any set, but when we have 99xx on boards like T72r, my hand shouldn't block a significant amount of value hands in my range.
midori says:
why?
maybe we can't do it in PQL right now, but it is mathematically well-defined: we calculate the equity of our actual hand vs villain's range, and we calculate the set of equities of all the hands in our range vs villain's range, and we see how the former ranks inside the latter.
@GT: Yeah, I was about to add that too. So in most cases where we have some sort of blocker (in a broader sense), comparing our hand to our range might not be very accurate, hmm.
@CH: Of course it is well defined in theory, but doing this with PQL might not be very trivial. Most likely, ranking/aligning the hands should be a lot of tedious work :(
Word of caution:
Based on my experience with modeling, I sense this is a topic where it's easy to fall into a "black hole" where lots of effort can be spent to generate little actual usefulness.
Various models can be used here, more or less refined, but we will never get it totally right. A model that is simple, both conceptually and practically, is probably the way to go. Because we won't be able to use it very quantitatively anyway. But as a qualitative guide to playing well, sure.
I agree with you, and I was by no means suggesting what I was trying is a very quantitative approach. In some spots we can guess where each hand in our range stands rather accurately and construct our range accordingly, and there are also spots where our intuition (or at least, my intuition) doesn't work very well. I just thought this 2-liner PQL code can provide me with a quick and qualitative guideline of roughly constructing ranges. :)
What is your PQL code now for comparing hand vs range and range vs range?
HvHequity and HvRequity? Or were you referring to something else?
People generally don't post enough PQL code in this forum. We should do it more, because it's so neat :-)
Well technically speaking, HvRequity on the river is not the same as the code I posted in OP because of non-linear equity distribution. So if we were to be accurate, I think we can try something like the following:
This is off the top of my hand, and again, there might be a more elegant way of doing this.
midori: Might you consider posting an analysis where you apply this ranking usefully?
<---- Curious, but lazy.
Will think about it. Not sure if I can come up with anything very useful, but gonna be interesting. :)
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