Poker-AI.org

Today I have been thinking about how to obtain the most unbiased ranking of hands at any point in a hand (preflop, flop, turn, river).
River is pretty obvious, nothing to say about that. Best hand wins.

However, I don't really like the approach of expected hand strength (EHS) as this is ranking hands based on their ranking against a 100% range and is therefore biased.

Maybe I am missing something but why is average hand strength not a good metric? By average hand strength I mean rolling out all possible boards and taking the average of the resulting set of absolute hand strengths on the river. This is assuming that we are using a 7 card hand ranking function that is gapless but AFAIK this is true for most hand ranking implementations, isn't it?

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Cheers.

I think there is no universal "unbiased ranking of hands" - it always depends on the intended usage. The problem with current approaches I have is a) that they make implicit assumptions (e.g. the range we calculate against is 100%) and b) condense the result into a single value. For example, building abstractions based on metrics like HS, EHS or EHS2 just doesn't work great as the strategic properties of a hand are not distinguished well. Hence, we "just" need to find a metric, that separates hands according to the strategic properties well, which is again dependent on the use case of the metric.

Which is why I was hoping average hand strength would be unbiased but I actually have never tried it.
If this isn't enough I always wondered if using average hand strength + it's variance would be helpful at all.

Just to clarify AHS != HS or EHS, it's the average rank of a hand given all 7 card combinations... which now thinking about it might actually turn out to be pretty similar to EHS.


Regardless, another approach would be to rank against a top 10% range to get away from the 100% range. Or something more elaborate that apparently has been around since 2006 and earlier: http://pokercoder.blogspot.com/2006/07/ ... hands.html which is what propokertools.com is using for its rankings.

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Cheers.

I think EHS2 is just an attempt to summarize strength in a single number. Using average and variance strength is definitely worth a try. Drawing hands will have high variance. In the early days of computer poker UofA and others used the 5 card hand strength on the flop plus potential which I think was a rough and ready way of doing the same thing.

I used the strength of the top 20% preflop hands as a parameter in the machine learning of oppo action prediction with some success so that might work in this context too. Actually, the more I think about that idea the more I like it. I'm not familiar with the literature on clustering flop boards, but it seems you could categorize boards using their strength in conjunction with preflop hand strength.


https://www.google.co.uk/search?hl=en&b ... cbL7ixBxtY

https://www.google.co.uk/search?hl=en&n ... es4TSeTueQ

Can you elaborate on what you mean by this? I'm assuming you don't mean wins + draws / 2 against all possible two card combinations?

AHS then ignores the distribution a hand can flop. In PLO its even more extreme: a hand like AA72 rainbow is strong according to this metric, but no PLO player would consider it a great hand as you never have a high equity hand on flops without an Ace or like trips textures. On the other hand, JT98 double suited has tons of good flops where it can get the money in. With pokerprotools you can see the equity distribution and a different shape should result in a different strategy. The same is true for NLH (even though to a lesser extend).

If you havent read it yet, check Johansons latest paper and the approaches he uses there. My new abstraction is build on ideas from there.

What I meant with AHS is this:

Construct a ranking of all possible 7 card combinations, which is what 7 card evaluators are doing.
If you want to get the AHS of a hand on a given flop, then you roll out all possible turns and rivers and add up the rankings. Divide by the number of ranks that you added up. Done.

However, thinking about this a little bit more, this would probably be pretty similar to evaluating against a 100% range in the end since we are using the ranking of all possible combinations, which kinda is the same thing. I just liked the idea in the beginning because we don't need to roll out 9 cards to figure it out. So all this might be, is an idea to construct EHS LUTs a lot faster...

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Cheers.

I think its exactly EHS. And you won't be faster in the LUT construction too imo, as the fast hand evaluators are so fast because they use elaborate bit operations leasing to a non-continuous HR index on the river, while you'd need a continuous one, which would slow down the hand evaluator significantly.

Alright scratch that idea then. But fret not, I have a new one. Watch for another thread on hand ranking

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Cheers.