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#1
09-21-2006, 09:18 AM
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Another Hand Strength vs Range .. will this work?
I have been thinking about if it is possible to get a good estimate of your hand strength vs a range by just knowing the %strength in relation to the range.
For example say you have pocket nines which is the 70th percentile of the starting hands (Im guessing here with the actual perecntile but its just an example) If think your opponent will call with any hand above the 20th percentile. It seems to me like you should be able to figure out your winning chances by just using the percentiles, 70 and 20 in this case, but I cant figure it out and am not 100% sure if it is possible. Can any of the brilant probablility folks here either tell me I am following the wrong path or give me a hint about how to figure it out. thx [img]/images/graemlins/smile.gif[/img] 
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#2
09-22-2006, 04:36 AM
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Re: Another Hand Strength vs Range .. will this work?
A decent, but by no means perfect, approximation could be worked out, I suppose.
To see that it is not possible in general, observe that if your opponent plays only AA, there are a whole bunch of suited-connector hands that are better than KK, but against a larger range, KK is much better than 76s. (The effect isn't unique to AA -- suppose your opponent's range is {AA,KK,QQ,JJ} which makes AK and 65s good but TT and AJ bad.) What it boils down to is that there is no such thing as a unique list of starting hands from best to worst -- every such list has some assumptions built into it, and the lists for (for instance) allin preflop vs random hand and 'if the cards are dealt face up' are very different.
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#3
09-25-2006, 07:49 PM
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Re: Another Hand Strength vs Range .. will this work?
You need more than the percentiles.
Suppose these are just numbers between 1 and 100. You have 70. The other player calls only with 80 or above. You always lose. On the other hand, take the same game, but each of you are going to get a random number uniformly drawn from 1 to 1 million added to your number before showdown. Now you're very close to 50% (49.9993%). Hold'em is more complicated. Pokerstove can do the computation for you, but it has to look at a lot of possibilities to get the answer.
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