Re: Chances Question
Aaron - I am partial (in theory, perhaps not in practice) is a simplified credibility theory approach, where you combine the observed data (10 for 10) with a full-credibility criteria and a "default" rate of a check-raise meaning strength.
For example, you may guess that the average opponent has the goods 75% of the time when he CR. However, you acknowledge that it actually varies by opponent. You estimate that if you were to see someone CR 100 times, you would say that that observed player has an actual rate equal to his observed rate. For a player with < 100 obseravations, you would combine the default rate with the observed rate. For the example above:
Estimated rate (given you've seen 10 for 10) = 100% x Z + 75% x (1 - Z),
Z = (10/100)^0.5
(This square-root rule is typical).
The problem with my suggestion is that you need a default rate and a full-credibility threshold. The problem with your approach is that you often end up with ranges too wide to be useful. It's a matter of taste as to which short-comings you'd rather live with.
As an aside, I think that credibility theory is the most underappreciated tool for evaluating poker statistics. Perhaps because it's less commonly understood that confidence intervals, which are first-year stats course material.
I'd be interested in your comments. I've read your posts and value your opinions (I'm sure that makes you feel like you've really accomplished something in life [img]/images/graemlins/wink.gif[/img] )
|