Confidence & Betting Sports

[rjp]

For those of you with a more formal foundation in statistical analysis, what do you consider to be an acceptable confidence level for approximating true odds?

For the sake of discussion, assume I observe 250 successes out of 500 trials. I can construct the following confidence intervals: 95% (45.53%,54.47%); 99% (44.16%,55.84%); 99.9% (42.59%,57.41%); 99.99% (41.27%,58.73%).

This has recently become a topic of major interest for me as I do not wish to overestimate my edge when betting half Kelly. As such, I've been using the lower tail (actually just one sided) of a 99.99% confidence interval as the true probability based on an observed sample.

I guess what I really want to know is: is this the best method for estimating a probability based on a sample for betting purposes?