chi test - skewed by extreme odds?

[algorithmbetting]

this is a question to those who know this stat. It strikes me that calculating the expected number of winning/losing bets is unduly influenced by extreme odds. eg if i have made 100 bets at average fair odds of 2.00 i expect 50 wins/losses. but if i just add 1 further bet at fair odds of 100 i get average fair odds of 2.97 for 101 bets ([2*100]+[1*100])/[100+1]. and therefore expected wins of roughly 34 (101/2.97) and 67. how do you adjust for this apparent bias? multiply by stakes to get a risk adjusted weighted average method? has anyone considered this before?

[muppet77]

Re: chi test - skewed by extreme odds? when you work out average odds use PERCENTAGES rather than prices. loads of people do this! so your calculation is ((0.5*100)+(0.01*1))/(100+1) =

0.495149

(6dp) or 1/0.495149 is the equivalent of a price of

2.019596

[slapdash]

Re: chi test - skewed by extreme odds? Yes, when the odds vary the average odds (with the usual meaning of "average") don't correspond to the expected number of winners. You really want to take the average probability of winning, which comes to the same thing as taking the "harmonic mean" of the odds (i.e., rather than looking at the average of "odds", you should look at the average of "1/odds"). E.g., in your example, "1/odds" is 0.5 (100 times) and 0.01 (once) giving an average of 50.01/101. So the harmonic mean of the odds is 101/50.01, or about 2.0196. By the way, if you're doing a chi-square test on something with only two possible outcomes (win/loss), this comes to exactly the same as doing a simple significance test on the number of wins, assuming that this number is normally distributed.

[algorithmbetting]

Re: chi test - skewed by extreme odds? cheers guys. ive used the harmonic mean and the fluctuations appear to be lessened when adding extreme odds.