root <NoEMail@home.org> wrote: > A friend of mine enjoys horse racing and is a regular small > time bettor. He has roughly broken even over several decades > of betting. I do not bet, but I am interested in the processes > he uses to determine his bets. > > Along those lines I came up with an idea to possibly increase > his handicapping success. I asked him, for every race, to > divide the horses into three groups, group Y included horses > which had a chance of winning the race. Group M were those > horses that could, maybe, win. And group N were horses he > thought had no chance of winning. Of course, some races were > won by horses in groups M and N. > > After some time we computed the ratio of horses in group Y > which went on the win the race. That ratio is W/Y > where Y is the total number of horses ranked Y, and W is > the number of those that did win. Some, even most, races > have more than one Y candidates. It turns out the ratio > of W/Y was 3/8 for my friend. > > What I was hoping to achieve is a measure of what odds > a Y rated horse should pay before that horse would > be bet. It isn't enough to reckon that a horse is the > best choice to win, the odds that horse pays must be > high enough to overcome the uncertainty. > > I have stumbled on to a conceptual error in my thinking. > In some ways, W/Y does represent a probability but I > am unable to rationalize that interpretation given > that some horse must win every race, and that the > a-priori probabilities for the various horses must > add up to 1. Given that most races have more than one > Y candidate, their chances of winning are not independently > related to W/Y. Clearly W/Y does not represent the > probability that a Y candidate will win. > > Everything becomes simpler if I interpret W/Y as the > chance (probability) that in a given race with at > least one Y rated horse, that a(any) Y rated horse > will win. Given that interpretation I can say that > if there are m Y rated horses in a given race > then the probility that one of them will win > is, on average, W/Y. Given that, and assuming that > all Y rated horses are equivalent, then each Y rated > horse has a probability of W/(m*Y) of winning. > To be a good bet, then, the Y rated horse must > pay better than m*Y/W. > > I would appreciate any comments. > Thanks.
Quick follow up: I can see W/Y does not represent the chance that some Y rated horse will win a given race. So I am back to thinking is the determination of W/Y of any betting value?