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Originally Posted by Cratos
As I understand the problem, it is not a 80% hit rate of a given race, it is a 80% hit rate of a subset of a given race and the probability of that subset having a contender is 3/X where “X” is the size of the field. This problem becomes a conditional probability or Bayesian analysis.
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If he was selecting the horses at random, the probability would be as you state, 3/X. However, he is not selecting them at random. The probability of his selection method producing a winner in various size fields has not been established. He simply states that field sizes and winners' odds varies and that low-priced horses win more frequently than high-priced horses.
