harville

The Harville method for exacta, quinella and trifecta probabilities

The basic Harville method for estimating place, show, quinella, exacta and trifecta probabilities from win probabilities. Used and abused by bookmakers and punters the world over.

There are many valid critiques of this formula. Most recently "Explaining the Favorite-Longshot Bias: Is it Risk-Love or
Misperceptions" by Erik Snowberg and Justin Wolfers. See also
"discounted harville formula" (google).