Thread: Equation for a First 4

I need some help in creating a probability equation for an exotic bet type. I have found equations for exactas and trifectas but I need an equation for a first four. An exacta is picking the first two horses past the post in order, a trifecta is the first three in order and a first four is the first four in order.

x = the percentage chance (in whole numbers) of Horse X winning
y = the percentage chance (in whole numbers) of Horse Y winning
z = the percentage chance (in whole numbers) of Horse Z winning

Here is the equation for an exacta:


Here is the equation for a trifecta:


For example if x has a 60% chance of winning and y has a 25% chance of winning and z has a 15% chance of winning then the price for the trifecta would equal $2.67.

Could someone please give me the equation for a first 4?

Just knowing the probability a horse will win does not tell you anything about the probability that is will place or show or come in fourth so you cannot calculate the probability of an exacta or trifecta.

I realize its not going to be the exact probability of the exacta, trifecta or first 4 however an approximate is fine for what I am doing...