| The formulae for win, place, and show payoffs are normally as follows
in North America. There are various modifications used when there are
dead heats or when coupled entries finish in the money.
The payoffs below are quoted per $1 bet. Multiply by 2 if you want the
usual quoted payoffs.
The variables are as follows:
b = breakage. This is the fraction of 1$ that the payoff is
truncated to. If payoffs per $1 are truncated to the
nearest dime then b=0.10. Common values for b are 0.05 and
0.10. b=0.05 is known as nickle breakage and b=0.10 is
known as dime breakage.
c = the minimum profit per 1$ bet that you receive if you have
a winning ticket. Normally, c=b.
t = track take. The fraction of total moneys wagered in the pool
that are withheld for taxes, expenses, and profits. Common
values are between 0.15 and 0.19 for win, place, and show
betting.
w = the total amount bet to win on all horses
p = the total amount bet to place on all horses
s = the total amount bet to show on all horses
w[i] = the total amount bet to win on horse i
p[i] = the total amount bet to place on horse i
s[i] = the total amount bet to show on horse i
floor(x) = is the greatest integer <= x
max(x,y) = the greater of x and y
/ w*(1-t)-w[i] \
horse i to win: 1 + max [ c, b*floor | ------------ | ]
\ w[i]*b /
/ p*(1-t)-p[i]-p[j] \
horse n to place: 1 + max [ c, b*floor | ----------------- | ]
i,j finish 1,2 \ 2*p[n]*b /
n=i or j
/ s*(1-t)-s[i]-s[j]-s[k] \
horse n to show: 1 + max [ c, b*floor | ---------------------- | ]
i,j,k finish 1,2,3 \ 3*s[n]*b /
n=i,j, or k
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| Re: .2
Ah, yes, sounds like you got caught in an infamous "minus pool". This
sometimes happens even with the formulae in .1. In this situation, there
isn't enough money not bet on the winners to pay them their minimum
profit. In this case, the track, has to dig into its pockets to make
up the deficit. Sometimes, the track anticipates minus pools when
there are too few horses in a race or when they expect some extreme
favorites in the race. In these cases they will often cancel show
betting and sometimes even place betting for such a race.
Despite the small negative t, I hope you enjoyed the Derby.
- Don
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