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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1088.0. "horsecents" by VINO::JMUNZER () Thu Jun 08 1989 16:53

Does anyone know how horseracing payoffs are calculated?  I think that the
simple case has six payoffs:

	*  for a bet on the 1st horse to win
	*  for a bet on the 1st horse to place
	*  for a bet on the 1st horse to show
	*  for a bet on the 2nd horse to place
	*  for a bet on the 2nd horse to show
	*  for a bet on the 3rd horse to show

Can these be calculated from the total dollars of these bets plus the total
dollars of all other win, place, and show bets?

John
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1088.1Win, place, and show payoff formulaeVAXRT::BRIDGEWATERSun Jun 11 1989 02:0254
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
1088.2nonprofessional inquiryVINO::JMUNZERTue Jun 13 1989 17:525
    Thanks.  I was the bookie at a Kentucky Derby party (for very low
    rollers), and made up my own formulas.  They were simpler, and a small
    negative t was needed to round things off.
    
    John
1088.3A Minus PoolVAXRT::BRIDGEWATERTue Jun 13 1989 22:5914
    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