What's Luck Got to Do with It? by Mazur Joseph

Author:Mazur, Joseph
Language: eng
Format: epub
ISBN: 9781400834457
Publisher: Princeton University Press

However, rounding down to a nickel when dealing with large sums can have significant advantages for the track. We shall see this in the rationale for this strange payoff.

First, the track and state deducts from the total for its take. That leaves (1 – r)T in the win pool. Next, W is deducted, leaving (1 – r)T – W to be divided among the winners. So each $2 bet should pay

in addition to the original $2, or

The problem is that the track deals with real dollars and real cents. The quantity

is likely to be a decimal with non-zeroes beyond the hundredths. For example, let’s say the total amount bet to win is $300,000, that $200,000 is bet on the winner, and that r = 0.15. Then the track takes $45,000 and computes that the dollar payoff on the winner is 27.5 cents. The track would round this payoff down to the nearest nickel (the breakage) and so the dollar odds would become 25 cents. Each $2 bet would have a payoff of $2.50. The track would keep the breakage, $.025 × 200,000 = $5,000. So, adding up: the track and state gets $45,000, the track gets an additional $5,000, and the group of winners gets $250,000 for a total of $300,000, the total amount bet.

It may seem as if we’ve forgotten about bets to place, to show, and so forth. Not really; those bets are pooled separately. The computations are slightly different. The dollar paybacks for place bets are similarly computed except for the fact that the bettors of two horses will have to share the winnings in proportion to the sizes of the bets on each horse. Let’s say that T is now the total amount bet to place and that P1 and P2 are the amounts bet for horse 1 and horse 2 to place, respectfully. Then the per dollar payback for horses 1 and 2 are, respectively:

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