Improve your Horserace Profits on Exactas and Quinellas

Getting More Bang for your Quinella Buck

by Dunbar
[From Blackjack Forum Vol. XXII #4, Winter 2002/03]
© 2002 Blackjack Forum

Imagine walking into a casino and seeing two side-by-side blackjack games that are identical except that one of them is offering a promotional 2-1 on naturals. Is there any question which game you would play?

Likewise, if you find two Jacks or Better video poker machines with the only difference being that one pays 9 coins for a full house and 6 for a flush, while the other pays 8 and 5, we know which is the better machine. If you are going to play, it’s an obvious decision where you sit down.

A similar opportunity occasionally presents itself to horse bettors, but the bettors very often make the wrong choice.

Some tracks offer quinella bets and exacta bets in the same race. (A quinella is a bet on two horses that wins when those two horses come in first and second, regardless of order. An exacta is a bet that wins when the two picked horses finish first and second in the exact order specified.)

Let’s say you want to make a quinella bet on Blazing Bishop and Flying Curtis. You could either bet the quinella, or you could make exacta bets for different amounts on the Blazing Bishop/Flying Curtis exacta and the Flying Curtis/Blazing Bishop exacta. If you bet the right proportions on each of the two exactas, you can make it so that you would profit the same amount no matter which exacta came in—in other words, you can make it look just like a quinella.

A bettor at the racetrack can look at the toteboard or video monitors to find out how much exactas and quinellas will likely pay, based on what has been bet so far. There will always be some uncertainty in the final payoffs due to last minute bets and off-track bets that are added to the pari-mutuel pools after the close of betting. But the projected payoffs displayed in the last couple of minutes of betting will usually be sufficient for the purpose of deciding whether to play the quinella or to create your own pseudo-quinella from exactas.

How to Decide Whether to Use Exactas Instead of a Quinella

It’s very easy to tell when it would better to use exactas to create your own quinella. Using the probable payoffs, you need only see if

Q/E_x + Q/E_r < 1. the “Q-Test”

where

Q = the quinella payoff

E_x = the exacta payoff

E_r = the reverse exacta payoff .

In other words, you divide the quinella payoff by each of the exacta payoffs and see if the sum is less than 1. Let’s call this the “Q-Test”. If the sum is greater than 1, then you are better off simply betting the quinella. But if the sum is less than 1, then you are better off using the exactas to create your own pseudo-quinella.

Definition: A pseudo-quinella is created when an exacta and its reverse are bet in such a way that a bettor would get the same net profit regardless of which exacta hits.

How Much to Bet on Each Exacta or Quinella

Okay, you might ask, if the Q-Test says I’m better off betting the exactas, how much should I bet on each exacta? Let’s say you want to bet $Z on a quinella. Then you should bet

$Z x E_r/(E_x+E_r) Eq. (2)

on the exacta that will pay E_x. Bet the remainder of your $Z on the reverse exacta.

Example: E_x= $10 and E_r=$20, for $2 bets. Say you want to bet $60 on the quinella, and you have already used the Q-Test to determine that it is better to use exactas. According to Eq (2), you should bet

$60 x 20/(10+20) = $40 on the exacta that will pay $10, and

$60 – $40 = $20 on the exacta that will pay $20. Note that no matter which exacta comes in, your net profit would be the same, $140.

In the next section, I am going to show why the Q-Test works. If you don’t like algebra, you can jump right to the “Real World Examples” section.

Derivation of the Result

Here’s why Q/E_x + Q/E_r = 1 is the breakeven point for deciding between the two ways to make a quinella bet.

Assume for the moment that Q, E_x, and E_r are payoffs for a $1 bet. We can either bet $Z on a quinella bet, or we can divide our $Z into two exacta bets.

If we bet $Z on a quinella and it wins, our profit is (Z * Q) – Z.

Alternatively, we could bet $Z total on the exactas. We will bet B_x on the exacta that pays E_x and B_r = Z-B_x on the exacta that pays E_r. If the exacta paying E_x hits, our total profit will be:

E_x x B_x – Z.

If the reverse exacta hits, our total profit will be:

E_r x (Z-B_x) – Z, because B_r = Z-B_x.

If we want the same profit on each exacta, then we set those 2 payoffs equal to each other:

E_x x B_x – Z = E_r x (Z-B_x) – Z.

Solving for B_x,

B_x = Z x E_r/(E_x+E_r) Eq. (3) This is the same as Eq. (2) above.

So, betting B_x on the exacta and Z-B_x on the exacta reverse will yield the same net profit, B_x x E_x – Z. The question is, how does this net profit compare to the profit on a winning quinella bet? We want to compare

Z x Q – Z (the quinella profit) to B_x x E_x –Z (the exacta profit)

If Z x Q – Z < B_x x E_x – Z, then it is better to play the exactas.

Canceling the “-Z”s and substituting for B_x with Eq. (3), we get

Z x Q < Z x (E_r/(E_x+E_r)) x E_x , which reduces to

Q < (E_xxE_r)/(E_x+E_r). Multiplying both sides by E_x+E_r we get

Qx(E_x+E_r)/(E_xxE_r) < 1. A little more multiplying and canceling brings

Q/E_r + Q/E_x < 1, which is precisely the Q-Test. That is, we’ve shown that if Q/E_r + Q/E_x < 1, then using the exactas will return more profit.

Real-World Examples

Is there much difference in the real world between the payoffs on the quinella and the pseudo-quinella? Santa Anita offered both quinellas and exactas on all its races on Sept 5. I used Youbet.com to compare the final payoffs on the winning quinella to what could have been collected by betting exactas.

As Table 1 shows, in six races there was little difference between the payoffs on the winning quinella and the pseudo-quinella. In the 10^th race, the quinella was 22% better than a similar bet constructed from exactas. But in the 1^st, 6^th and 7^th races, an extra 6%, 23%, and 12% was available to bettors who created a pseudo-quinella rather than bet the quinella. Taking advantage of this kind of opportunity can make the difference between a losing bettor and a winning bettor.

Table 1. Quinellas and Exactas on Oct. 5 at Santa Anita

Legend: Payoffs for the winning quinella, the winning exacta, and the exacta reverse are given in the first three columns to the right of the Race # column.

“Q-Test” refers to Q/E_x + Q/E_r.

If Q-Test < 1, then exactas were better.

“% Gain” is how much more could be gained by using exactas to create a pseudo-quinella.

Let’s take a closer look at the 7^th race. The quinella paid $27.40, the winning exacta paid $81.80, and the exacta reverse was between $48.00 and $48.80, so I use $48.40. Applying the Q-Test, we see:

27.40/81.80 + 27.40/48.40 = 0.90,

which is less than 1. So we know that the pseudo-quinella was superior to the quinella. If we wanted a $20 quinella-type bet, we should have bet $20 x 48.40/(48.40+81.80) = $7.40 on the exacta, and the remainder, $12.60, on the exacta reverse, producing a pseudo-quinella win of $302.60-$20=$282.60. This is 12% more than the quinella win, $274-$20=$254. Of course we would have rounded these bets to $7 and $13, or $8 and $12; in either case we would have won more than on the quinella.

Additional Comments

Whenever I have said “exactas are better” or “the quinella is better” in this article, I am speaking only of a bettor who is trying to make a quinella-type bet. If the bettor has a strong preference for a specified order for the 1^st two horses, then that is a different matter.

An alternate form of the Q-Test would be to ask if E_xxE_r/(E_x+E_r) > Q. The left side is the payoff on the pseudo-quinella.

Quinellas and exactas are offered in other pari-mutuel settings such as dog racing and jai alai. The pseudo-quinella method described here applies equally well to those situations.

There is an additional advantage of creating a pseudo-quinella. Exacta pools are generally much bigger than quinella pools. This means that a bettor can bet more into an exacta pool without affecting the payoff.

Summary

Exactas can sometimes be used to create a pseudo-quinella that will pay an extra 20% or more above the payoff for a quinella. The simple “Q-Test” uses the probable payoffs to determine whether the pseudo-quinella will pay more than the quinella. When the pseudo-quinella is better, Eq. (2) states how much to bet on each exacta. By selectively choosing either the quinella or the pseudo-quinella, it’s possible to get the maximum return on your quinella-type bets.

Acknowledgments

I first described some of these ideas in posts between Sept 25 and Oct 5, 2002 in the Racing Forum on Sharpsportsbetting.com. A post by Defenestrator was helpful in focusing my thoughts toward developing Eq. (2). Thanks also to Barry Meadow for a good discussion of some issues related to quinellas, especially the relative pool-size factor. Finally, thanks to “P” and Colin Caster for helpful comments on a draft. ♠