How to Improve your Horserace Betting Return on Exactas and Quinellas 

FROM ET FAN: 
Getting More Bang for your Quinella BuckBy Dunbar[From Blackjack Forum Vol. XXII #4, Winter 2002/03] © 2002 Blackjack Forum Imagine walking into a casino and seeing two sidebyside blackjack games that are identical except that one of them is offering a promotional 21 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
offtrack bets that are added to the parimutuel 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 pseudoquinella from exactas. How to Decide Whether to Use Exactas Instead of a QuinellaIt'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 “QTest” 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
“QTest”. 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 pseudoquinella. Definition: A pseudoquinella
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 QuinellaOkay, you might ask, if the QTest 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
QTest 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 QTest
works. If you don't like algebra, you
can jump right to the "Real World Examples" section. Derivation of the ResultHere'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} = ZB_{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 (ZB_{x}) – Z, because B_{r}
= ZB_{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 (ZB_{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 ZB_{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_{x}xE_{r})/(E_{x}+E_{r}). Multiplying both sides by E_{x}+E_{r}
we get Qx(E_{x}+E_{r})/(E_{x}xE_{r})
< 1. A little more multiplying and
canceling brings Q/E_{r} + Q/E_{x} < 1, which is precisely
the QTest. That is, we've shown that
if Q/E_{r} + Q/E_{x} < 1, then using the exactas will return
more profit. RealWorld ExamplesIs there much difference in the real world between the
payoffs on the quinella and the pseudoquinella? 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 pseudoquinella. 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 pseudoquinella 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.
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 QTest, we see: 27.40/81.80 + 27.40/48.40 = 0.90, which is less than 1.
So we know that the pseudoquinella
was superior to the quinella. If we
wanted a $20 quinellatype 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 pseudoquinella 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 commentsWhenever 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 quinellatype 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 QTest would be to ask if E_{x}xE_{r}/(E_{x}+E_{r})
> Q. The left side is the payoff on
the pseudoquinella. Quinellas and exactas are offered in other parimutuel
settings such as dog racing and jai alai. The pseudoquinella method
described here applies equally well to those situations. There is an additional advantage of creating a pseudoquinella. 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. SummaryExactas can sometimes be used to create a pseudoquinella that will pay an extra 20% or more above the payoff for a quinella. The simple “QTest” uses the probable payoffs to determine whether the pseudoquinella will pay more than the quinella. When the pseudoquinella is better, Eq. (2) states how much to bet on each exacta. By selectively choosing either the quinella or the pseudoquinella, it's possible to get the maximum return on your quinellatype bets. AcknowledgmentsI 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 poolsize factor. Finally, thanks to “P” and Colin Caster for helpful comments on a draft. ♠ Back to the Professional Gambling Library Back to Blackjack Forum Online Home

© 20042005 Blackjack Forum Online, All Rights Reserved  

Maximize Your Wins on Quinellas and Exactas
This article provides a formula for choosing between quinellas and exactas to maximize your winnings with horserace betting. 