Question for Mathcapper

[ajkreider]

So, I had exactly two bets down for the 9th at GP on Saturday:  A win bet on Farz and an exacta of Lukes Alley over Farz.  Was feeling pretty good about things (and myself) through the stretch, as it was going to be between these two.  Farz was on the board at 10-1, even money on Lukes, so I figure I\'m getting at least an ROI of 7-1 either way.  Of course they dead heat so, Woohoo I get paid twice!

The win bet paid $7.80 and the $2 exacta paid $17.20, for a total ROI of closer to 6-1.  Meaning, hitting both bets paid out less than hitting either one by itself. I tried figuring out how they divvied up the pools, but my head started to hurt, so I quit.

Can you shed any light on the matter?

Edit:  Should have said the win bet was twice the size of the exacta bet.

[Dick Powell]

The 5 / 6 exacta paid $31.20 and the 6 / 5 exacta paid $17.20

[Mathcapper]

ajkreider Wrote:
-------------------------------------------------------
> So, I had exactly two bets down for the 9th at GP
> on Saturday:  A win bet on Farz and an exacta of
> Lukes Alley over Farz.  Was feeling pretty good
> about things (and myself) through the stretch, as
> it was going to be between these two.  Farz was on
> the board at 10-1, even money on Lukes, so I
> figure I\'m getting at least an ROI of 7-1 either
> way.  Of course they dead heat so, Woohoo I get
> paid twice!
>
> The win bet paid $7.80 and the $2 exacta paid
> $17.20, for a total ROI of closer to 6-1.
> Meaning, hitting both bets paid out less than
> hitting either one by itself. I tried figuring out
> how they divvied up the pools, but my head started
> to hurt, so I quit.
>
> Can you shed any light on the matter?
>
> Edit:  Should have said the win bet was twice the
> size of the exacta bet.

aj --

It's possible some late action may have driven down the price you were expecting to get on that 6-5 exacta, which may in part explain you're observation. I don't know what the 6-5 exacta was going  to pay if it had come in that way, but based on the equivalent win probabilities, it should've paid around $33.60, which wouldn't have given you a 7x ROI if you had only bet half the amount of your win bet on that combination.

Regardless, since you're dealing with different pools, with different probability distributions, there's no guarantee that you would've made the same profit when the result came back a dead heat anyway. It's not like dutching within the same pool via win bets on each horse, where you can size each bet accordingly so that you make the same profit whether the #5 wins or the #6 wins (or they finish in a dead heat). Depending on how much you bet in each pool, and the associated probabilities, the profit you get can and will vary with each given scenario.

To illustrate, I ran the numbers for each of the three win scenarios (#5 wins, #6 wins, 5-6 dead heat) for this race below, assuming a $40W bet on the #5 and a $20Ex bet on the 6-5:

Scenario 1: #5 wins race outright
$40W #5 at odds of 10.9-1 returns $476
$20 Ex 6-5 returns $0
Net profit = $476 - $60 = $416
ROI = $416/$60 = 6.9x

Scenario 2: #6 wins and #5 runs second
$40W #5 returns $0
Expected 6-5 exacta payout = $33.60 (based on win odds using discounted Harville formula)
$20 Ex 6-5 returns $336
Net profit = $336 - $60 = $276
ROI = $276/$60 = 4.6x

Scenario 3: #5 & #6 dead heat for win
$40W #5 returns $156
$20 Ex 6-5 returns $172
Net Profit = $156 + $172 - $60 = $268
ROI = $268/$60 = 4.5x

You would think that when there's a dead heat, you'd at least make as much profit as the least you would have made in either of the other scenarios, but as you can see above, that doesn\'t appear to be quite necessarily the case either.

Rocky R.


Ancillary calculations
Exacta pool: $563,309
Takeout: 20%
Portion of exacta pool distributed to bettors: $450,647
6-5 Ex: $450,647/$33.60 = 13,412 tickets
5-6 Ex: $450,647/$68.86 = 6,544 tickets

Profits to be distributed to 5-6 and 6-5 dead heat exacta winners: $450,647 – (13,412x$2) – (6,544x$2) = $410,735 ($205,368 to each combination)
6-5 Ex: $205,368/13,412 = $15.30 + $2 = $17.30 expected payout
5-6 Ex: $205,368/6,544 = $31.40 + $2 = $33.40 expected payout

[ajkreider]

Wow.  Thanks for running the numbers.  Very much appreciate the effort.