estimating fair exacta payouts
 

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every writer I've ever read on this subject states that this is the correct way to do it is this - or something very similar to this:

9/1 over 11/1_________9*11 +(1) = $108_______for a $1.00 exacta

but isn't it true that a 9/1 shot over a 11/1 shot will usually pay much more in a 12 horse field than a 5 horse field?

I don't recall any of the discussion of this including field size

it would probably be very difficult or maybe even impossible to prepare a matrix which factors in field size

I certainly couldn't do it_________I'm not a mathlete



but, in all the writings I've seen on this subject field size was never mentioned

so, if it's not considered aren't the writings on this, unless they mention or consider field size, lacking?



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It is 108-1 or $109 for $1 not $108. These are based off of fair value assessment not the actual odds of the horse. The number of runners in a field is already incorporated into you fair line estimation, because you assign an odds line to each horse. So even if you have 3 horses you make 50-1 in the race they still eat up 6% of your odds line and you only have 94%(points) to give to the rest of the runners. Also some might make a fair value place line, because some horses are more apt to run 2nd than win, some horses are feast or famine types......

Of course all of this is theoretical. If you can't make money lining a race and betting horses you make 4-1 when they are 6-1 or higher, you aren't going to start making money because you are playing exactas that should pay $21 based off of your line that are paying $35. The bottom line is you can line races until you are 100 years old and doing so will help you at least isolate "value" plays in your mind from non value plays(which might help to some degree). But it will only make you a winner if you can make a fairly accurate line and that it is much easier said than done. Also exacta prices are subject to the same after the bell adjustments that win prices are so just like that horse you bet at 4-1 that gets hammered to 5/2 after they are off so does that exacta that you rated to pay $8 is paying $12 and ends up paying $6.60.

Regarding your point about exactas paying better in large fields than in small fields, I think that is the nature of the beast. If you have a 20% take on say 110 exacta combinations instead of on 20 it seems pretty logical you will get better payoffs on 11 horses fields instead of 5 horse fields.

I've seen these calculations too...and they've never made any sense to me. When you multiply the odds of the winner to those of the runner up...you get the exact same total as if the race outcome were reversed. A 2-1 winner and a 10-1 runner up pays the same as a 10-1 winner and a 2-1 runner up. Which, of course, is RIDICULOUS.

By the way Half Smoke is correct, $108, not $109. The math is pretty simple probably not very accurate in the extremes probably more accurate in the middle range(say with 3-1 to 8-1's).. Take a horse you make 1-1 over a horse you make 3-1. 1-1 over 3-1 should pay $4 (1*3)+1=$4. or (3*1)+3=$6. 1-1 has a 50% chance of winning 3-1 has a 25% chance of winning. 50% chance 1-1 wins, should he win the 3-1 would have a .25/50 or 50% chance of coming 2nd. 50% * 50% is 25% chance of the 1-1 over 3-1 exacta coming in or fair price of $4 for a $1. Should the 3-1 win .25 there is theoretically a .50/.75 .667% chance of the 1-1 coming second. .25*.667 or about 16.67% of the 3-1 over 1-1 exacta coming in or 5-1 fair odds or $6.

Why is it inaccurate? Horses on the low end of the odds board, say 3/5 shots, even if you can accurately assess their fair odds value, I am pretty sure you will find that they will not come in 2nd as likely as the assumptions in this formula lays out. In other words in the above example, the 1-1 doesn't not actually have a .667 % chance of coming 2nd should the 3-1 win, imo. On the high end I think you will have horses coming 2nd more often than they should. I am sure the whales have the correct formulas, I don't. I am to busy trying to figure out why the horse I make 6/5 is going off at 2/5 and winning under wraps :lol:

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this is only one example and of course proves nothing - still kind of interesting

race 11 yesterday KY Downs - 9/1 over 11/1 paid $175 - an 11 horse field

when I saw that I went back and looked at some races at Saratoga, IIRC this race wasn't from yesterday, anyway

I don't have it at hand to link but I saw a race in which a 37/1 over a 16/1 paid only $217 in a 7 horse field

Thaskalos's point is a great one - I was going to mention that but he beat me to it



https://www.equibase.com/premium/cha...1&cy=USA&rn=11



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If you line races (and you don't even have to make your own line-you can use the final odds/1.17 to get a correct fair odds line and probably would be better for the excercise I am laying out). Calculate the fair exacta prices and fair double prices and look at the final payoffs. Do so on a number of races and you will see betting biases. Which combos are close to fair value, which are far lower? Any paying better? You can probably learn something that will help you make better decisions in the future.

The rule of thumb is win price of the winner multiplied by place price of the runner up. So for example looking at Woodbine today race 4, winner paid $5.20 and the place horse $7.20, multiply those and you get $37.40 for the exacta and it paid $36.10.

More rules of thumb, the place price is ballpark 40% of win odds to the $1.

If you're looking at an 8/5 horse should pay $5.20 in the win slot. Place horse was 10-1, 40% of that is $10 to place, it only paid $7.20 however it ran second to the favorite so that would have to be part of the place estimate.

In other words 40% of 10-1 is an overall ballpark number, it doesn't accurately estimate the likely place payoff when paired with the favorite, which you would need to do if you want to pinpoint place payoffs. I've never dug into it more deeply but you might be able to use that as a starting point anyway.

THE EXACTA MATRIX HAS BEEN MY HOBBY,


THE PROBABILITY OF A HORSE WINNING IS (1/(ODDS+1))/ THE RACES TOTAL BOOK PERCENTAGE .
THE TOTAL BOOK PERCENTAGE FOR A TRACK WITH A 15% TAKE OUT SUMS TO ABOUT 1.18
THE PROBABILITY OF ANY HORSE WINNING IS (1/(ODDS+1))/1.18
TAG THE WIN HORSES WIN PROBABILITY WITH "A"
TAG THE PLACE HORSE WIN PROBABILITY WITH "B"
EXACTA PROBABILITY PROBABILITY FOR A/B IS:
A X (B/(1-A))
EXAMPLE: A HORSE ODDS =2-1, B HORSE ODDS = 3-1, TRACK TAKE OUT IS 15%
A HORSE WIN PROBABILITY IS (1/(2+1))/1.18 = .282
B HORSE WIN PROBABILITY IS (1/(3+1)/1.18 = .212

PROBABILITY FOR THE A/B COMBINATION IS,
.282 x (.212/(1-.282)) = .083
THAT EQUATES TO A $1 RETURN OF (1/.083)= 12.04
THE FAIR $1 PAYOUT IS $12.04


IN EXCEL FORMAT:

my calculations

misread your odds .
minimum $1 return for that play was $52.30, it returned only $18.05

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re calculating a exacta payout:

the actual payout is often not even remotely close to the fair payout as indicated in my earlier examples

then how about calculating a fair tri and superfecta payout

I'm sure it can be done

but I'm all but sure that many of the actual payouts won't be anywhere near the calculation of the fair payout




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I wrote a program to calculate the fair exacta prices on boxing up to 7 horses.

My kind of guy.

The only way I can calculate the fair odds is by using the results charts to determine final win and exacta payout and the racing booking percentage.
then I convince myself i should stay with the pass line at craps (1.14 vig):)

Good luck in all your endeavors

My program uses the odds that the user inputs. Anyone should be able to operate it. Just enter up to 7 odds values, that's it.