27 August 2008

Mathematics Of Betting: The Daily Double

Intuitively, if you make bets into a pool that offers a lower takeout, you would expect to do better in the long run. But when we are dealing with win bets versus multi-leg or other exotic bets, this is not the case.

The takeout on daily doubles averages around 20% across North America, while the takeout on win bets averages around 16% (incidentally, Woodbine's takeout on win is 16.95%, and 20.5% on exactors; don't try finding those numbers at their site, it is a secret).

I wanted to devise a way to prove without a doubt that a gambler should expect a better return on daily doubles over the parlaying of two consecutive winners. I think I've found the way using a very simple example.

In my example, there are four horses in 2 consecutive races and each horse has attracted the exact same money bet on them, and each daily double combination has also attracted the same exact money bet on them as well. Each pool has also attracted exactly $10,000 bet.

In the win pool, $2,500 has been bet on each horse. The total amount the track will payout is $8,400 (taking the 16% or $1,600 the track takes out). 8,400 divided by 2,500 equals 3.36, which means the odds on each horse will show up as 2-1, but the payoff odds would be 2.35-1. Without breakage it would be 2.36-1, and jurisdictions where they pay off to the dime instead of the nickel, the payoff would be 2.30-1.

So for a $20 win bet, you would get back $67. Now if you parlayed the $67 onto the winner of the second race, you would get back $224.40 (actually $224.45 without breakage, but even if you could parlay without breakage, you would be parlaying $67.20 onto a horse that paid $6.72, you would get back $225.79)

Now for the Daily Double. There are 16 combinations, which means that there is $625 bet on each combination. The track will pay out only $8,000 ($10,000 minus the 20% takeout). 8,000 divided by 625 equals 12.8, which means that each daily double has a probable payoff of $25.60. So if you took a $20 daily double, you would get back $256.00.

$256.00 is more than 13% higher what you would get by parlaying both horses breakage or no breakage.

It is like magic.

Lets see what would happen if you took a $20 wheel versus an $80 straight be in the first race.

You would get back $256.00 for your daily double bet, but you would get back $268 if you bet the $80 to win (4.6% higher than the daily double return).

Confusing? You bet.

Regarding daily doubles, generally you can get better than the 13% overlay if you stay away from program picks or newspaper selected doubles. Another time you could expect an underlay is when one or more of the horses wins at over 20-1 and the pools are on the small side.


Anonymous said...

CanG I don't see where you took into account the takeout for the parlayed money going into the 2nd race pool.
If there is one horse in the 1st and one horse in the 2nd and you are the only one betting...
$2 in the double pool would return you($2 x .8 = $1.60).
Parlay would be ($2 x .84 x .84 = $1.41). You get approx 12% less on a parlay. You'd be ok betting with a bookmaker.
That program for the 101st Plate you posted rings a bell. Pine Lake the dam of Garden Greek was a horse that I either bet on and lost or he beat the horse I bet on. Detroit Fairgrounds on the turf 1949.

Anonymous said...

I take into account the takeout on the parlay.
The horse in the second would pay exactly what the horse in the first paid because of the takeout. They would both pay $6.70 all things being equal.
I'm assuming of course the parlayed money that is bet, is part of the $2500 wagered on the horse in the second race.

Anonymous said...

You made a mistake. You forgot to deduct the $ bet on the winning horse(s) from what's left of the pool to distribute among the winners.

The Win Pool has a higher takeout AND they get you twice. A $2.00 Parlay in your example pays $8.82. The DD pays $12.44.

Anonymous said...

whoops make that $9.24 and $12.44.

Either way lower takeout always = higher payback.

Anonymous said...

OK on third thought disregard my figures altogether. I need to try again at work with Excel. In any case, though, the flaw in your example is you counted the winning $ twice.

Anonymous said...

I don't see the flaw? The first winner would pay $6.70 and so would the second winner. Both were done at 16% win takeouts. You are risking $20 in both cases, if the second horse loses, you are out $20 regardless of if you bet the double or the parlay.
And the amounts cashed if the second horse wins are correct too.
What flaw?

Anonymous said...

oops #4. I'm at work with my real computer (and no beer) and your #'s are right.

The one thing I got right was that the 'magic' arises because in the 2 win method the pools get scraped twice, albeit at a lower rate.

Anonymous said...

Hey Can Grumble.You should update your blog more often.

Anonymous said...

CanG, I just realized that 1. I misspelled your handle on the HANA site when I replied to your comment, and 2. You are a blogger. I apologize for the first and am glad I discoved the second. Look foreward to reading your postings and continuing to (respectfully)argue with you.