The Answer to the Horse Betting Quiz

Among many ingenious ideas/scenarios/scams proposed by blog readers in response to my horse betting quiz, the answer I was looking for finally appeared. Jim Vanasek is the reader who nailed it. Here is what he wrote:

The scenario: You are alive in going in to the final leg of the pick six. There is going to be a payout of $100,000 to the winning tickets. There is a very strong favorite in the race with 97 percent of the money bet on him. Your horse has 2 percent of the money bet on him. The last horse has 1 percent of the money bet on him. You KNOW Horse A cannot win. These numbers are consistent in the pick six pool as well as the win pool.

Assume there are 100 live tickets. 97 on the favorite, 2 on Horse B (we have one of the tickets), and 1 on Horse A.

There is one minute to post. There is $970 bet on the favorite, $20 bet on Horse B, $10 bet on Horse A.

Suddenly, the favorite is scratched at the gate. He flips in the gate, the track vet scratches him, whatever. This is what happens:

All win money on the favorite is refunded. The win pool is now $30. There is still $20 on Horse B (now the favorite – this is important) and $10 on Horse A.

The pick six rules are different. The rules state that in the event of a late scratch, all tickets with the scratched horse go to the favorite. That is Horse B. The pick six pool is now 99 tickets on Horse B, still only one ticket on Horse A (the horse that cannot win). When Horse B wins, you will win the pick six with 98 other people and receive $1010.10.

But wait, you have time! You must now go bet on the horse you KNOW cannot win, Horse A. Bet $11 on him. This makes the pool $41. Twenty dollars on Horse B, $21 on Horse A, our sure loser.

The pick six pool changes suddenly! Since Horse A is now favored, the 97 tickets on the scratched horse go to Horse A. Now there are 98 tickets on Horse A, only two on Horse B. Now, when Horse B wins the race, each winning ticket is valued at $50,000. Investing $11 on a sure loser (Horse A) increased your returns from $1010.10 to $50,000 (admittedly it will be $11 less since you bet on A, so really you’re getting $49,989.

THAT is how you can bet to win on a horse to lose and get more money returned.

This is exactly the scenario I had in mind.

Supposedly, it actually happened once. A big horse-betting syndicate had placed a huge pick six ticket, faced this situation, bet enough to ensure that the horse they wanted in the pick six was not the favorite, and ended up winning the pick six. The investment in betting on a horse they thought (and hoped) would lose paid off. As one might expect from people smart enough to recognize and solve this problem in real time, they went on to bigger and better things, graduating from horse race betting to running one of the world’s most successful hedge funds.

Caleb Powers

This is a good story. This could work as written. But, the arcana of racing law being what it is, it doesn't have to.

Here's why. When you look into the racing rules, you see that they've covered most every contingency. For example, this problem suggests that, but for one last minute bet, two horses would have gone off with exactly the same win pool on each. The New York rules of racing provide, at Rule 4011.23 that should this occur, you break the tie for purposes of the pick six by taking the horse with the lowest program number. So, if the horse you "knew" would not win had a lower program number, you could save your dollar and let all the other cards go to it anyway for the same return. The California rules provide the same thing.

Or, if the race were in California, the rules there provide that you get to make an alternate pick for each race. If you don't make an alternate pick, or that one gets scratched, too, then you get the favorite. And you wouldn't know who anyone else's alternate pick was. So, this only works at tracks that don't have alternate picks.

And, since we're throwing around acts of God, such as horses getting scratched by the vet at the last minute, let's add some weather to it. Say after the third or fourth race, at some point after the pick six cards have to be turned in, it starts raining. And it rains all day. And the track conditions get changed between the fifth and sixth race on the Pick Six from fast to sloppy. Under both New York rules, everyone who has five winners gets the sixth one automatically because of the track change. So, the above still works, but only if it doesn't rain that day.

It's a nice problem, though. It had me stumped, and I know a little bit about racing.



Very in interesting, I dont know much about playing the ponies but sounds like it would be fun


So just how much time do you guys spend at the track, anyway?


A lovely solution, but it of course requires the knowledge that tickets on scratched horses are transferred to the favorite. Most of your readers don't know much about the rules of betting. Perhaps a tip was warranted, like "You have to know the game to know how to break it." As it is, there were a lot of uselessly furrowed brows about external incentives (monetary and otherwise).

On the other hand, you did introduce it as a "quiz for people who like to bet the ponies," a qualification that plenty of respondents ignored. But if you'd been able to link to a more detailed description of the system, they (we) would have been able to play along too...


Professor, you switched horses in mid bitstream from "you knew for sure that the horse would lose the race" to "a horse they thought (and hoped) would lose". That is horse of a different color, maybe even a red herring. Not that I would have gotten it even with that clarification.


The actual correct answers were given on the questioning page, by 'acidtest'. Unless the race is fixed you can not know for sure a horse will lose the race. See Sarava, Belmont Stakes 2002. 70-1. Yes I had a winning ticket.
November 28th,
10:42 am

OK, the horse is old and crappy. The jockey a loser. Nobody, i said nobody, had put a single buck on this horse.

Why not put a single dollar, just as a lottery ticket. If you are the only one, one dollar is enough to collect the jackpot collected for the winner without sharing it. One dollar, You would have a huge return, never reached at the bookies

— Posted by acidtest
November 28th,
10:49 am

In a non economic understanding

The race is fixed. you are an insider.
The winning horse is already chosen.
you just take this small bet as a proof of innocence. Of course, your neighbour will share the winning heavy ticket with you.


You own the horse, you want it to have a nice odd to qualify for other races, more prestigious, which is valueless (your name is al Maktoum, money's not a problem)

— Posted by acidtest



still - how do you KNOW a horse can't win.
this is important - I'm going to the Meadowlands track on Friday!
Help make me rich!


I don't really understand how you calculated the $1010.10 and $50,000 dollar valuations. Anyway, I don't think anyone had a chance at this trivia question except die-hard horse betters since it revolved around some obscure horse-betting rule. Sorry I wasted my time.


Re: kendo's #4 "Professor, you switched horses in mid bitstream from “you knew for sure that the horse would lose the race” to “a horse they thought (and hoped) would lose”. That is horse of a different color, maybe even a red herring. Not that I would have gotten it even with that clarification."

It isn't really different. A real-world case would obviously not involve certain future knowledge; there is arguably no such thing. But qualifying the question in that way excludes weak responses like those crow appears to be arguing for in comment #5.

The ideal example, as in the quiz given, is supposed to preempt any thoughts or hope on the actor's part that the horse could actually win. The point is that they bet on the horse to win, 100% expecting it to lose. In fact, they want it to lose. An explicit, but unnecessary, framing would be to ask: In this system, why would one bet on a horse to win that one (1) absolutely believes will lose and (2) absolutely wants to lose?

The question also makes little sense if we introduce outside factors, as some have suggested (including myself). Otherwise, a response to any question about "Why might a rational economic actor do X?" can always be "Because Mr. Megabucks is paying him [arbitrarily high amount of money] to do so." The 'correct' answer could therefore be expected to be within the closed system of the parimutuel betting; and, of course, it was.



You still don't know that your horse is going to win, even if you know of a few horses that have no chance (unless there's only a few horses in the race).

As well as loading up the dud horse to inherit the bets of the scratched favourite, you might put a buck on any other horses running.

Then again, any other punters who see a horse with no bets on it could do likewise.


#7 - Those numbers come from the grand purse($100,000) divided by the number of people betting on the winning horse. When horse B is weighted 20-10, all 99 people betting on B split the purse to the tune of $1,010.10. When you bet on A with $11, A is then the favorite and will steal the floating pool. B is now the underdog, A cannot win, and only the 2 people who bet B in the first place need to split the $100,000 purse.


"As one might expect from people smart enough to recognize and solve this problem in real time, they went on to bigger and better things, graduating from horse race betting to running one of the world's most successful hedge funds."

Just a guess here, but are you talking about Jim Cramer?


okay, sorry to hijack..

I didn't see a post about this, but my Freakonomics feed hasn't updated on Google Reader since 11/21... are other people having this problem?


I would also like to know which hedge fund you are talking about =)

Jed Christiansen

I, too, would be interested in who solved this in real-time and/or which hedge fund they run!


re #12 " Freakonomics feed hasn't updated on Google Reader"

i experienced the same problem. i solved it by deleting the feed then adding it back. good luck.

Jim Vanasek

I got quite the laugh from the comment at the end, considering that I also run a hedge fund. Apparently the line between the stock market and the ponies is a fine one.


When series bets reach the final leg (pick six, pick four, etc) there's quite a lot of hedging that goes on at the track. The track provides “will pays” on the television monitors, allowing players ways to hedge against results they may not have covered in their serial tickets.

As other folks have pointed out, there are few sure things in racing, but I know the story of a fatalist sure-thing that happened to someone.

I know of a very good handicapper who hooked up with a friend with a big bankroll. On a day with a big carryover (jackpot), the handicapper constructed a ticket he knew would cost a certain amount. But when Bankroll put the ticket in, somehow he forgot a horse in the last leg – a race where Handicapper had selected five of the seven horses as possible winners.

You know how the story turns out. They sweep through the first five races and are alive with five horses in the last race. There's even a scratch that moves favoritism to a sixth horse, so now these guys have all but one horse covered – the horse Bankroll left off the ticket. Handicapper couldn't get to the windows and Bankroll wasn't at the track. Handicapper told another friend: “If you want to make some money, I know exactly which horse will win the last race today. Bet everything you have.” Sure enough...that uncovered horse won. Handicapper's friend made some bucks on the hedge and the pick six with the horse Bankroll forgot paid in the high five figures.



MV at No. 8: In an earlier post on this puzzle I speculated that what was meant was not "you know the horse will lose" but "you consider the horse likely to lose, so much so that its chance of winning does not figure in your decision." Even that formulation may overstate the bettors' actual thinking in the real world situation. Anyway, Professor Levitt is a scientist, and one should be able to parse his phrasing with that in mind. It also would have been helpful to have hinted more strongly that highly technical knowledge of specialized parimutuel rules was required to solve the puzzle.


#12, dd:
I also had a problem with my google feeder, thankfully not for the Freakonomics blog.
Try this: unsubscribe from Freakonomics and then subscribe again. It worked for me!
Good luck