DRF Legend Steven Crist on Value Investing and Horse Betting by John Szramiak was originally published on Vintage Value Investing

I’m not at all a gambler.

In fact, I used to be proud to say that, thinking that gambling was only for chumps.

But after reading **Crist on Value**, I’m beginning to reconsider my position on the activity.

*Let me explain…*

### Steven Crist on Value

Steven Crist is a legend in the world of horse betting.

A Harvard graduate, Steve Crist took a different approach to betting on horses than most other people, applying math, logic, and probability in making wagers, instead of simply picking the most likely horse to win the race. While by no means was this revolutionary, Steven Crist *has* been one of the most outspoken advocates for using this approach of **finding value** in wagers, and he’s used it to great success (Crist’s nickname is “King of the Pick Six” – the pick six is a wager where the bettor must select the winners of six consecutive races and is considered the most difficult type of bet).

In 1998, Steven Crist teamed up with Alpine Capital to purchase *Daily Racing Form (DRF*), a newspaper that has published the past performances of race horses since 1894 and is the gold standard statistical service for horse race handicappers (as one journalist put it, *DRF *is to horseplayers what the *Wall Street Journal* is to investors). While running *DRF*, Steve Crist also wrote a weekly column and a blog, where he often talked about his method of horse betting.

In 2001, Steven Crist wrote a chapter for the book *Bet With the Best: Strategies from America’s Leading Handicappers*. That chapter was simply called **Crist on Value**.

While Steven Crist doesn’t mention stocks, markets, the economy, companies, or investing anywhere at all in Crist on Value, the parallels between horse betting and investing are incredibly interesting. In fact, most of Crist on Value seems like it belongs in Benjamin Graham’s *The Intelligent Investor*, not a book on how to bet on horses!

Michael Mauboussin, a value investor and one of the sharpest thinkers in finance today, has called Crist on Value “one of the best 13 pages on investing I have ever read.”

I’d probably agree with that.

Click here to read **Crist on Value** now… or keep reading below.

### The Similarities Between Horse Race Betting and Investing

As it turns out, the connection between horse betting and investing runs pretty deep.

As a kid, Warren Buffett used to bet on horse races at Omaha’s Ak-Sar-Ben Race Track. And here’s Charlie Munger talking about horse race betting in his famous *Worldly Wisdom* speech:

“The model I like — to sort of simplify the notion of what goes on in a market for common stocks — is the pari-mutuel system at the racetrack. If you stop to think about it, a pari-mutuel system is a market. Everybody goes there and bets and the odds change based on what’s bet. That’s what happens in the stock market.”

Now, before you invite me to sit next to you at the bank of slot machines at the nearest casino, remember that what we’re talking about here are **pari-mutuel betting** systems – gambling games like horse betting and poker where you’re betting against all the other betters – and NOT **fixed-odds betting** – games like roulette or craps where the odds are fixed.

Winning these fixed-odds games is pure chance and making money off of them over the long-term is impossible because the casino is setting the odds. In roulette, for example, there are 38 spaces. If you were to bet $1 on each of 1,000 spins, you would have bet a total of $1,000 – but you would only have won back a total of $936, for a total loss of $64. The longer your play, the more you lose and the more the house wins (hence the phrase “the house always wins”).

Pari-mutuel betting games, on the other hand, are an entirely different story because it’s the public – not the house – that is setting the price of the bet. And somewhere between frequently, occasionally, and rarely, the public makes the wrong price.

Michael Mauboussin expands on this point in his book *More Than You Know: Finding Financial Wisdom in Unconventional Places*:

“One way to think about it is to contrast a roulette wheel with a pari-mutuel betting system. If you play a fair game of roulette, whatever prediction you make will not affect the outcome. The prediction’s outcome is independent of the prediction itself. Contrast that with a prediction at the racetrack. If you believe a particular horse is likely to do better that the odds suggest you will bet on the horse. But your bet will help shape the odds. For instance, if all bettors predict a particular horse will win, the odds will reflect that prediction, and the return on investment will be poor.

The analogy carries to the stock market. If you believe a stock is undervalued and start to buy it, you will help raise the price, this driving down prospective returns. This point underscores the importance of expected value, a central concept in any probabilistic exercise. Expected value formalizes the idea that your return on an investment is the product of the probabilities and the various outcomes and the payoff from each outcome.”

This is similar to what I wrote about in *Why the Stock Market is So Hard to Predict*. You see, roulette and craps are “level one” chaotic systems – chaos (i.e. randomness) that does not react to predictions made about it. Everybody in the casino can bet on red 32 if they want, but the roulette wheel won’t care and it won’t affect the 1/38 chance that the ball has of landing on red 32. Likewise, the casino could care less which numbers are played – the payoff remains the same.

In contrast, pari-mutuel betting games like horse betting and poker are “level two” chaos systems – these games react to predictions made about their outcomes. While the horses don’t care who’s picking them as a favorite to win and the cards that are dealt aren’t affected by a poker player’s wager, the betting *within the game itself* IS affected by the actions of other bettors. In horse race betting, your bet helps shape the odds for that wager – which might be better or worse than the actual odds a certain horse has of winning the horse race. In poker, the players determine the size of the pot – which might be large or small relative to the odds your hand has of winning. And the same is true of the stock market, where investors’ predictions of a company determine the price of that company’s stock – which might be more or less than the company’s true intrinsic value.

### A Quick Primer on Some Important Horse Betting Terms

Before we actually get to Crist on Value, I think it’s helpful to know some of the most important horse betting terms (so that you can understand some of the nuances of what Steven Crist is actually talking about). Here are the horse betting terms you should know:

**Pari-mutuel betting**: In pari-mutuel betting, all bets are placed together in a pool, the “take” is paid to the house (*see below*), and the remaining amount is disbursed to the winners in proportion to the amount wagered. This is in contrast to**fixed-odds betting**, where the odds are set by the bookmaker. In pari-mutuel betting, the final payout is not determined until the pool is closed. In fixed-odds betting, the payout is agreed at the time the bet is sold.**The house**: The institution organizing the betting (e.g. the racetrack, casino, or bookmaker).**Takeout**: Also called the take, cut, rake, or vigorish, this is the amount the house takes before paying out the winnings. For horse race betting, this is often 15-25% depending on the type of wager.**Breakage**: The winning payoff is always rounded down to the nearest 10 or 20 cent increment. This is called breakage, and the delta is kept by the racetrack.**Payoff**: This is the amount actually paid to the winning bettors. Here is an example of how payoff is calculated:- If $1,000 is bet in total on win bets, and $200 is bet on the winning horse, then:
- First, the track collects it’s cut. Let’s say the takeout is 17%, which leaves $830 ($1,000 x 83%).
- This ratio of winnings to winning bet is $830/$200 = 4.15. This ratio is then applied to the minimum $2 bet: 4.15 x $2 = $8.30. The $8.30 is rounded down to the nearest 20-cent increment, or $8.20.

- So $8.20 is the final payoff per $2 bet. All winning bettors will be paid at this ratio. For example, a $100 bet will win $100 x (8.20/2.00) = $410.

- If $1,000 is bet in total on win bets, and $200 is bet on the winning horse, then:
**Odds**: Converting percentage probabilities (like a horse’s winning chance) into betting odds is easy. If I think a horse has a 20% chance of winning, then that horse will win 1 out of every 5 times – in other words, it will win once (20% of the time) and will lose 4 times (80%) out of every 5 races. So the odds of that horse winning are 4-1 (80%/20% to 1). If I think the horse has an 80% chance of winning, then the odds of that horse winning are 1-4. As you can see, odds of winning are listed as LOSE-WIN. Converting odds into probabilities is a similar task. If a horse is listed as paying off at odds of 3-2, then the implied probability of that horse winning is 2 / (3+2) = 40%. In the case of 3-2 payoff odds, the payoff on a $2 wager would be $5 ($2 original bet + $3 in profit).**Horseplayer**: Some one who bets on horse races.**Daily Racing Form****(****DRF****)**: The*Daily Racing Form*(*DRF*) provides the past performances of all the horses running on the day’s program and includes informative horse racing articles and handicapping by*DRF*staff. The cost of a*DRF*issue is usually just $4.**Handicapping**: The practice of assigning predicting the outcome of horse races by assigning percentages to each horses chance of winning.**Long / short odds**: A horse with long odds has apparently no chance of winning (e.g. 19-1, or a 5% chance of winning). A horse with short odds is favored to win (e.g. 2-3, or 60% chance of winning).**Overlay / underlay**: An overlay is a good bet – the horses odds of winning are longer (worse) than they should be. An underlay is a bad bet – the horses odds of winning are shorter (better) than they should be).**Win, place, and show**: The most basic bet is picking the horse that you think will finish first (win). You can also bet on a horse that you think will finish first OR second (place) or will finish first, second, OR third (show).**Exacta, trifecta, and superfecta**: The exacta is a bet on the horses you think will finish first and second – but they must be in the correct order. The trifecta is the same type of wager but on the horses you think will finish first, second, and third, and the superfecta is a bet on the horses you think will finish first, second, third, and fourth (again, the horses must finish in the correct order).**Daily double, pick three, pick four, or pick six**: The daily double is a bet on the first place horse in two consecutive races (usually the first two of the day). The pick three and pick four are bets on the first place horse in three or four, respectively, consecutive races. The pick six is a bet on the first place horse in six consecutive races (usually the last six of the day). If nobody calls all six correctly, part of the winning pool is paid to those correctly picking five of the winning horses (or less if nobody picked five), and the rest is carried over to the next pick six pool.**Minimum bet amounts**: A minor – but important – detail: the minimum bet at racetracks is generally $2 on win, place, and show bets, and $1 on all other types of bets.

### Steven Crist on Value (Investing) and Horse Betting

Sweet! Now we’re at the exciting part – breaking down Crist on Value.

Here are my 6 key takeaway insights from Steven Crist on value investing and how to make better decisions:

**Price versus Value**

“The point of this exercise is to illustrate that

even a horse with a very high likelihood of winning can be either a very good or a very bad bet, and the difference between the two is determined by only one thing: the odds.”

As Steven Crist explains, a horse with a 50% chance of winning is a good bet if his payoff is better than 1-1 and a bad bet if his payoff is less than 1-1. For example, a 10-1 shot (which would imply a winning chance of 9%) would be a great overlay (good bet) if you think he actually has a 15% chance of victory, and a terrible underlay (bad bet) if his true chance is only 5%.

What Crist is doing here is separating out **price** (the payoff and the payoff’s implied winning percentage) and **intrinsic value** (the horse’s actual chance of winning). This is the fundamental principle of value investing that Benjamin Graham and David Dodd first set forth in *Security Analysis* in 1934:

*Price ? Intrinsic Value*

This, of course, is directly applicable to investing. Any stock can be a great investment or a bad investment – even if the company is amazing. It all depends on the stock’s price and it’s comparison to that company’s true intrinsic value.

**You Need to Have the Right Temperament**

“Now ask yourself honestly: Do you really think this way when you’re handicapping? Or do you find horses you “like” and hope for the best on price? Most honest players will admit they follow the latter path.

This is the way we all have been conditioned to think: Find the winner, then bet. Know your horses and the money will take care of itself. Stare at the past performances long enough and the winner will jump off the page.

The problem is that we’re asking the wrong question.

The issue is not which horse in the race is the most likely winner, but which horse or horses are offering odds that exceed their actual chances of victory.This may sound elementary, and many players may think they are following this principle, but few actually do. Under this mindset, everything but the odds fades from view. There is no such thing as “liking” a horse to win a race, only an attractive discrepancy between his chances and his price. It is not enough to lose enthusiasm when the horse you liked is odds-on or to get excited if his price drifts up.

You must have a clear sense of what price every horse should be, and be prepared to discard your plans and seize new opportunities depending solely on the tote board.If you begin espousing this approach, you are sure to suffer abuse from your fellow horseplayers. When one of them asks you who you like in a race and you say, “I think the 4 is a bigger price than he should be,” the likely response is, “So what? Who do you like?” Your cronies are apt to tell you that you should be betting on horses, not on prices, and

after an inevitable stretch of watching some of their underlays win, you will begin to doubt yourself.

Sticking to your guns is easier said than done, but it is the only way to win in the long run. The horseplayer who wants to show a profit must adopt a cold-blooded and unsentimental approach to the game that is at variance with both the “sporting” impulse to be loyal to your favorite horses and the egotistical impulse to stick with your initial selection at any price. This approach requires the confidence and Zen-like temperament to endure watching victories at unacceptably low prices by such horses.“

There’s so much wisdom is this short passage. Let’s break it down.

First, Steve Crist is saying you shouldn’t be asking which horse in the race is most likely to win. Your job is to figure our which horse is offering odds that exceed its actual chance of victory. This is what famous value investor Howard Marks calls “second-level thinking” in his book *The Most Important Thing Illuminated: Uncommon Sense for the Thoughtful Investor*.

First-level thinkers only consider one variable at a time, often the one that is the most obvious: What horse is the best? What company is the best? Second-level thinkers take many thing into account and ask the complicated questions: Which horse is disliked by the crowd but actually provides a good return given its true chance of winning? Which company does the market dislike due to certain short-term headwinds, but actually has great long-term value that everyone else is overlooking?

Then, Crist says that you MUST stick to your guns, even when your friends and your own emotions are tugging at you to abandon your approach and join the crowd. Rudyard Kipling would remind you to “keep your head when all about you / are losing theirs.”

It’s the only way to win in the long run. If you want to make money – whether it’s in horse betting or in the stock market – **you must adopt a cold-blooded and unsentimental approach** to the game. And you have to do this despite the **egotistical impulse to stick with your initial selection at any price**.** **

You have to be willing to change your mind and strong enough to walk away from an investment if the price isn’t right. **This approach requires the confidence and Zen-like temperament to endure watching victories at unacceptably low prices by such horses ** – or to watch other investors make money on a stock that they bought for far more than its intrinsic value (a product of luck,

instead of skill).

**Invest with a Margin of Safety**

“I made Two Item Limit 60 percent to win the race, giving a 35 percent chance to Tap Dance and the remaining 5 percent to their three overmatched opponents. Odds of 2-1 or better on Tap Dance would make her playable.

Unfortunately, everyone else seemed to have had the same idea about Tap Dance waltzing to the lead. With five minutes to post, both fillies were even money, and I felt neither remorse nor disloyalty as I went to the window to make the only logical bet: Two Item Limit to win, which she did at $4.40. Betting 6-5 shots to win is not my usual style, but I saw no other way to play the race and was convinced I was receiving outstanding value. When I first began playing the races, I probably would have bet on both Dollar Bill and Tap Dance instead of Monarchos and Two Item Limit, out of loyalty to my initial selections and the sense that you “should” bet on the horses you initially like.

The success of these two plays, though, was ultimately based upon the probability of victory I had assigned to each winner.

I cannot argue in good conscience that Two Item Limit had precisely a 60 percent chance of victory as opposed to 57 or 63 percent, and I doubt that such calibration is in fact achievable. It is, however, possible through experience to get close enough that if you demand sufficient value to cover the margin of error, you should outperform the competition – your fellow horseplayers.“

I included Steven Crist’s entire anecdote about betting on the horse Two Item Limit so that we could set the stage for his last two lines.

Crist calculated Two Item Limit’s chance of winning to be 60%. But this is a rough calculation – Crist admits that he wouldn’t be able to argue that the horse’s victory was exactly 60% and not 57% or 63%. In fact, that degree of precision is probably impossible. What Crist DID do, however, was apply his considerable experience in horse race handicapping and combine that experience with a margin of safety.

The 6-5 odds on Two Item Limit right before the race started implied that the other bettors thought the horse only had a 45% chance to win, not the 60% Crist had calculated. The 6-5 odds result in a payoff of $3.60 for every $2 wager (assuming a 16% takeout and normal breakage), which translates into an 80% return – given that Two Item Limit wins. Run this scenario 50 times with Two Item Limit winning 60% of the time, and Crist would have bet $100 and won $108. The difference between Crist’s calculated 60% chance of winning and the implied 45% chance of winning gave Crist a big margin of safety. He would’ve had to have been way off on his prediction of the race’s outcome to not come away with a profit – even after takeout and breakage.

(An important note here: Crist, of course, had a 40% chance of losing that wager – something that he isn’t able to control. And he wouldn’t be able to repeat this scenario 50 times like I described above. But he COULD bet on 50 other races with similar probabilities – something a professional horseplayer would naturally do. Over time, the law of averages makes the percentages true – even if in any one scenario the outcome isn’t favorable).

Warren Buffett has talked about margin of safety using similar terms:

“You have to have the knowledge to enable you to make a very general estimate about the value of the underlying business. But you do not cut it close. That is what Ben Graham meant by having a margin of safety.

You don’t try to buy businesses worth $83 million for $80 million. You leave yourself an enormous margin.When you build a bridge, you insist it can carry 30,000 pounds, but you only drive 10,000 pound trucks across it. And that same principle works in investing.”

When betting on horses, you don’t bet on a horse that you think has a 45% chance of winning the race if the odds imply it has a 40% chance of winning the race. That margin of safety just isn’t big enough for you to be wrong. As Steven Crist writes, you need to **demand sufficient value to cover the margin of error**.

The same thing works in investing. You don’t try to buy businesses worth $83 million for $80 million. You try to buy business worth $150 million for $80 million. Then you’ll have a margin of safety – the main purpose of which is to make an accurate estimate of the future (of a business or of a horse race) unnecessary in the first place.

**Market Efficiency**

“Does that mean today’s player faces nothing but higher vigorish and the remaining sharpies? Not at all. I firmly believe that, in general, the nitwits still outnumber the sharpies. More important, most sharpies aren’t as sharp as they think, and even the winning sharpies make plenty of egregious mistakes on individual races. As long as the volume of ill-informed money exceeds the takeout, **there can be a positive expectation for the true sharpshooter who waits for the competition to make mistakes.**“

Many people bring up the Efficient Market Hypothesis, claiming that the stock market is completely efficient and that it’s impossible to find undervalued securities. Any outperformance versus the market can only be attributable to luck.

Warren Buffett – and his incredible track record of 20% returns per year for over 50 years! – would obviously disagree.

It might be true that the market is more efficient today than it was decades ago and that it’s harder to beat the market – just like it’s become harder to make money from horse betting since attendance at horse races has declined (meaning less uninformed bettors) and takeouts at race tracks across the country have been increased to make up for that decline.

But if you’re sharp, there’s still value to be found. You just need to be patient and wait for your competition – and the market – to make a mistake.

**Wait for the Right Race**

“There are also plenty of races in which your competition will make no actionable mistakes. Everyone seems to be at about the right price, and there is no compelling reason to jump into the pool. It is worth remembering that the whole is better than the sum of its parts: The betting public’s post-time favorite wins more often than any individual public handicapper, and over time first choices win more than second choices, which win more than third choices, and so on down the line.

There is no shame in passing a race because you just don’t see any value in it. Nor should you force yourself to play a race in which you have no confidence in your own odds line.That doesn’t mean you have to sit on your hands – $1 boxes for action were made to fill the spaces between races where you have a legitimate edge or opinion.”“

It’s not an easy game, but you’re not playing against “the game.” You’re betting against the other bettors.It doesn’t matter if they pick as many winners as you do, or even more, if you are betting only whenthe price is right.“

Despite my earlier comments on market ineffiency, that doesn’t mean that every single stock is mispriced. Sometimes, the price IS right. In these instances, your best action is to – do nothing! Just wait for the race where you have a real advantage.

As Warren Buffet likes to say, “the stock market is a no-called-strike game. You don’t have to swing at everything – you can wait for your pitch.”

Of course, when your pitch does come, then you need to bet big on it – since great opportunities to pop up as often as they ought to. Here’s another quote from Warren: “When it rains gold, put out the bucket, not the thimble.”

**Beating Estimates Says Little About True Value**

“A track’s morning line has even more pitfalls. It is typically prepared by a track employee in the racing office or simulcasting department whose primary skill in life may not be oddsmaking and whose agenda is different from yours. Tracks want to advertise their races as being competitive rather than mismatches, which is why horses we all know are going to be 3-5 are routinely listed at 6-5 on the morning line. Similarly, nearly every race card features several horses who are legitimately 99-1, but few morning-line prices exceed 30-1. Racing offices do not want to offend the horsemen filling their cards by saying their horses have virtually no chance.

Given all that, it is astounding how many horseplayers believe there is some magical significance to the morning line and to any discrepancies between it and the actual betting.If a horse is 4-1 on the morning line and 2-1 in the actual betting, plenty of your competitors will decide that this horse is a “good thing,” the focus of an international betting coup orchestrated by the mysterious “they” who “know.” If the same horse is instead 8-1 as post time approaches, the same conspiracy theorists will pronounce the horse “dead on the board.”In fact, in either case, all that has happened is that the linemaker, an overworked and fallible human being like the rest of us, made a bad guess about how much the public would fancy a particular horse.“

This is exactly like earnings estimates for stocks. When a stock beats consensus earnings estimates – either once, or say over a period of consecutive quarters – many investors automatically assume that it’s a great investment. But at the end of the day, the fact that the stock beat earnings estimates only tells you one thing – that the analysts covering the company got their earnings estimates wrong.

As Benjamin Graham used to say, a “stock investor is neither right or wrong because others agreed or disagreed with him; he is right because his facts and analysis are right.” In much the same way, a stock is not a great investment because it’s performing better than others’ expectations. A stock is a great investment only if you can buy it for much less than YOUR OWN calculation of its intrinsic value.

## Warren Buffett on Horse Betting

I mentioned earlier that Warren Buffett used to actually bet on horse races when he was a kid. Well, Buffett’s biography *The Snowball: Warren Buffett and the Business of Life* tells the full story.

“The art of handicapping is based on information,” Buffett said in *The Snowball*. “The key was having more information than the other guy – then analyzing it right and using it rationally.”

Growing up, Buffett used to go to the race track – either Ak-Sar-Ben Race Track in Omaha (notice that it’s Nebraska spelled backwards?) or Charles Town, West Virginia when the Buffett family lived for a short time in Washington, D.C (Buffett’s father served in the House of Representatives for two non-consecutive terms). Since Buffett senior didn’t like attending the races, Warren usually went with his uncle or the mother of his friend Bob Russell.

**Stooping for Tickets**

Buffett, who wasn’t even a teenager when he started going to Ak-Sar-Ben, was too young to bet so he made money stooping for tickets. According to Buffett:

At the start of racing season you get all these people who’d never seen a race except in the movies. And they’d think that if your horse came in second or third, you didn’t get paid, because all the emphasis is on the winner, so they’d throw away [second-] and [third-place] tickets.

The other time you would hit it big was when there was a disputed race. That little light would go on that said ‘contested’ or ‘protest.’ By that time, some people had thrown away their tickets. Meanwhile, we were just gobbling them up.

It was awful; people would spit on the floor. But we had great fun.

That analogy is highly reminiscent of the cigar butt strategy that Benjamin Graham used to use when investing in stocks (he would look for companies that other investors had essentially thrown in the crash, but that still had some value left in them).

**Stable-Boy Selections**

Buffett and his friend Bob Russell also began a tip sheet called *Stable-Boy Selections*, which they hawked at the race track:

“We got away with it for a while. They weren’t the hottest sellers in the world. I mean, a couple of little kids selling this thing we typed up in my basement on an old Royal typewriter.We were at the track, yelling ‘Get your

Stable-Boy Selections!’ But the Blue Sheet was the number-one tip sheet, and the race track was getting a commission on it. The Blue Sheet sold for a little more. At 25-cents, we were a cut-rate product. They shut down theStable Boy Selectionsfast because they were getting a cut on everything sold in the place except us.”

**Hundreds of Books on Horse Race Betting**

And when the Buffett family moved to Washington, D.C., Warren just had one request for his dad:

“When we got to Washington, I said, ‘Pop, there’s just one thing I want. I want you to ask the Library of Congress for every book they have on horse handicapping.’ And my dad said, ‘Well, don’t you think they’re going to think it’s a little strange if the first thing a new Congressman asks for is all the books on horse handicapping?’”

But Buffett reminded his father of the help he gave him during the winning campaign, and pledged to be there for him again during his re-election. So Howard got Warren hundreds of books about handicapping horses.

“Then what I would do is read all these books. I sent away to a place in Chicago on North Clark Street where you could get old racing forms, months of them, for very little. They were old, so who wanted them? I would go through them using my handicapping techniques to handicap one day and see the next day how it worked out. I ran tests of my handicapping ability – day after day – all these different systems I had in mind.”

**Buffet on Value and ****DRF**

Buffett noted that a bookie actually took action inside Washington’s Old House Office Building.

“You could go to the elevator shaft and yell, ‘Sammy!’ or something like that and this kid would come up and take bets.”

Even Buffett himself did some bookmaking for guys who wanted to get down on the big races like the Preakness Stakes. “That’s the end of the game I liked, the 15 percent take with no risk,” Buffett said.

Buffett got along well with his high school golf coach, Bob Dwyer, and the two frequently rode the Chesapeake & Ohio railroad together from Silverspring, MD to Charles Town racetrack in West Virginia. Dwyer taught Buffett how to better understand the *Daily Racing Form.*

“I’d get the

Daily Racing Formahead of time and figure out the probability of each horse winning the race. Then I would compare those percentages to the odds,” said Buffett, who bet from $6 to $10 to win. “Sometimes you would find a horse where the odds were way, way off from the actual probability. You figure the horse has a 10 percent chance of winning, but it’s going off at 15-to-1.”

That last part sounds a lot like Crist on Value, doesn’t it?

**Going broke one day at Charles Town**

One day, Buffett went to Charles Town by himself. He lost the first race and his performance went from bad to worse until he was down $175. Feeling depressed, he went to an ice cream shop and bought himself a sundae with the last of his money.

While eating, Buffett thought to himself that he had just lost more money than he made in a week.

“And I’d done it for dumb reasons. You’re not supposed to bet every race. I’d committed the worst sin, which is that you get behind and you think you’ve got to break even that day. The first rule is that nobody goes home after the first race, and the second rule is that you don’t have to make it back the way you lost it. That is so fundamental.”

This was an important lesson that definitely influence Buffett’s investing later in life. *You’re not supposed to be every race.* Instead, just wait for the right pitch.

### Charlie Munger on Horse Betting

Here’s an excerpt from a speech Charlie Munger gave at the USC Business School in 1994 called *A Lesson On Elementary, Worldly Wisdom as it Relates to Investment Management & Business*. In this segment, Charlie Munger gives his thoughts on horse betting, pari-mutuel betting systems, and investing in the stock market:

Any damn fool can see that a horse carrying a light weight with a wonderful win rate and a good post position etc., etc. is way more likely to win than a horse with a terrible record and extra weight and so on and so on. But if you look at the odds, the bad horse pays 100 to 1, whereas the good horse pays 3 to 2. Then it’s not clear which is statistically the best bet using the mathematics of Fermat and Pascal. The prices have changed in such a way that it’s very hard to beat the system.

And then the track is taking 17% off the top. So not only do you have to outwit all the other betters, but you’ve got to outwit them by such a big margin that on average, you can afford to take 17% of your gross bets off the top and give it to the house before the rest of your money can be put to work. Given those mathematics, is it possible to beat the horses only using one’s intelligence? Intelligence should give some edge, because lots of people who don’t know anything go out and bet lucky numbers and so forth. Therefore, somebody who really thinks about nothing but horse performance and is shrewd and mathematical could have a very considerable edge, in the absence of the frictional cost caused by the house take. Unfortunately, what a shrewd horseplayer’s edge does in most cases is to reduce his average loss over a season of betting from the 17% that he would lose if he got the average result to maybe 10%. However, there are actually a few people who can beat the game after paying the full 17%.

I used to play poker when I was young with a guy who made a substantial living doing nothing but bet harness races…. Now, harness racing is a relatively inefficient market. You don’t have the depth of intelligence betting on harness races that you do on regular races. What my poker pal would do was to think about harness races as his main profession. And he would bet only occasionally when he saw some mispriced bet available. And by doing that, after paying the full handle to the house—which I presume was around 17%—he made a substantial living. You have to say that’s rare. However, the market was not perfectly efficient. And if it weren’t for that big 17% handle, lots of people would regularly be beating lots of other people at the horse races. It’s efficient, yes. But it’s not perfectly efficient. And with enough shrewdness and fanaticism, some people will get better results than others.

The stock market is the same way—except that the house handle is so much lower. If you take transaction costs—the spread between the bid and the ask plus the commissions—and if you don’t trade too actively, you’re talking about fairly low transaction costs. So that with enough fanaticism and enough discipline, some of the shrewd people are going to get way better results than average in the nature of things.

It is not a bit easy. And, of course, 50% will end up in the bottom half and 70% will end up in the bottom 70%. But some people will have an advantage. And in a fairly low transaction cost operation, they will get better than average results in stock picking.

How do you get to be one of those who is a winner—in a relative sense—instead of a loser? Here again, look at the pari-mutuel system. I had dinner last night by absolute accident with the president of Santa Anita. He says that there are two or three betters who have a credit arrangement with them, now that they have off-track betting, who are actually beating the house. They’re sending money out net after the full handle—a lot of it to Las Vegas, by the way—to people who are actually winning slightly, net, after paying the full handle. They’re that shrewd about something with as much unpredictability as horse racing. And the one thing that all those winning betters in the whole history of people who’ve beaten the pari-mutuel system have is quite simple. They bet very seldom. It’s not given to human beings to have such talent that they can just know everything about everything all the time. But it is given to human beings who work hard at it—who look and sift the world for a mispriced bet—that they can occasionally find one. And the wise ones bet heavily when the world offers them that opportunity. They bet big when they have the odds. And the rest of the time, they don’t. It’s just that simple. That is a very simple concept. And to me it’s obviously right—based on experience not only from the pari-mutuel system, but everywhere else.”

### About Steven Crist

Steven Crist, who retired in July 2016, was a longtime executive, editor, publisher, innovator, and columnist of *Daily Racing Form* (*DRF*). *DRF* is a newspaper that was founded in 1894 and publishes the past performances of race horses; the paper is the gold standard statistical service for horse race handicappers in North America. As one journalist puts it, “*DRF* is to horseplayers what the *Wall Street Journal* is to investors.”

Steven Crist attended Harvard and served as editor of The Harvard Lampoon. It was in college that he fell in love with horse racing: “The stats and numbers stuff is there. Plus the animals, the gambling – and the weird subculture: the racetrack is… well, like people who ran away and joined the circus.”

Crist graduated from Harvard in 1978 and got his start in the industry as a reporter and columnist covering the sport for *The New York Times* from 1981 to 1990. In 1990, he became the founding editor-in-chief of *The Racing Times*, where he introduced statistical innovations, including Beyer Speed Figures (which help standardize race performances across different tracks and distances), detailed race conditions, and timing in hundredths of a second, all of which have become industry standards.

In 1992, Crist was appointed by New York Governor Mario Cuomo as a member of a state advisory commission on racing, where he was the catalyst for several reforms. Crist was a vice president of the New York Racing Association from 1994 to 1997.

In 1998, Steven Crist teamed up with Alpine Capital to purchase *Daily Racing Form*. Crist expanded the publications statistical and journalistic content, introduced new weekly print publications, created a book-publishing division, and introduced new products. Crist continued to write a weekly column and a blog, frequently advocating for player-friendly changes to the racing game.

While Steve Crist was an important institutional figure in the sport, his most enduring legacy was probably as a horseplayer. Crist took a unique approach to picking horses, specifically applying math, logic, and probability in making wagers. His skill led to him being nicknamed “King of the Pick Six,” as he was incredibly successfully in cashing in on pick six bets (considered the most difficult type of bet, the pick six is a wager where the bettor must select the winners of six consecutive races).

In 2010, Crist was named to the Media Honor Roll in the horse racing Hall of Fame. In 2015, he was inducted into the Hall of Fame for the National Handicapping Championship (an event he helped create in 1999).

Crist is the author of several books about horse betting, including the memoir *Betting on Myself: Adventures of a Horseplayer and Publisher* (2003) and *Exotic Betting: How to Make the Multihorse, Multirace Bets that Win Racing’s Biggest Payoffs *(2006). In 2001, he contributed an entire chapter to the book *Bet With the Best: Strategies from America’s Leading Handicappers*. That chapter, which is reprinted here, focuses on value. Crist also contributed to the follow-up book *Bet With the Best 2: Longshots* in 2008.

Steve Crist lives in Hempstead, New York with his wife and two retired racing greyhounds.

### Bet With the Best: Expert Strategies from America's Leading Handicappers – Chapter 3: Crist on Value – by Steven Crist

Download **Chapter 3: Crist on Value** here or read on below.

*Crist on Value:*

A typical liberal-arts education sets a graduate loose upon the world with a tremendous amount of knowledge he will never need or use again and some gaping holes about how actually to function in society. He may know the abbreviations for the periodic table of elements and the names of the leading Renaissance poets, but have no idea how to make a cup of coffee or write a business letter.

A similar situation exists for the American horseplayer, self-taught through handicapping literature and days of hard knocks at the old horse park. He has vast amounts of handicapping data swimming through his head – names, dates, running lines, speed figures, pedigrees, trainer patterns and angles – all devoted to the goal of discovering the likeliest winners of horse races. When it comes time to go to the betting windows, however, nearly every one of these well-informed enthusiasts almost immediately surrenders his edge. He is like the chemistry scholar who knows the molecular structure of the coffee bean but has no idea how much water to put into the percolator. Each is unable to convert his knowledge into something useful and pleasurable-a steaming cup of java, or a consistent profit on racetrack bets.

This is not to suggest that universities should stop teaching chemistry or literature, or that horseplayers should not continue to develop and enhance their skills as selectors. Like a liberal-arts education, the study of horses and how they perform is a worthy pleasure in itself, and in the case of handicapping, the world’s savviest bettor cannot win with bad opinions. The point is that pure handicapping is only the first half of the battle in winning at the races.

Most horseplayers intuitively know this, but don’t do much about it except complain. How often have you or a fellow trackgoer opined that you’re a pretty good handicapper but you really need to work on your betting strategies or your so-called money management? This is sometimes an exercise in denial for people who are in fact bad handicappers, but it is probably true for many who can select winners as well as anyone. The problem with this line of thinking is that it suggests betting is some small component of the game, which is like pretending that putting is a minor part of championship golf. In fact, if you handicap well and bet poorly, you’ve failed. It’s as useless as crushing your tee shots while three-putting every green.

Turning your enthusiasm for racing and proficiency at handicapping into profitable betting requires an entirely new way of thinking about playing the races. It would take a far longer treatise than this chapter to explore fully the mathematics and mechanics of racetrack betting, and the strategies available to optimize one’s wagering through different types of bets. Instead, the purpose here is to raise three fundamental concepts that may help the serious handicapper to focus on profit rather than prediction, making money instead of just picking winners: probability and odds; handicapping the competition; and using multiple bets to improve your prices.

**Probability and Odds**

Forget for a moment everything you know about parimutuel betting and pretend that horse racing is set up like sports betting or a game of blackjack: If you pick the winning horse, the track doubles your bet. Every winner, regardless of how many people bet on him, pays $4.

Now ask yourself two questions:

- Do you want to play?
- How would you handicap and bet differently from the way you do now?

Most horseplayers will realize after a moment of thought that the correct answer to the first question is yes. It might not be a great deal of fun, but you could sit around and wait for mismatches, races in which one horse is so clearly superior to the competition that anyone could fairly agree that he has a better than 50 percent chance of winning the race. You would never bet a horse you honestly believed had less than a 50 percent chance of winning.

If you could find 50 races in which you discovered a horse with a legitimate 70 percent chance of winning, you would invest $100 – 50 $2 bets – and get a $4 payoff on 35 of those 50 races for a return of $140. A $140 return on a $100 investment is a 40 percent profit, and you could quit your day job and spend the rest of your life refining your criteria for horses with a 70 percent chance of winning.

Racing unfortunately does not work this way. Horses that everyone perceives as having a 70 percent chance of winning pay substantially less than $4 because the odds are determined by the amount of money actually bet on each horse, and because track takeout and breakage further depress the payout.

It’s worth examining the mechanics of this situation. Let’s look at a $1,000 win pool on a hypothetical four-horse race in which every contestant attracts an amount of betting that accurately reflects his chance of winning:

Horse |
Winning chance |
$ Bet |

A | 50 percent | $500 |

B | 30 percent | $300 |

C | 15 percent | $150 |

D | 5 percent | $ 50 |

Now, what will these horses actually pay to win? Based on the percentages, most horseplayers would guess about 1-1 ($4), 5-2 ($7), 6-1 ($14), and 20-1 ($42). In fact, the payouts are significantly lower.

Let’s say this race is being run in Kentucky, with a 16 percent takeout and breakage that rounds payoffs down to the nearest 20-cent increment. That leaves only $840 of the original $1,000 pool to split up among the winning ticket-holders. (The other $160 goes to pay the race purses, maintain the track, and fatten the coffers of the Bluegrass State.) So Horse A does not pay $4, but $3.36, which is rounded down to $3.20. Horse B does not pay $7, but $5.60. Horse C returns $11.20 instead of $14, and the longshot returns $33.60 instead of $42.

In each of these cases, the actual return is lower than what is required to break even, much less show a profit, over time. If you bet horses who win 50 percent of the time and pay $3.20, you will lose 20 percent of your investment.

The point of this exercise is to illustrate that even a horse with a very high likelihood of winning can be either a very good or a very bad bet, and the difference between the two is determined by only one thing: the odds. A horseplayer cannot remind himself of this simple truth too often, and it can be reduced to the following equation:

*Value = Probability x Price*

This equation applies to every type of horse and bet you will ever make. A horse with a 50 percent probability of victory is a good bet at better than even money (also known as an overlay) and a bad bet at less (a.k.a. an underlay). A 10-1 shot to whom you take a fancy is a wonderful overlay if he has a 15 percent chance of victory and a horrendous underlay if his true chance is only 5 percent. There are winning $50 exacta payoffs that are generous gifts and $50 exacta payouts where you made a terrible bet.

Now ask yourself honestly: Do you really think this way when you’re handicapping? Or do you find horses you “like” and hope for the best on price? Most honest players will admit they follow the latter path.

This is the way we all have been conditioned to think: Find the winner, then bet. Know your horses and the money will take care of itself. Stare at the past performances long enough and the winner will jump off the page.

The problem is that we’re asking the wrong question. The issue is not which horse in the race is the most likely winner, but which horse or horses are offering odds that exceed their actual chances of victory.

This may sound elementary, and many players may think they are following this principle, but few actually do. Under this mindset, everything but the odds fades from view. There is no such thing as “liking” a horse to win a race, only an attractive discrepancy between his chances and his price. It is not enough to lose enthusiasm when the horse you liked is odds-on or to get excited if his price drifts up. You must have a clear sense of what price every horse should be, and be prepared to discard your plans and seize new opportunities depending solely on the tote board.

If you begin espousing this approach, you are sure to suffer abuse from your fellow horseplayers. When one of them asks you who you like in a race and you say, “I think the 4 is a bigger price than he should be,” the likely response is, “So what? Who do you like?” Your cronies are apt to tell you that you should be betting on horses, not on prices, and after an inevitable stretch of watching some of their underlays win, you will begin to doubt yourself.

Sticking to your guns is easier said than done, but it is the only way to win in the long run. The horseplayer who wants to show a profit must adopt a cold-blooded and unsentimental approach to the game that is at variance with both the “sporting” impulse to be loyal to your favorite horses and the egotistical impulse to stick with your initial selection at any price. This approach requires the confidence and Zen-like temperament to endure watching victories at unacceptably low prices by such horses.

Two prominent races run during the spring of 2001 illustrate the principle of seeking overlays and being flexible in your approach.

My handicapping of the 2001 Kentucky Derby led me to the opinion that the race was most likely to be won by one of the three quality closers in the field of 17 – Point Given, Dollar Bill, or Monarchos. I allotted only a combined 45 percent chance to the other 14 horses in the race and split up the 55 percent likelihood of victory by my three choices at 25 percent for Point Given and 15 percent each for Dollar Bill and Monarchos.

I now faced two totally unrelated decisions: Whom to “pick” in *Daily Racing Form* as my selections for the race, and then which horse to back on Derby Day.

If the Derby were being run at Utopia Downs and each of the 17 entrants were paying off at odds of 16-1, I would simply have picked the likeliest winner, which to my mind was Point Given. However, at probable odds of 2-1, I would be recommending a fundamentally bad bet – tripling your money on a horse with a 25 percent chance of victory only gets you to 75 percent, or a 25 percent loss. So I knew I would have to pick one of my other two, both of whom figured to be at least the 5-1 needed to make them square bets. With Monarchos listed at 6-1 and Dollar Bill at 10-1 on the early lines, I selected the superior value and picked the race Dollar Bill-Monarchos-Point Given.

By post time two days later, however, I invoked the handicapper’s prerogative of changing his mind when it comes time to wager. The following table shows the probability I had allotted to each starter, the odds necessary to receive fair value, and the actual odds at post time:

Horse |
Probability |
Req. Odds |
Actual Odds |

Point Given | 25 percent | 3-1 | 9-5 |

Dollar Bill | 15 percent | 6-1 | 6-1 |

Monarchos | 15 percent | 6-1 | 10-1 |

Millennium Wind | 8 percent | 12-1 | 9-1 |

Congaree | 8 percent | 12-1 | 7-1 |

Balto Star | 4 percent | 24-1 | 8-1 |

Fifty Stars | 4 percent | 24-1 | 40-1 |

Jamaican Rum | 4 percent | 24-1 | 20-1 |

A P Valentine | 4 percent | 24-1 | 19-1 |

Thunder Blitz | 4 percent | 24-1 | 25-1 |

Express Tour | 4 percent | 24-1 | 18-1 |

Each of 6 others | <1 percent | >100-1 | From 35-1 to 102-1 |

Point Given was still the likeliest winner in my mind, but 9-5 was still an unacceptable return for a horse with a 25 percent chance of victory. To nearly everyone’s surprise, Dollar Bill had been bet down to 6-1 and Monarchos had floated to 10-1. Dollar Bill now offered no real value relative to my assessment of his actual chances, but Monarchos was offering well above the return I thought was fair, as was Fifty Stars. My lack of regard or appreciation for Invisible Ink, the eventual runner-up, cost me all my multi-horse bets on the race, but win bets on Monarchos and Fifty Stars saved the day.

Thirteen days later at Pimlico, an uninspiring five-filly Black-Eyed Susan Stakes caught my interest because there were only two legitimate contenders and I thought one of them might be severely overbet. Two Item Limit had the superior speed figures and experience to be a worthy odds-on favorite, but I thought there was a scenario under which Tap Dance, the second choice, might end up very loose on the lead. While Two Item Limit was the better filly, she might lag too far back off slow fractions and fall short at the end.

I made Two Item Limit 60 percent to win the race, giving a 35 percent chance to Tap Dance and the remaining 5 percent to their three overmatched opponents. Odds of 2-1 or better on Tap Dance would make her playable.

Unfortunately, everyone else seemed to have had the same idea about Tap Dance waltzing to the lead. With five minutes to post, both fillies were even money, and I felt neither remorse nor disloyalty as I went to the window to make the only logical bet: Two Item Limit to win, which she did at $4.40. Betting 6-5 shots to win is not my usual style, but I saw no other way to play the race and was convinced I was receiving outstanding value. When I first began playing the races, I probably would have bet on both Dollar Bill and Tap Dance instead of Monarchos and Two Item Limit, out of loyalty to my initial selections and the sense that you “should” bet on the horses you initially like.

The success of these two plays, though, was ultimately based upon the probability of victory I had assigned to each winner. I cannot argue in good conscience that Two Item Limit had precisely a 60 percent chance of victory as opposed to 57 or 63 percent, and I doubt that such calibration is in fact achievable. It is, however, possible through experience to get close enough that if you demand sufficient value to cover the margin of error, you should outperform the competition – your fellow horseplayers.

**The Competition**

One of the great romantic myths of racing is that the players are a merry band of brothers united in their quest to smoke out the winner of each race. This is the case at the blackjack table, where everyone is playing against the house and all the players win when the dealer busts out. At the racetrack, however, every bettor is playing only against the other bettors. The house takes its cut off the top and has no financial interest in how the remaining money is carved up.

If every horseplayer but you were a certifiable idiot, betting at random on names and colors, you would win every day. Conversely, if the only people betting into the pool were the small number of professionals who make a living this way, your chances for long-term victory would be slim.

Either way, what would make you a loser or a winner would not be a change in the number of winners you bet, but solely the odds that these horses would return. To put this another way: Your opportunity for profit at the racetrack consists entirely of mistakes that your competition makes in assessing each horse’s probability of winning. In that first happy scenario, where the escaped lunatics are betting at random, you would win because you would bet on high-probability horses at fat odds. Every horse in a seven-horse field would be 5-1 (after takeout) and you would just bet on those with a better than 20 percent chance of winning. Playing purely against the pros, every horse would be bet in accordance with his true chances, and takeout would reduce each return below an acceptable price. You would be taking the worst of it every time.

Reality combines these two situations, since both nitwits and sharpies populate the betting pools every day. Has the balance shifted? There has been much carping in recent years that the game has become much tougher, or even “too tough.” The game almost surely was easier 50 years ago when takeout was lower and track attendance was much higher, due primarily to racing’s near-monopoly on legalized gambling. Unfortunately, the hordes of fabled two-dollar bettors of that era have mostly been seduced away by the jackpots of state lotteries and slot machines, and the industry has raised takeout to compensate for lost business.

Does that mean today’s player faces nothing but higher vigorish and the remaining sharpies? Not at all. I firmly believe that, in general, the nitwits still outnumber the sharpies. More important, most sharpies aren’t as sharp as they think, and even the winning sharpies make plenty of egregious mistakes on individual races. As long as the volume of ill-informed money exceeds the takeout, there can be a positive expectation for the true sharpshooter who waits for the competition to make mistakes.

How do we identify, and thus attack, this ill-informed money? There is no such thing as a bet that cannot possibly win, since every horse has a theoretical, if infinitesimal, chance of winning any race, if only because every single opponent theoretically could fall down. What defines sucker money is not the horse selected, but the acceptance of odds on that horse that are substantially out of line with its chances of winning.

For an example, let’s return to the 2001 Kentucky Derby. Balto Star to win is not necessarily a bad proposition. However, Balto Star at 8-1 is a horrendous proposition. A one-dimensional front-runner does win the Derby about once every eight or 10 years, but never when there is a glut of other high-quality speed in the race. So perhaps Balto Star is a legitimate 8-1 shot in a vacuum. For Balto Star to have won this Derby, however, Songandaprayer and Keats both would have had to take back off the lead. Even if you thought there was a 50 percent chance that each of them would be taken back, that makes it only 25 percent that both would, so you have to apply that against Balto Star’s 8-1 in a vacuum and now he’s more like 32-1. My assigning him a 4 percent chance of victory may have been overly generous.

At 8-1, however, Balto Star was eating up over 10 percent of the win pool, better than half the takeout. Eliminating him alone still left you better than 95 percent likely to win while cutting the takeout to 6 percent. Tossing others with even more microscopic scenarios for victory – Songandaprayer, Keats, Talk Is Money – would have allowed you to have a positive expectation on the race.

There are races run every day in which a similar strategy can be employed. Knowing that a single 5-1 shot in fact has a true chance closer to 50-1 wipes out the entire takeout on a race. An intense dislike of a 3-1 shot can be an extremely powerful tool and the entire motivation for playing a particular race.

There are also plenty of races in which your competition will make no actionable mistakes. Everyone seems to be at about the right price, and there is no compelling reason to jump into the pool. It is worth remembering that the whole is better than the sum of its parts: The betting public’s post-time favorite wins more often than any individual public handicapper, and over time first choices win more than second choices, which win more than third choices, and so on down the line. There is no shame in passing a race because you just don’t see any value in it. Nor should you force yourself to play a race in which you have no confidence in your own odds line. That doesn’t mean you have to sit on your hands – $1 boxes for action were made to fill the spaces between races where you have a legitimate edge or opinion.

Players who have never undertaken a value-based approach to handicapping will almost surely find it useful to begin making their own true-odds lines. It is cumbersome at first, but over time it becomes second nature, to the point where it can be done in your head and becomes the way you instinctively approach every race. However you choose to handicap horses is work that you do before the betting opens. As soon as those first prices go up on the board, you are looking for discrepancies between your odds and those set by your opponents.

Of course, it’s tempting to anticipate those discrepancies by comparing your personal line with the early ones published in *Daily Racing Form*, which are made by either a *DRF* handicapper or the track’s morning-linemaker. No mortal can resist a peek, but these early lines are widely misunderstood and misused – yet another opportunity for you to take an advantage.

A *Daily Racing Form* line is made 48 hours before a race. (A Saturday *DRF* is printed Thursday night so that you can buy it Friday and do your homework the night before the races.) It is a sincere effort to predict how the race will be bet, but because of the required printing window, it cannot incorporate early or late scratches, jockey changes, and prevailing track or weather conditions.

A track’s morning line has even more pitfalls. It is typically prepared by a track employee in the racing office or simulcasting department whose primary skill in life may not be oddsmaking and whose agenda is different from yours. Tracks want to advertise their races as being competitive rather than mismatches, which is why horses we all know are going to be 3-5 are routinely listed at 6-5 on the morning line. Similarly, nearly every race card features several horses who are legitimately 99-1, but few morning-line prices exceed 30-1. Racing offices do not want to offend the horsemen filling their cards by saying their horses have virtually no chance.

Given all that, it is astounding how many horseplayers believe there is some magical significance to the morning line and to any discrepancies between it and the actual betting. If a horse is 4-1 on the morning line and 2-1 in the actual betting, plenty of your competitors will decide that this horse is a “good thing,” the focus of an international betting coup orchestrated by the mysterious “they” who “know.” If the same horse is instead 8-1 as post time approaches, the same conspiracy theorists will pronounce the horse “dead on the board.” In fact, in either case, all that has happened is that the linemaker, an overworked and fallible human being like the rest of us, made a bad guess about how much the public would fancy a particular horse.

It is this sort of flawed thinking among your parimutuel opponents that creates incorrect prices on the board and thus opportunities for you. If some horses in a race are being overbet, that means that the prices are too high on the other horses and this is where you should be looking.

Is your competition offering you enough value to make this a profitable undertaking? Without discussing or judging anyone’s method of handicapping, the answer is surely yes. There are enough people betting virtually at random, not even consulting complete past performances, to cover the takeout. Even among your well-informed opponents, the vast majority are betting with little consideration for the mathematics of value, which means that at least half the time they are betting on underlays and thus jacking up the prices on the overlays.

It’s not an easy game, but you’re not playing against “the game.” You’re betting against the other bettors. It doesn’t matter if they pick as many winners as you do, or even more, if you are betting only when the price is right.

**Using Multiple Bets to Improve Your Prices**

Despite facing higher takeout and fewer casual opponents, the 21st-century horseplayer has a tremendous opportunity that his counterpart of 50 years ago did not enjoy: The ability to bet a race in a dizzying array of options beyond win, place, and show. Nearly every race in America now offers both multi-horse bets – the exacta, trifecta, and superfecta – and also is part of at least one multi-race bet – a daily double, pick three, four, or six.

For the purposes of this discussion of value betting, we will not attempt to examine the mechanics and optimal strategies for each of these wagers, an exercise that would require an entire volume. Instead, the question is how multiple wagers can give the value-oriented horseplayer an additional opportunity for profit.

Many old-timers and other curmudgeons dismiss all multiple bets as some newfangled work of the devil and begin and end their argument by pointing to the higher takeout on these wagers. A typical takeout structure is New York’s, where one-horse (win, place, and show) bets are subject to a 15 percent takeout, two-horse bets (daily doubles and exactas) face a 20 percent bite, and all wagers involving three or more horses or races are hit with a 25 percent takeout. No matter how you slice it, say the defenders of straight betting, over time you will do better playing against a 15 percent takeout than a 20 or 25 percent takeout. Isn’t that a fundamental of value betting? Isn’t choosing to play into a 25 instead of a 15 percent takeout the equivalent of getting $7.50 on a horse who should pay $8.50?

There are two good answers to this cranky argument. The first and most important is that a higher takeout is meaningless if the greater opportunity for profit exceeds the difference in the toll. Would you rather make a pre-takeout 35 percent profit and give back 25 percent for a 10 percent profit, or make 16 percent and give back 15?

The second answer is that multi-race bets allow a player to spread the effect of takeout over several races, so that he is actually facing a smaller bite per race than if he played them separately. Consider the difference between making win bets on three consecutive races and playing a pick three. In the first case, you are taxed 15 percent three consecutive times so your original dollar is sliced first to 85 cents, then to 72 cents, and finally to 61 cents. Playing those same three races via the pick three devalues your dollar just once, to 75 cents.

Wrapping your mind around this idea leads to an appreciation of the value opportunity in multiple betting. If you are playing a second or third race or horse at a reduced takeout, you are getting better odds on that additional race or horse than you normally could. This is why, over time, multi-race payoffs are higher than an equivalent parlay of the individual winners would be.

Let’s look at the simplest version of how this works, a daily double. Suppose that in each of the two races, there is a horse paying exactly 2-1 who you think is actually 50 percent likely to win. If you parlay the two horses with $100 win bets, your $100 turns into $300 after the first race, and $900 after the second horse wins.

Not bad – an $800 return, and 8-1 on a proposition you believed was 3-1 (50 percent times 50 percent).

But what will the daily double of these two horses pay? At a 15 percent takeout, each 2-1 horse has 28.3 percent of the win pool on him, meaning he will pay $6 to win. Assuming that these horses are bet the same way in the double pool, that means 28.3 percent of all tickets have the first winner, but out of those tickets, only 28.3 percent combine him with the second winner. Multiply those two probabilities, and it means that only 8 percent of the daily-double pool is bet on the winning combination.

At a 20 percent takeout, a double that accounts for 8 percent of the pool returns $20, and your $100 double gets you $1,000 instead of the $900 you would get for parlaying the same two horses – despite betting into a pool with a higher takeout. In effect, you are getting a $20 mutuel instead of an $18 mutuel.

This may not seem like a thrilling difference, but a 10 percent increase in payoff is enough to make many a chronic loser into a chronic winner. Moreover, the difference increases in pick threes and fours as you add more races, and can often be far more than 10 percent. Add a third 2-1 winner to the example above and the $18 parlay becomes a $54 three-horse parlay. The $20 double, however, even with a 25 percent takeout, becomes a $66 pick three.

What is happening here is the powerful, hidden effect of reducing takeout and thus getting “free” odds on additional horses or races. Now take this to the next logical step: If you are getting inflated odds on one part of the bet, you can now tolerate getting only even odds, or even slightly unfavorable odds, on the other. This can make an otherwise unplayable race or races attractive.

An obvious example of this is the race with a heavy favorite you can neither bet nor beat. Let’s say you think a 9-10 favorite in a four-horse field has a 50 percent chance of winning. He is actually being slightly underbet by the public, because if 50 percent of the pool were on him, he would pay $3.40, not $3.80. So there is a “mistake” being made by the public – a horse with a 50 percent chance of winning is attracting only 44 percent of the pool – but it is a mistake you cannot capitalize upon because the takeout eats up your edge.

However, by using this horse in the first leg of a multi-race bet or the top half of an exacta, you can realize the value of the gap. Only 44 percent of the exacta tickets will have this horse on top, and only 44 percent of the doubles or pick threes will have this horse winning the first leg.

Let’s use the same race to see how a multiple pool can present a value opportunity that otherwise would not exist. Suppose that of our favorite’s three opponents, you think two of them are inseparable but the third is badly overmatched. The public, however, gives the horse you despise nearly the same chance as the other two.

Here is how the win pool and odds on the race might look:

Horse |
Probability |
Req. Odds |
Actual Odds |

A | 50 percent | 1-1 | 4-5 (44% of pool) |

B | 22 percent | 7-2 | 3-1 (19% of pool) |

C | 22 percent | 7-2 | 3-1 (19% of pool) |

D | 6 percent | 16-1 | 7-2 (18% of pool) |

Every single win bet in the race is unplayable because all the odds are below your acceptable price for value. Thirty years ago, you would have been obliged to pass the race or make a bad bet. But in the world of the multiple, what about making two exactas, A-B and A-C? If your assessment of their chances is correct, what are your chances of collecting and what will your return be?

To understand the mathematics of exacta odds, it is helpful to think of an exacta as if it were a daily double. The first race is the four-horse race that includes the favorite you are using on top. The second race is a three-horse race for second. Since you believe Horse A has a 50 percent chance of winning, you are 50 percent to “win the first race.” Since horses B and C account for 44 of the remaining 50 percent, together they are 88 percent to win the “second race” for second place. So if your probabilities are correct, you are now 44 percent (50 percent x 88 percent) to have an A-B or A-C exacta come in.

What should these exactas pay? Here is where you take advantage of the otherwise unexploitable differences between your assessment of probability and the actual betting. Horse A is on top of only 44 percent of the exactas, not 50 percent. Eliminate him from the race for second and increase the other horses’ percentages of the pool to add up to 100. If they were 19, 19, and 18 percent of the original remaining 56 percent, those numbers now increase to 34, 34 and 32 percent. Here’s your second edge: While you think B and C have a combined 88 percent chance of running second to A, the pool has them at only 68 percent.

So the A-B and A-C exactas account for only 44 percent x 34 percent of the pool, roughly 15 percent. At a 20 percent takeout, the A-B and A-C exacta would each return $10.60.

If you bet $4 to win on Horse A and he wins 50 percent of the time, you collect $3.80 for every $4 you bet. If you bet the A-B and A-C exactas, you win only 44 percent of the time but when you do, you collect $10.60.

This translates, over 100 plays, to a $20 loss on the win bet and a $66 profit on the exacta, a 5 percent loss as opposed to a 16.5 percent profit. What made the difference? Only your unspectacular assessment that the longest shot in the field had a 12 percent rather than 32 percent chance of finishing second.

An important side note: This example made an assumption, for simplicity’s sake, that horseplayers should not routinely make about exactas. We took it as a given here that horses B, C, and D had the same comparative chance to finish second to Horse A as they did to win the race. There is a fruitful line of thought that this is often not the case, for reasons of pace or consistency. An erratic front-runner who can win when he breaks well and sets a moderate pace may have a 20 percent chance of winning but a much smaller chance of ever finishing second, since he stops badly when challenged early. Conversely, a chronic early lagger may clunk up for second far more often than he ever wins.

These kinds of horses present additional opportunities because they are rarely bet proportionately to these different likelihoods in the exacta and trifecta pools. So many players insist on wasting their money with lazy betting techniques such as wheels and boxes that they overuse these horses in the wrong positions. A horse who is only 5 percent to win a race but perhaps 15 percent to run second is a terrible win bet at 10-1 but a great horse to use underneath in exactas if he is being bet there at the same rate.

Several of the examples in this chapter were chosen or constructed for their relative simplicity in illustrating a concept rather than for their real-world popularity. There are not many recreational horseplayers who find it sufficiently challenging or rewarding to turn $4 into $10.60 44 percent of the time. (Perhaps more of them should, if only to finance their sexier parimutuel undertakings.)

The same principles of value betting, however, apply regardless of the complexity or size of mutuels you are chasing. To summarize:

- Recognize the difference between picking horses and making wagers in which you have an edge. The only path to consistent profit is to exploit the discrepancy between the true likelihood of an outcome and the odds being offered.
- You are playing against only the other bettors at the track, not against the game or the house. Although they do a pretty good job on the whole, your opponents make more than enough mistakes for you to win.
- Multiple bets can make apparently valueless races highly playable, and can multiply the existing value in a race because of the opportunity to capitalize on more than one discrepancy on the board.

If all of this seems too calculating and joyless, by all means feel free to forget about it and enjoy yourself at the races betting horses you fancy regardless of their price. You’ll have plenty of company, and the rest of us could use your money.

*Article by Vintage Value Investing*