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Latticework of Mental Models: Pari-mutuel System

You don’t win by predicting the future; you win by getting the odds right. You can be right about the future and still not make any money. ~ Will Bonner

The way to win in stock market, according to Charlie Munger, is to work, work, work, work and hope to have a few insights.

Now, the question is – how many insights do you need in your investing lifetime?

Not many, as Munger says…

…you don’t need many in a lifetime. If you look at Berkshire Hathaway and all of its accumulated billions, the top ten insights account for most of it. And that’s with a very brilliant man—Warren’s a lot more able than I am and very disciplined—devoting his lifetime to it. I don’t mean to say that he’s only had ten insights. I’m just saying, that most of the money came from ten insights.

So you can get very remarkable investment results if you think more like a winning pari-mutuel player. Just think of it as a heavy odds against game full of craziness with an occasional mispriced something or other. And you’re probably not going to be smart enough to find thousands in a lifetime. And when you get a few, you really load up. It’s just that simple.

Munger uses horse racing’s Pari-mutuel betting system as one of his mental models to make sense of stock market investing. He is asking us to think like a Pari-mutuel player and look for the mispriced bets.

So what’s a Pari-mutuel system and how does one find a mispriced bet in such a system?

Pari-mutuel System

Pari-mutuel is a system of betting in which the winners divide the total amount bet, after deducting management expenses, in proportion to the sums they have wagered individually. Unlike many forms of casino gambling, in Pari-mutuel betting the gambler bets against other gamblers, not the house. The simplest and most common example of a Pari-mutuel system is horse race betting.

Let’s assume a hypothetical horse race with 5 horses where people can bet their money on their choice of horse. Following the start of the event, no more wagers are accepted. So here’s the distribution of money bet on each horse just before the race starts.

Horse 1: Rs. 20,000
Horse 2: Rs. 3,000
Horse 3: Rs. 2,000
Horse 4: Rs. 500
Horse 5: Rs. 4,500

Thus, the total pool of money on the event is Rs. 30,000. Let’s say that horse-1 wins the race. The payout is now calculated. First the commission or the take for the house (company organising the race) is deducted from the pool. For example, with a commission rate of 15% the house keeps 30,000 x 15% = Rs. 4,500. This leaves a remaining amount of Rs. 25,500. This remaining amount in the pool is now distributed to those who bet their money on the winning horse i.e. horse-1. So people who bet their money on winning horse get 25,500 / 20,000 = 1.2 for each rupee wagered. Their payout ratio were 1.2. So the payout ratio for each horse is as follows –

Horse 1: 25,500 / 20,000 = 1.2
Horse 2: 25,500 / 3,000 = 8.5
Horse 3: 25,500 / 2,000 = 12.7
Horse 4: 25,500 / 500 = 51
Horse 5: 25,500 / 4,500 = 5.6

This is a simplified example. In real-life horse racing the pool size often extends into millions of dollars with many different types of outcomes (winning horses) and complex commission calculations.

From this example you can see that if one puts money on a horse which is a favorite of most people, the payout isn’t much. However, the payoff ratio for horse-4 is 51-to-1. Now the payoff ratio isn’t necessarily same as the odds of winning. However, in a world where everyone has the same information the payoff ratio acts as proxy for the odds.


When the odds aren’t commensurate with the payoff ratios, the opportunity for making disproportionate returns arises for the handicappers. The science of predicting the outcome of a race is called handicapping. It is the practice of predicting and quantifying the results of a horse race. Handicappers attempt to determine the odds and see if the payoffs are skewed compared to those odds. Put simply, it’s a way to find the mispriced bets.

Steven Crist, CEO and editor of the Daily Racing Form argues that even a horse with a very high likelihood of winning can be either a very good or a very bad bet, and that the difference between the two is determined by only one thing: the odds. So a horse with a 50 percent probability of winning can be either a good or bad bet based on the payoff. In other words, it is not the frequency of winning that matters, but the frequency times the magnitude of the payoff. That’s the idea behind expected value analysis for the events ruled by probabilistic outcomes including gambling, horse race handicapping and investing.

In the example used above, if a handicapper, based on his knowledge and analysis (about horses, tracks and past races) figures out that the odds of winning for the horse-4 is 10 percent then his expected value for the bet would be 0.1×51 – 0.9×1 = 4.2. Based on this he can take a call if he wants to make a bet or not.

The upfront commission of 15-17 percent makes Pari-mutuel system hard to beat for most people. Charlie Munger writes –

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 damn 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 seventeen percent off the top. So not only do you have to outwit all the other bettors, but you’ve got to outwit them by such a big margin that on average, you can afford to take seventeen percent 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 using only 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 seventeen percent that he would lose if he got the average result to maybe ten percent. However, there are actually a few people who can beat the game after paying the full seventeen percent.

At 16 years of age Warren Buffett had mastered the art of handicapping. He was introduced to the world of Pari-mutuel betting very early in his life. He learned that the key was having more information than the other guy—then analysing it right and using it rationally. Buffett implemented his handicapping strategies in Ak-Sar-Ben race track. He recalls –

…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 my mind.

Buffett was back testing his handicapping strategies in 1940s when there were no computers. No wonder his obsessions with handicapping lead him to read every book on the subject available at the Library of Congress.

One of the greatest insight that Buffett and Munger had early in their investing career was about market inefficiencies. And the insight came from their knowledge about Pari-mutuel system. Charlie Munger, in his lecture at UCSB in 2003, said –

It was always clear to me that the stock market couldn’t be perfectly efficient, because, as a teenager, I’d been to the racetrack in Omaha where they had the pari-mutuel system. And it was quite obvious to me that if the ‘house take’, the croupier’s take, was seventeen percent, some people consistently lost a lot less than seventeen percent of all their bets, and other people consistently lost more than seventeen percent of all their bets. So the pari-mutuel system in Omaha had no perfect efficiency. And so I didn’t accept the argument that the stock market was always perfectly efficient in creating rational prices.

Stock market has lower frictional costs than horse race betting. In the absence of high transactional costs, it’s easier to be profitable in stock market than horse races. Munger writes –

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…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.

Drawing analogy between investing and Pari-Mutuel system, Munger says –

To us, investing is the equivalent of going out and betting against the pari-mutuel system. We look for a horse with one chance in two of winning and which pays you three to one. You’re looking for a mispriced gamble. That’s what investing is. And you have to know enough to know whether the gamble is mispriced. That’s value investing.

Pari-mutuel system is wonderful mental model to think about the stock market. Like a horse race track, people go to stock market offering to buy/sell stocks and based on the price paid the odds of winning keep changing.

One of the most important learning from the Pari-mutuel system is: making infrequent bets. In his lecture, A Lesson on Elementary, Worldly Wisdom As It Relates To Investment Management & Business, Charlie Munger said –

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 seventeen percent – he made a substantial living.

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.


Understanding how a Pari-mutuel system works gives you important clues about stock market. We learnt that market, like a Pari-mutuel, are efficient but not always. However, it’s not easy and with all the frictional costs and house’s commission, on average people end up losing money in Pari-mutuel set up.

But you can make money by learning to handicap and betting infrequently. Buffett wrote this in his 1993 letter to shareholders…

Charlie and I decided long ago that in an investment lifetime it’s just too hard to make hundreds of smart decisions. That judgment became ever more compelling as Berkshire’s capital mushroomed and the universe of investments that could significantly affect our results shrank dramatically.

Therefore, we adopted a strategy that required our being smart – and not too smart at that – only a very few times. Indeed, we’ll now settle for one good idea a year.

To think in a multidisciplinary way you have to stop sweating the small ideas in your own discipline and reach out for big ideas in other disciplines. Stepping into different disciplines expands your mind’s ability to experience radically different thoughts, perceptions, and ideas.

Building a latticework of mental models will require you to embrace differences, ambiguity, conflict, and tension. Consider them signposts to better solutions and better problems.

That’s the only way to developing better lens on the bewildering phenomenon we call the world.

Take care and keep learning.

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About the Author

Anshul Khare worked for 12+ years as a Software Architect. He is an avid learner and enjoys reading about human behaviour and multidisciplinary thinking. You can connect with Anshul on Twitter.


  1. Abhishek says:

    Great post , Anshul !! Keep posting 🙂

  2. Hi Anshul, Nice Article ! now that’s the best explanation of pari – mutuel system I have read..

  3. Vijay Kumar says:

    Dear Anshul,

    Which mode (hard copy, kindle, tablet, etc..) you prefer for reading books?

    Please reply

    • Anshul Khare says:

      Hi Vijay,

      I prefer hard copy. But I don’t mind reading on kindle also since its portable and I can carry it anywhere.

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