Entrepreneurs Math: (.9)^10 = 1

I had a wonderful time interviewing Larry Gold last night at Entrepreneurs Unplugged. Larry is a special guy and someone I learn from every time I’m with him. Among the many great stories he told, including a doozy about the time he was a sophomore at Yale, he had a powerful one about how entrepreneurs assess potential outcomes. It resulted in a fun version of entrepreneurial math.

Envision a scenario where you there are 10 separate things you need to do to have a successful outcome. Each one has a 90% probability of success. What’s the probability that you will achieve a successful outcome?

I struggled with 6.041: Probabilistic Systems Analysis and Applied Probability (the probability course I took as an undergraduate) – it was one of those courses where I felt like I was a week behind for the entire semester. I did better in 15.075: Statistical Thinking and Data Analysis – maybe I was a little older, it was a little easier than 6.041, or I was more interested because I liked the professor better. If you are having trouble with a quick answer, both courses are available to you on MIT OpenCourseWare.

Back to the question. If you guessed around 35% you are correct. It’s actually 34.87%, which is (.9)^10. Now, by using the word separate, I’m implying 10 independent events, but this is the nuanced joy of theory versus practice.

Larry pointed out with glee that regardless, entrepreneurs believe when they start down the path of doing these 10 things there will be a successful outcome. Hence entrepreneurs math is (.9)^10 = 1.

Whether you agree with the math or not, it’s a great anecdote. So many things that we try as entrepreneurs and investors fail. We never make an investment thinking “this isn’t going to work”; we always invest thinking “this will work.” I don’t know any entrepreneurs who started their business thinking “this will fail” or even “this only has a 35% chance of working out.”

This shit is hard. And it’s low probability. Even if you have an ultimately successful outcome, many of the things you are going to try along the way are going to fail. But to do them, you’ve got to believe they are going to work. You’ve got to enter into the illusion that (.9)^10 = 1.

  • André Thénot

    With enough persistence, that square peg WILL fit in the round hole… 🙂

    • Bang! Bang bang bang bang bang. The sound of a square peg being mashed against a round hole.

      • André Thénot

        Ha! Under pounding, the peg gets a lot rounder and the hole gets a little more square.

      • Cha-ching Scratch Bang – The sound of an entrepreneur sourcing sandpaper to buff the edges of the square peg to fit in the round hole 😉

  • A reader told me there’s a MOOC version of 6.041 on @edxOnline at https://www.edx.org/course/mitx/mitx-6-041x-introduction-probability-1296

  • Prime

    If the entrepreneur simply makes a small adjustment, their chances are much higher. The entrepreneur who fails can try again with another .9 probability option, and again a 3rd time if the 2nd time fails. 0.9 becomes 0.999 and 0.999^10 is 99% Not a square peg in a round hole, simply working hard/smart to find the right peg. Of course, the .9 only applies if you were headed in the right direction in the first place…

  • Simplifying the Math a bit

    Focus on 3 things

    1) Get 1 RIGHT
    2) Get 1 KIND-OF RIGHT
    3) 1 ALMOST-RIGHT on the last one

    If you have a success of 1 to 2 out of 3, you are:

    1) Eligible for election into the Baseball Hall of fame with a .667 batting average success OR
    2) The value in the 1 to 2 successes enables you to have leverage to scale.
    So, the Math is (2/3 * $$$) = VALUE

    JEMSS = 1 ALMOST-RIGHT – Waiting on SEC Rule committee to get final comments (http://jemss.co)
    Robotics Incubator in Highlands Ranch (See picture of the winning kids that will seed the Incubator modeled after TechStars) = 1 KIND-OF RIGHT (http://RoboKid.co)
    Agile Salesforce = 1 RIGHT (http://AgileSalesforce.com)

    Swizzle-stick it together – Add a pinch of sugar to sweeten the deal


    Why that darn teddy-bear picture still appears from Facebook as my Avatar picture? Who knows?

  • Love this equation. It’s so true how us entrepreneurs and investors throw out the actual statistical facts and push forth anyway. I think there needs to be a “gut” factor added to the equation.

  • Maybe the overriding theory is: Entrepreneur vs Businessman.
    A bussinessman has the luxury of knowing someone else has done it before and he just needs to do the math to see if he can get the resources to do the same thing. But an entrepreneur is pretty sure others haven’t done what he is doing yet. So his math is simpler. The code is thus: If !works then failed = true;

  • God, this brings back memories. Yep, 15.075 was more “grok-able” than 6.041 for me as well…

    “So you’re telling me there’s a chance???”…

  • ((.9)^10) x (patience + persistence) x luck = 36% with a bullet

  • Sounds like a batter in baseball. Every time they get up thinking that they’re going to hit the ball out of the park, and yet a .350 career average would put you in the hall of fame (and a shoo-in if you also averaged more than 1 HR very 4 games). I also think that a ~35% rate of total success across all the “things you need to do” in business is good enough to have a great career and build a great business. Sometimes it’s okay to get a single and move he runners, and given that you have to do those things well every day, if you strike out there’s always “tomorrow’s game”. But strike out too much and you’re career is over…

  • It is harder to raise e(individual_success) beyond 90%. It is easier to raise e(overall success) if we reduce the # of independent items that need to occur. For instance cutting it from 10 to 5, raises e() to almost 60%. I think this is the mathematics that powers the lean startup movement.

  • Silverborn

    Entrepreneur’s math reminds me of Tolkien’s essay “On-Fairy Stories” where he talks about the “suspension of disbelief”. As an Entrepreneur I am a sub-creator and to succeed I not only have to suspend my own disbelief but I have to get my co-founders and investors and early employees and initial customers to suspend theirs as well. Of course it’s easier if you have a “reality distortion field” like Steve Jobs handy. 🙂 BTW, I was an Art Major and took Symbolic Logic to satisfy my math requirement. Not as easy as I thought it would be but I was good at it and so found it enjoyable.

    “Children are capable, of course, of literary belief, when the story-maker’s art is good enough to produce it. That state of mind has been called “willing suspension of disbelief.” But this does not seem to me a good description of what happens. What really happens is that the story-maker proves a successful “sub-creator.” He makes a Secondary World which your mind can enter. Inside it, what he relates is “true”: it accords with the laws of that world. You therefore believe it, while you are, as it were, inside. The moment disbelief arises, the spell is broken; the magic, or rather art, has failed. You are then out in the Primary World again, looking at the little abortive Secondary World from outside. If you are obliged, by kindliness or circumstance, to stay, then disbelief must be suspended (or stifled), otherwise listening and looking would become intolerable. But this suspension of disbelief is a substitute for the genuine thing, a subterfuge we use when condescending to games or make-believe, or when trying … to find what virtue we can in the work of an art that has for us failed.”

  • Its been a while, but I think that 35% refers to the chance of 10 successes. You still have 90% chance, per-event, of a success. Like a coin toss, you have 50% chance of winning one. To win two in a row, your odds are 25% etc.

    I get your point, 10 shots at 90% still doesn’t *guarantee* a win. But, if you do the math, the chance of NOT having a single success is really, really low – (0.1^10)*100 = 0.00000001%

    So I guess it depends on how much you win per event……

    • StevenHB

      But you need all 10. One failure out of the ten results in overall failure. And the chance of having on of those failures is about 65%.

      I just read Thinking Fast and Slow (http://www.amazon.com/Thinking-Fast-Slow-Daniel-Kahneman/dp/0374533555). Kahneman makes a number of points about entrepreneurs and VCs. Worth reading.

      • You are the nth person that has suggested Thinking Fast and Slow. It is now on the Kindle to be read.

  • Philip Smith

    I have had discussions very similar to this in the past . . . usually having to do with financings and milestones. The entrepreneur rarely wanted to raise the amount of money that I thought was appropriate. Hence the discussion on how long the current money would last.

    I usually made the following points:

    Needed belief/confidence => (.9)^10 = 1.

    Basic Math => (.9)^10 = 35%

    Reality => (.9)^10 < 25%

    Once I walked them through the basic math (with people usually a lot smarter then me), I was usually asked why my number for reality was so much lower then the basic statistical probability. I never realized at the time I was channeling Brad Feld with my answer:

    "This shit is hard. And it’s low probability."

    I suggested the initial estimates were probably low. I usually followed this question up by asking if they would rather own 20% of a company with extra cash or 30% of a company desperate to raise cash.

  • Of course this applies to engineering in a big way when there are dozens or hundreds of different big buckets that each have to click into place for the product to fly. Moreover buckets are often “probabilities in progress” in stereotypical
    relationships between [over-reactive] Managers and [under-reactive] Makers.

  • Doug Alexander

    I think the chance of at least one successful outcome given all 10 events are independent = 1 – (.1)^10 which is effectively 1. Therefore an entrepreneur would be making a pretty good bet. The chance of all 10 being successful would be (.9)^10 or roughly 34.9%.

  • StevenHB

    If I remember correctly, Brad, you missed a lot of 6.041 lectures. I also remember not working on problem sets together. I don’t recall why that was.

    • I missed a lot of lectures in ALL my classes. I don’t learn by listening, I learn by reading. I knew that even at MIT. So I read everything, but only went to about 50% of the lectures. That’s the only way I could have a semester with 103 units… Clearly that strategy didn’t work for me on 6.041.

      Regarding on working on problem sets together, I don’t think I did that with anyone for any classes. I never liked that – it wasn’t an anti-social thing, I just didn’t really learn if I didn’t work it out on my own.