# Roulette, Startups, and the paradox of the infinite bankroll

There’s a well-known way to win in Vegas, and famously some people have done it systematically. Maybe it works for startups too?

Suppose you’re betting on “red” in a game of Roulette.

There are 41 places a Roulette ball can land — numbers 1 through 40, plus a “double-zero” and sometimes a “zero.” (So it’s a CHAR(2) not an INT(2)). The numbers also alternate red and black — twenty of each plus that special double-zero which is considered neither color. (For the ensuing math we’ll assume a wheels with 00 and without a 0.)

When you gamble on “red,” say, you double your money if you guess right and lose your money if you guess wrong. If it weren’t for that pesky double-zero, this would be perfectly even odds, but there’s 20 ways to win and 21 ways to lose, so the house always gains in the long run.

Still, it’s close enough to even-odds (is that an oxymoron?) that an interesting algorithm presents itself — an algorithm that guarantees you’ll make money.

You start by betting \$1 on red. If you win, you take your winnings and leave with an extra \$1.

If you lose, next time you bet \$2. If you win, you earn \$2 and, even though you previously lost \$1, you’re still \$1 ahead, so you’ve made money.

If you lose, next time bet \$4. If you win, you earn \$4, you previously lost \$3, so you still made \$1.

And so on, doubling the amount of money wagered each time. If you play enough times you have to win at some point, in which case you’ll walk away \$1 richer. It might be a boring, inefficient way to earn \$1, but you always win. Multiply all these numbers by 1000 and it becomes interesting.

But this is even more interesting: You can perform a similar process by betting on a number instead of a color. Betting on number 12 pays 40:1, so if you hit that you win big.  Of course there’s just a 1/41 chance you’ll hit, so the process of re-betting has to be done longer — much longer. It could easily require 50 bets.

But when you win, you really win, because the payoff is 40x, not 2x your last bid. So if you won on the \$16 bet, you would have lost \$15 so far but won \$16 x 40 = \$640.

So what’s the catch? Nothing really, it’s simple math. It does require one thing: An infinite bankroll. That is, you must always have the money to plunk down; if you run out, then you just lost a bunch of money. You can’t re-bet 50 times, because that requires a bet of \$250 = a thousand trillion dollars. Oops…

This reminds me of startup investment theory. You make an angel bet, then double-down with a Series A, then a B, etc.. Hopefully you explode with a 40x return and it’s worth it — but more likely you’ll run out of bankroll before finding that explosion.

It also reminds me of the financial difference between going for the reasonable success versus going for the massive win. When you’re betting on red, there’s lots of ways to win, and you don’t need to try many times before you hit on something good enough to pay the bills and, if you want, slowly grow into something bigger. But if you’re chasing the 40x exit — if it’s go big or go home — you’ll probably go home.

Of course startups are not analogous to roulette, are they? Roulette is a random process; startups are determined by human beings and systematic processes like Lean and AdWords. Roulette has known odds and a binary outcome — payoff or loss — whereas startups generate a spectrum of outcomes and nearly always produce memorable life experiences and relationships.

True, but inspecting the track record of startup-bettors — the VCs — sure makes it look like roulette. On average 9% of companies in a fund have the desired outsized outcomes, and 3/4ths of the funds themselves in the past ten years haven’t produced interesting returns. Assuming VCs are better than chance at picking winners, we must assume the chance for an arbitrary startup is no better than these odds, and in fact possibly closer to betting on “number 12.”

If it the story ended there, this would be a depressing article about how startup successes are so rare that it’s foolhardy to try. But actually the point is exactly the opposite: Using this logic, you can guarantee that you, personally, will succeed.

The trick is to realize that your Roulette game is your entire life, not your current startup, not your current idea. This idea can fail; then you have another idea. That one was good but execution wasn’t there; then you find a co-founder for another concept. That turned into a consulting company, but in consulting you found the intersection of need with budget and spin out another company. Or you go work for another startup who’s latched onto something and get experience and a small exit for yourself which funds the next one.

I think 1/3 of the people at WP Engine right now are in this last category. (There’s room for more — we’re always hiring.)

The path doesn’t matter; what matters is that you’re seeking your own definition of success, and willing to recognize and stop when the current path isn’t right.

The only thing that actually kills you is willful blindness — for example deciding your idea is good without first finding 30 people willing to pay for it, like I repeatedly did until I finally succeeded. And that blindness is what I see most often in startup founders, and what I know will ultimately kill off their companies. They’re wasting time to protect their ego.

Precious time, time to spin the wheel a few more times.

It’s the number of times you spin, not whether you win on the next spin.

Keep spinning.

### 30 responses to “Roulette, Startups, and the paradox of the infinite bankroll”

1. Bill says:

The highest number on a roulette wheel is 36 not 40. The strategy you describe is called the Martingale System.

• brumbo björn says:

Thank you :). It was the first system I heard about when I started to play. I had limited success before losing everything. There are much better systems. And also you can also play No Zero Roulette where you have the same chance of winning as the Casino!

2. Connor says:

The martingale betting system will never work in a casino because all tables have a minimum and maximum bet size to prevent anyone from actually winning anything using this strategy.

Walk into any casino, announce that you use a martingale system, and they will give you a free room, free food, and proceed to take all of your money.

3. Connor says:

The martingale betting system will never work in a casino because all tables have a minimum and maximum bet size to prevent anyone from actually winning anything using this strategy.

Walk into any casino, announce that you use a martingale system, and they will give you a free room, free food, and proceed to take all of your money.

4. The martingale betting system will never work in a casino because all tables have a minimum and maximum bet size to prevent anyone from actually winning anything using this strategy.

Walk into any casino, announce that you use a martingale system, and they will give you a free room, free food, and proceed to take all of your money.

• Of course, it’s more of a thought experiment. The point is an analogy.

5. And the Martingale System is infinitely losing system. It’s expected value is infinitely negative. Plus those real life limitations of bet size and bankroll size.

6. and somehow my comment got posted 3 times! :-(

7. I agree completely, though I said it a different way here: http://bit.ly/OnRKqK. It’s about diversification: VC’s do it in parallel but founders have to do it serially, and it has a better shot of working when they do it over their entire career.

8. I love to read all of the comments from the hardcore gamblers who read your blog. These are the guys who have truly mastered the odds. Doesn’t it really just come to something more fundamental like having the right item at the right price for the right customer at the right time/place and in the right quantities.

• It’s easy to say that it “just comes down to” and then list a bunch of things which are almost impossible to do and which are largely outside your control, where randomness or chaos or luck is a major factor, possibly the biggest factor.

To ignore randomness and believe you’re in total control is just wrong. So to ask how you can more intelligently operate in randomness is a better question.

9. c0ff says:

The betting strategy doesn’t work *with any fair odds*, but for a reason that hasn’t been quite called out yet.

Suppose that you start with \$1023 in your wallet, betting at 50% fair odds. You start the first series of doubling bets: you bet \$1, if you lose you bet \$2, if you lose you bet \$4, continuing until you either win or spend all \$1023.

There are two possible ways this series of bets ends:
1. With 1023/1024 probability, you are up \$1
2. With 1/1024 probability, you lose 10 bets in a row, losing all \$1023

Notice the pattern: with a big probability, you win small, and with a small probability, you lose big.

In fact, if you start with \$1023 and set out to double your money betting on fair 50% odds, you’ll have an exactly a 50% chance that you’ll reach \$2046 before going bust.

So, with fair odds, the betting system is no better at “earning money” than any other arbitrary betting system, such as always betting \$1 or \$1000. The size of bets does not influence the probability that you’ll go bust before you double your money – it only influences how *fast* you’ll find out.

* I started with \$1023 because the calculations are less messy for a number that is one less than a power of two. The conclusion holds for all starting amounts.

* The calculations assume fair odds. Casinos obviously don’t offer fair odds.

* I realize that the discussion of the betting system wasn’t the real point of the article, but I still think that some people may want to understand why it doesn’t work.

• If you re-read the article you’ll find that I didn’t say “fair odds” and also I made the same point you made about the amount of money used and the odds.

10. Ugly American says:

Ben? Ben Bernanke? Is that you?

You got the number of spots wrong.

You got the data type wrong.

You got the payout wrong.

Your fundamental idea has been proven wrong.

Every step of your process has a negative expectation.

But you’re certain that if you just keep doubling down you’ll magically come out ahead.

• Well…. no that’s not true, and the number of spots is irrelevant, and the fact that real casinos stop you is also irrelevant, because actually the post is about risk-management in your life and not about beating Vegas.

11. I love the parallels here between funding start-ups and financial trading. Although we do things to tip the odds in our favour, you can’t get far without recognising the huge role that randomness plays — and capital preservation is foundational to every decision to trade/fund or not, and how much, because no matter how good/lucky you are, once your bankroll is gone, you’re out of the game…

… and as long as you’re still in the game, you have the opportunity to “recognise and stop when the path isn’t right”, make changes and come closer to your definition of success.

12. NiceGuy01 says:

Love the analogy of Vegas and Start ups. I am learning more and more that I am less in control than I thought I was.

I also take the view that not everyone wants to “gamble big” and maybe smaller is ok now and bigger next time.. Some of us have kids and mortgages.

If I had a pound (English) for everytime someone asked me if I was a millionaire, I could literally be one. Some people have this misconception i think that if you run a business and you you aren’t a millionaire, you have “failed”, or not made it yet.

I hope being an Entreprenuer is a “career” for me.

PS Could the anal gambling fanatics, just keep it to themselves?

13. vlasta says:

If I had infinite bank roll, why should I bother with winning pennies? I would not even notice the win – infinity+something is still infinity. No, the only way to win in Vegas is to own a casino… I wonder what startup advice can be derived from that.

14. sharemywin says:

Most people chase ROI not a return. ROI has a time factor. which negates your process. Also, in vegas there is usually a max bet.

15. sharemywin says:

I think the problem with looking at start ups as a game is the successes change the rules. A harvard dropout was a good person to develope an app that college students could relate to which also happened to be something adults started using. But, building another college app would have to have a muhc higher bar to complete..

16. The described Vegas strategy is just nonsense. Don’t have time to fully explain it, but just consider this: every time you bet in the roulette, you probabilistically lose 1/37 of that money (2,7%). And this applies no matter what strategy you are applying (if you double the amount or not). So in your case, after N runs, you lost around (2^N)/37 money due to “0” spot. Plus you win/lose random money dependent on your luck. And there is absolutely no guarantee that this “won” money will be bigger than the money lost. Actually it’s the opposite – the more you play the bigger is the chance that lost money will outgrow won money.

• Nope! If you’re a coder, you can implement my strategy and see that the program always terminates with a win of one dollar.

• No need for me to code that. It was already done – check http://hspm.sph.sc.edu/courses/econ/Risk/riskdoubletest.html . There is good explanation on the page too. “There is no way a
bunch of negative numbers can add up to a positive number, no matter how
Just to make it clear: I don’t dispute that you can’t make \$1 with this strategy. I’m saying that it’s a losing strategy.

17. Appreciate the perspective your post has given me as a business person: “Roulette game is your entire life, not your current startup, not your current idea.” You may lose a game but you can’t stop playing. Adjust to stay in the game and get a win.

Richard Branson & Donald Trump are good examples of people who keep ‘spinning’ and have an ‘infinite’ reservoir of courage despite having lost millions in failed business ventures.

This is a relevant post, especially for young people (future job creators) who may give up on entrepreneurship after a few failed experiences.

18. I wish I could summarize this post in one simple eloquent sentence for people when they ask why I keep throwing darts at the dart board (on my 5th company/startup, (40% win ratio ;). Instead I just say “Because it’s fun, full of lessons, and I suck as an employee…”

19. bar kerark says:

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20. It is necessary for the beginners to choose a roulette system that is free and easy to use. You must bet on the outside chances and monitor the roulette table. Most important things to know the amount of bets you play and how to flip the coin during the game.

21. Some useful tips and information about roulette odds and infinite bankroll. If player are know the correct playing and betting strategy, then they easily be winning the game. It is advisable for the player to keep the playing session short and bet the minimum amounts when they are losing.

22. BobbyMcD says:

If you’re going to make a roulette analogy, it’s probably best to know how many spots there are on the wheel. :)