Bankroll management for entrepreneurs

Edit: After writing this post, I thought more about the topic and realized the entrepreneurial equivalent of good bankroll management is obviously “minimizing your burn rate.” So I’m kind of re-inventing the wheel here, but I think there are benefits to thinking about burn rate from a gambling perspective.

Among professional gamblers, there’s a concept called “bankroll management.” It works like this: say you’ve got $100 in your pocket. Someone offers you a bet: flip a fair coin, and if it comes up heads, you get $110, but if it comes up tails, you lose the $100. Should you take the bet? A naive expected value calculation says “yes”: $110 * 0.5 – $100 * 0.5 = $5, so you should expect on average $5 in profit.

But there are good reasons not to go by the naive expected value calculation. One reason is the diminishing marginal utility of money—a fancy way of saying that the more money you have, the less valuable each additional dollar is. Maybe you need the $100 in your pocket to buy food for the next week, but have no pressing need for the additional $110 dollars.

There’s another reason you might not want to take the bet, though. Suppose you’re a professional gambler who’s just starting out. The $100 isn’t all the money you have, but it does represent your entire bankroll—the money you’ve set aside for use in your new profession, because it’s all you think you can afford to lose. Should you bet it all on this positive expected value bet?

Probably not. Suppose that, in spite of your newness, you’re confident in your skills. You’re confident that you’ll encounter other profitable bets in the future. So by making that bet, you’re not just risking your $100—you’re risking the ability to make those hypothetical future profitable bets. Maybe you should go play some low-stakes poker for awhile to build your bankroll, before making any $100 bets.

I think something similar might apply to entrepreneurs. In the Effective Altruism community, it’s become widely known that altruism favors higher-risk, higher-reward career paths. If you’re planning on being like Bill Gates, and donating most of whatever you make as an entrepreneur to charity, the marginal utility of your money declines much slower. It’s “What would I do with a tenth Ferrari?” vs. “What am I going to do with my tenth vaccine? Vaccinate another kid!”

But I’m not sure this means you should naively maximize expected value, even after making some concessions to your self-interested need for financial security. If you have some extra money you could invest in your own startup, maybe you shouldn’t invest it all right away, even if doing so would have high expected value. This could also apply to a metaphorical bankroll of mental and emotional energy—which you may need to manage so you don’t burn out and say, “fuck it, I’m working for Google.”

It seems likely that I’m not the only person who’s thought of this. Is there advice out there for startup founders that incorporates it? It seems unlikely that I’m the first person to have thought of it. Or maybe I am: startup founders (as opposed to the venture capitalists who fund them) don’t seem to think in terms of expected value much. In any case, I’m not sure how to build on it. Thoughts?

  • josh

    I think there are a number of situations where just looking at the expectation value is too naive. Take the lottery: I had a statistics teacher in high school who told us he only played the lottery when the pot got so big it gave a positive expectation value. Which is a fine point for explaining the concept to highschoolers. But really, did something important change when you go from a 99 jillion payout to a cool 100-jillion? I don’t think so. Expectation values matter most when you expect to sample the distribution many times. You should not expect to make money when playing the lottery, and even when the expectation value is positive you aren’t going to make your dollar back unless you are going to play that situation hundreds of thousands of times. Conversely, a dollar is pretty insignificant to a lot of us, so the lottery may be worth it because the impact of winning is so big compared to the pittance you are risking, even though the chances are so small. If I win it changes my life and if I lose, I’ve lost essentially nothing. That’s not to say that you should play the lottery, definitely you shouldn’t if you are counting on it to make you money. But the expectation value isn’t a good argument against occasionally playing with money you can afford to lose.

    Or, more related to your point about betting, most of us think having catastrophic health and home insurance is a good thing. But in principle insurance is at best a zero expectation value and in reality negative since they are mostly profit driven corporations. If you had a thousand houses (or lives) you wouldn’t buy insurance since the out of pocket cost for the few that go really bad would be less than the total to insure them all. But for those of us with the one, the risk is unacceptable so we get the insurance, even though I expect to lose money on it.


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