All The Marbles

Step right up, let’s play a game!

In front of you are two opaque jars. The game is simple – reach into a jar and pull out a marble. If you pull out a green marble, you win a prize! If you pull out a red one, you don’t. There’s no cost to play other than your time.

If you pull a green marble out of Jar A, you win $50. If you pull a green marble out of Jar B, you win $100.

You want to know the ratio of marbles in each jar? Sure thing. Jar A has exactly one marble, and it’s green. That’s right, you’re guaranteed to win.

Jar B has ten marbles. Nine of them are green, and there’s one red one.

Now, if you can only choose one: Which jar do you choose?

From a coldly logical standpoint, Jar B is the better choice. A 90% to win $100 translates into the value of that choice being $90, whereas the value of the choice to pull a marble out of Jar A is $50. But some people are super, super risk-averse, and the idea of pulling the one red marble out of Jar B fills them with a sort of existential dread, so they might actually pull from Jar A.

But what if I changed the game up a bit – what if I said you could play the game 10 times in a row, with the one restriction being that you had to make the same choice each time?

Now “Choice A” is worth $500, but “Choice B” is worth $900, and the likelihood that you win nothing is extremely small. In fact, even if you pulled the one red marble 4/10 times, you’d still have won more with Choice B than with Choice A.

Okay, elementary stats discussion is done. Let’s make this a little more challenging, but also a little closer to reflecting reality.

I said in the beginning that there was no cost to play this game other than your time, so let’s keep that rule – but let’s say the game takes an hour to play. After all, it’s popular, so you’ve got to wait in line for an hour. Well, an hour isn’t nothing, and for some people it might not actually be worth it. If you don’t have any other way of turning that hour into at least $50, then it’s probably a good use of your time, but if you make $300/hour at your normal job, then it’s pretty pointless to do this.

But what if you make $70/hour?

Well, now we have an interesting discussion. If you normally can turn an hour into $70, then playing the game is still worth it – but only if you pick Jar B. Picking Jar A is a guaranteed “win,” but at the cost of twenty bucks! Picking Jar B is worth twenty extra bucks to you as a statistical measure, but also carries some risk; 90% of the time you’ll come out $30 ahead, and the other time you’ll lose the $70 opportunity cost you “paid” to play.

So the game is not worth it if you’re risk-averse, but it is worth it if you aren’t!

This is one of the biggest barriers to people becoming much more financially successful in their careers. There is a plateau in almost every career journey where in order to move up, you have to accept more risk. It might be because the best way “up” is entrepreneurship, it might just be that the competitive nature of higher tiers within your industry necessitates an increased willingness to “put yourself out there” and commit to projects or sample work without guaranteed up-front payment. No matter the source, however, there is more risk as you advance.

(Here’s a personal example: As part of my work, I do free consultations with people. Many, even most of these turn into paid work, but of course some of them don’t. If I was so risk-averse that I was never willing to do anything that wasn’t guaranteed to give me income, then I wouldn’t do those consultations, but clearly I’d be poorer overall as a result, given the value of the work they generate most of the time. In a very real sense, I play this marble game every week.)

Many people, at one point or another, find themselves in this position. They’ve reached a point where their “guaranteed” income level has largely maxed out. Their total income level could be much higher overall, but only by accepting some day-to-day statistical risk. And many people, because they don’t have the proper tools for evaluating the choice, make the wrong one. Hopefully this has given you a new tool – so that when it’s time for you to make that choice, you go for all the marbles – the red and green ones alike.

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