Which makes me wonder if it's related to another 'simple' game theory problem that came up in Matt Levine's money stuff:
"They made me do the math on 1000 coin flips. EV(heads) (easy), standard deviation (slightly harder), then they offered me a +EV bet on the outcome. I said “let’s go.”
They said “Wrong. If we’re offering it to you, you shouldn’t take it.”
I said “We just did the math.”
They said “We have a guy on the floor of the Amex who can flip 55% heads.”"
I like that anecdote and the takeaway, especially with regards to trading: if someone's offering you what seems obviously a +EV trade, why are they offering it to you and what are you missing? Whether that was Ballmer's intended lesson is another matter..
[0]https://www.bloomberg.com/opinion/articles/2024-05-14/amc-is...
If you're hiring a software developer, I am going to assume all probabilities are about physical processes or data distributions or such, and there is no "if we're asking it means we have something up our sleeve". The data going to be sorted by merge sort is not going to have anything up its sleeve, or set any traps for me.
Either way. The coin-flip example and Ballmer's binary search game could apply with simple extensions to complicated processes like SLAs on cloud services.
> The data going to be sorted by merge sort is not going to have anything up its sleeve
That's a curious example, since one reason to use mergesort rather than quicksort is the latter's susceptibility to pessimal inputs.
> Even when given explanations, simulations, and formal mathematical proofs, many people still did not accept that switching is the best strategy.[5] Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating Savant's predicted result.
On the contrary, in general yes you should, because life as a whole will give you a variety of these sorts of risks. Steve Balmer's offer is just one episode in a lifelong series of risks offered you by the universe at large.
Bankruptcy would suck but it is not like you have no possibility of another chance like death.
I suspect there is much muddled thinking in this area viewing the death of a LLC as equal to the death of a human.
A coin flip for 20 million dollars if tails, physical death if heads is much different than bankruptcy if heads.
One is a stupid gambler with their life and the other is basically a serial entrepreneur taking asymmetrical bets until the coin comes up tails.
Imagine you're in your bathroom, choose two tiles and step from A to B.
No problem. What if those tiles were all you had to stand on and you were 30 storeys up suddenly it's a whole different equation and your body instinctively knows it. In fact some of parkour training is learning to master your own fear and confidently execute things you know you can already do in the face of higher stakes.
If I offered you a dice roll and said guess the number, bet 1 dollar I'll pay you 12 on the right guess you'd bet 1 dollar but you wouldn't bet your life on it even though the EV was high. Even if the payout was 1 million you still might not take it (some might)
Edit Thinking about it more, my example is more about factoring in all the risks - a positive EV bet with a large downside risk is not a great one to take even if the risks are small which is where the picking up pennies in front of a steamroller analogy comes from
To be honest, I think Steve just didn't grasp the mathematical deepness of the problem.