[fortydegrees]

While it does seem that Ballmer doesn't have an understanding of the deepness of the problem, in his defence, he outscored BillG on the math SAT with a perfect score of 800, and graduated Harvard with a degree in applied mathematics.

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...

[lucianbr]

Is the interview for an engineering position or for sales?

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.

[Majromax]

> Is the interview for an engineering position or for sales?

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.

[rini17]

Physical processes are very often long tailed on the wrong end and thus adversarial though.

[dullcrisp]

You think they asked this on the SAT?

[eesmith]

You know that even smart mathematicians got tripped up by the Monty Hall problem, right?

> 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.