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The expected value of the game is positive regardless of Ballmer’s strategy

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Re: The expected value of the game is positive regardless of Ballmer’s strategy

#31

Post by nighthawk454 »

michaelt wrote: post #29
nighthawk454 wrote: post #19

This sort of misses the forest for the trees, although neat application. Ballmer's argument is essentially about tail risk. Expected value is absolutely not a good way to make bets if you value survival, because you only get one shot. Same reason you wouldn't go all in every time you get a poker hand that's "expected" to win. Because you'll (very probably) be bankrupt in a few hands. Sure the mean is +$0.07 or whatev…

> Ballmer's argument is essentially about tail risk. Expected value is absolutely not a good way to make bets if you value survival, If he was trying to make that point, why set the bet at $1 - a loss that wouldn't imperil anyone? The situation is entirely fictional, why not fictionally gamble with a five-figure sum?

You could? There's no reason you couldn't do $50,000 with bets of $10,000. The point is you get 5 guesses before you lose. The bet sizes don't really matter.

Re: The expected value of the game is positive regardless of Ballmer’s strategy

#33

Post by rustybolt »

OmarShehata wrote: post #6
qarl wrote: post #2

And this, friends, is the perfect example of why the modern tech interview process is pure insanity.

is it? If I was forced to ask this question as an interviewer, and the candidate said, "actually, you're wrong, here's why" that's a very good signal. Do most people not do this? (typically there's discussion with all the interviewers and it isn't just "did the candidate get the question right or not). I personally think a lot of big tech interview questions are dumb but I think the process isn't as broken as I thoug…

> Do most people not do this?

I'd say it's impossible to answer this question conclusively within the time frame of an interview. That makes it, in my opinion, a bad interview question.

My answer to this question would be to show that I understand what it would take to answer this question correctly (you'd have to find a mixed strategy that has a positive expected value for every choice of number), I wouldn't be able to give a confident "yes" or "no" answer on the spot. I think that's the only correct answer.

In practice, I think this question is advantegeous for those who confidently blurt out an answer and then make up a heuristic argument for it. But a heuristic argument can be found for both "yes" and "no".

Re: The expected value of the game is positive regardless of Ballmer’s strategy

#34

Post by cuu508 »

nighthawk454 wrote: post #28
rustybolt wrote: post #23

Earlier quoted context omitted.

I don't think this is true. Most people will not be bankrupt after losing a dollar. If this is true then Steve failed badly at communicating this context. To be honest, I think Steve just didn't grasp the mathematical deepness of the problem.

I think you've misread. The bankruptcy was in an analogy to poker. The point is if you get _one round_ to play - essentially all or nothing - should you play? No.

OK, if you value survival, at what odds should you play?

Re: The expected value of the game is positive regardless of Ballmer’s strategy

#35

Post by qsort »

nighthawk454 wrote: post #19

This sort of misses the forest for the trees, although neat application. Ballmer's argument is essentially about tail risk. Expected value is absolutely not a good way to make bets if you value survival, because you only get one shot. Same reason you wouldn't go all in every time you get a poker hand that's "expected" to win. Because you'll (very probably) be bankrupt in a few hands. Sure the mean is +$0.07 or whatev…

I don't agree, I think he was just plain wrong.

Unlike most people here I actually think questions like this are a decent way to see how people think. I would expect people with math/stats/cs background to be able to at least start the conversation about this problem.

However when you hide hypotheses or add your own BS constraints as a gotcha without explicitly stating them is where you lose me.

If the question is "would you play this game" the reasonable mathematical translation is "determine if the expected value is greater than zero". If you're going to talk about tail risk you need to specify utility functions (possibly asymmetric for the two players!) and you need to explicitly say that's what you mean.

Re: The expected value of the game is positive regardless of Ballmer’s strategy

#37

Post by thih9 »

qarl wrote: post #2

And this, friends, is the perfect example of why the modern tech interview process is pure insanity.

As long as it's used to figure out if the two parties would enjoy working with each other, I guess it's fine. But yes, increasingly often this turns into a quiz or worse.

At least we get some quality fiction like https://aphyr.com/posts/340-reversing-the-technical-intervie... and its sequels.

Re: The expected value of the game is positive regardless of Ballmer’s strategy

#40

Post by a-dub »

nighthawk454 wrote: post #19

This sort of misses the forest for the trees, although neat application. Ballmer's argument is essentially about tail risk. Expected value is absolutely not a good way to make bets if you value survival, because you only get one shot. Same reason you wouldn't go all in every time you get a poker hand that's "expected" to win. Because you'll (very probably) be bankrupt in a few hands. Sure the mean is +$0.07 or whatev…

agree about the EV stuff. it only makes sense over many draws and the problem states that he is thinking of "a number", that sounds like one game.

that said, the problem screams binary search and you know your opponent is a computer person, so i guess the question is: if you make a bet that your opponent is making an adversarial choice that assumes you're going to do a vanilla binary search, can you improve your odds of coming out ahead by modifying your own binary search to always assume the target is an adversarial one?

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