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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

#21

Post by nopinsight »

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…

Kelly Criterion

Betting more than the Kelly fraction increases the risk of ruin, especially in the long run.

https://en.m.wikipedia.org/wiki/Kelly_criterion

Note: Not saying that this is applicable in the original post's situation. It's relevant to the parent comment though, and very useful in many situations, such as investing.

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

#22

Post by nighthawk454 »

nopinsight wrote: post #21
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…

Kelly Criterion Betting more than the Kelly fraction increases the risk of ruin, especially in the long run. https://en.m.wikipedia.org/wiki/Kelly_criterion Note: Not saying that this is applicable in the original post's situation. It's relevant to the parent comment though, and very useful in many situations, such as investing.

Yes, precisely. Although that's more about bet sizing for optimal return in the long run, not quite about binary choice of whether or not to play. But conceptually bang on, I had it in mind

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

#23

Post by rustybolt »

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 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.

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

#25

Post by rustybolt »

Jalad wrote: post #10
qarl wrote: post #2

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

Is this a perfect example of broken modern tech interviews? Balmer's question seems fair for the complexity of the answer he was expecting. As the interviewee you would presumably provide the (mathematically) wrong answer, but you'd show your thinking along the way, including a small demonstration of CS principles. Keep in mind that Balmer had a long career, so if he ever asked this question, it was probably back in…

The question seems like a mathematical one.

What you're saying sounds to me like "your answer doesn't need to be correct, it just needs to sound reasonable". What you're filtering on with this question is good bullshitters.

To me, the only reasonable to this question is "I don't know". I think even a mathematical genius like Terrence Tao would not be able to give you the answer to this on the spot. (Although I can also totally believe that he would instantly see this from some obscure theorem that only like 5 people on the planet know.)

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

#26

Post by randomdata »

Jalad wrote: post #10
qarl wrote: post #2

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

Is this a perfect example of broken modern tech interviews? Balmer's question seems fair for the complexity of the answer he was expecting. As the interviewee you would presumably provide the (mathematically) wrong answer, but you'd show your thinking along the way, including a small demonstration of CS principles. Keep in mind that Balmer had a long career, so if he ever asked this question, it was probably back in…

Seems so. The broken tech interview idea stems from the idea that interview questions that do not pertain to the job will lead to hiring the wrong people.

And, indeed, what Microsoft really needed in the 80s was people who truly understood memory management in C, not gamblers left to hack their way into something that kind of worked sometimes. Microsoft's need to correct that hiring mistake later set them back significantly. Had they asked about the intricacies of C as it directly pertained to the job instead of unrelated trivia, they would be in a much stronger position now.

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

#28

Post by nighthawk454 »

rustybolt wrote: post #23
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 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.

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

#29

Post by michaelt »

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?

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

#30

Post by pavlov »

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…

It's kind of a given that you can't use the proposed mixed strategy for a single game, because it expects you to draw one of the patterns at the start of the game.

And some of the patterns are just obviously suboptimal if this is your only chance:

> With probability 0.9686%: Binary search, first guess is 1.

(I wonder what Ballmer would think that, when proposed to play this game, you first manually throw dice to draw a random number in the range 1 - 1,000,000 and if it's 9,686 or less, you start your binary search at 1. He might be impressed by your dedication to the mixed strategy.)

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