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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

#51

Post by nighthawk454 »

a-dub wrote: post #40
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…

That is an interesting question. I suppose it's equivalent to the 'worst case' performance for binary search, which would be a relevant topic. Finding the optimal strategy in the case where the opponent _may_ be adversarial could be interesting. I don't imagine the odds improve compared to the base situation, but not sure

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

#53

Post by randomdata »

roenxi wrote: post #47
rustybolt wrote: post #25

Earlier quoted context omitted.

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 al…

In fairness, if someone proposes a complex and contrived game which cannot be easily analysed but is potentially adversarial... you shouldn't play them.

Are you talking about Balmer's question or the aforementioned job being interviewed for?

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

#54

Post by nighthawk454 »

djtango wrote: post #46
cuu508 wrote: post #34

Earlier quoted context omitted.

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

I actually think parkour community and practice teach and handle this very well. Same for free solo climbing. 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 an…

Yeah, exactly - you wouldn't stake your life on hitting the average case in an n=1 scenario. Parkour community sounds really cool!

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

#55

Post by rustybolt »

IanCal wrote: post #42
rustybolt wrote: post #25

Earlier quoted context omitted.

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 al…

No, it's about understanding what an interview is for . They're not trying to get the answer. They're trying to find out what you know, how you think and how you communicate. Do you spot that it's different with one Vs many plays? Do you spot the binary search? Do you spot that an adversarial opponent can push things? Can you clearly communicate these? If you just say "I don't know" and that's it you are showing you…

That seems reasonable, and in that context I would think it's actually a good interview question.

But it seems that Steve Ballmer used this question as if it has a single right answer, and that answer is "no". Unless it's more about the question "do you want to play this game, right here, right now?", then it becomes more about heuristics and quick reasoning.

It's all about context I guess.

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

#56

Post by nighthawk454 »

cuu508 wrote: post #34
nighthawk454 wrote: post #28

Earlier quoted context omitted.

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?

It's a good question, sort of related to optimal bet sizing. Check out this wiki which another commenter also mentioned: https://en.wikipedia.org/wiki/Kelly_criterion?useskin=vector

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

#57

Post by cuu508 »

nighthawk454 wrote: post #54
djtango wrote: post #46

Earlier quoted context omitted.

I actually think parkour community and practice teach and handle this very well. Same for free solo climbing. 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 an…

Yeah, exactly - you wouldn't stake your life on hitting the average case in an n=1 scenario. Parkour community sounds really cool!

You are staking $1.

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

#58

Post by rustybolt »

corimaith wrote: post #9
weinzierl wrote: post #4

Earlier quoted context omitted.

It is the perfect example, why you should pay attention in your math class too.

I don't think the average CS curriculum is going to cover advanced game theory. And you certainly aren't going to doing most linear programming on the spot in a interview.

This is actually extremely basic game theory, but I agree that most CS programs would probably not cover it.

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

#59

Post by cbanek »

jimt1234 wrote: post #52
cbanek wrote: post #13

Of all the things that Ballmer was wrong about... I guess this is one of them.

My personal fav: https://www.youtube.com/shorts/rCszxibClKE

My favorite Ballmer practice is stack ranking. It completely screwed up the entire company.

I worked on Windows Mobile at the time the iPhone came out. We were all shitting ourselves.

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

#60

Post by larsnystrom »

draluy wrote: post #43

I dont get this. If this is true, then he found a more efficient algorithm than binary search. Why are we not using it in CS?

I'm no mathematician, but I think that if you know something about the probability distribution before searching, then you can be more efficient than blindly using binary search. And if you assume Ballmer is out to get you (i.e. the distribution is not random) then you can use that information to improve the search speed.
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