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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

#41

Post by nighthawk454 »

qsort wrote: post #35
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 "w…

> If the question is "would you play this game" the reasonable mathematical translation is "determine if the expected value is greater than zero".

Not really! And that may be the point of the question. It's not testing if you can pattern match to plausible CS concepts.

If you get one play, and the goal is to win, do you take the chance? The whole question is about the difference in likelihood in the limit (expected value, infinite plays) and what is a likely outcome _of one round_.

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

#42

Post by IanCal »

rustybolt wrote: post #25
Jalad wrote: post #10

Earlier quoted context omitted.

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 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 don't know how to communicate important information and miss soft skills about understanding the context of an interview.

If you say "I don't know" and talk through your thoughts then great. The point is talking things through, even if you have gotten the wrong answer.

Maybe you'd be able to say "and here's how I'd code a simulation to check"

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

#44

Post by fnord123 »

> I’m thinking of a number between 1 and 100.

I guess this is part of the clarifications one normally asks when in an interview setting, but he has specified numbers and not integers. One could choose (pi*2)/2 and you will owe a lot of money.

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

#45

Post by ahtihn »

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…

> 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.

You're calling an all-in 100% of the time in a cash game if your expected value is positive. If you don't, you can't afford to play at that table.

You're not going all-in with any hand expected to win because that's not how you maximize profit. It has nothing to do with the risk of going bankrupt. Because again, if that's a concern you shouldn't be sitting at the table.

Tournament poker is a bit different because there are certain points where you have positive chip EV and negative $ EV and the math changes.

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

#46

Post by djtango »

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?

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 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

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

#47

Post by roenxi »

rustybolt wrote: post #25
Jalad wrote: post #10

Earlier quoted context omitted.

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 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.

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

#48

Post by carlmr »

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…

>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?

The question is whether Ballmers ego would allow him this flexibility if it's his own question.

Some people might be very emotionally attached to the questions they created, but not so much to those they've been given as an interviewer.

I've fared well pointing out issues with questions in the past and gotten the job. I'd try to be diplomatic about it though and not outright say they're wrong. Instead pointing out how with a classical binary search the expected value is negative, but there are strategies from game theory to deal with adversarial picks and here you could reach a positive expected value.

Kind of a "yes, and..." approach. You acknowledge their view, and then you add a new perspective. But don't say they're wrong.

Funny enough in situations where I suspect the interviewer was given the question it probably wouldn't have helped, not due to emotional attachment, but because the interviewer had a tenuous grasp of the topic themselves and couldn't stray from the script they were given.

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

#49

Post by nighthawk454 »

ahtihn wrote: post #45
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…

> 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. You're calling an all-in 100% of the time in a cash game if your expected value is positive. If you don't, you can't afford to play at that table. You're not going all-in with any hand expected to win because that's not how you maximize profit. It has nothing to do…

People are really zeroing in on the word 'bankrupt' here. The point was if you used that strategy, all in 100% of the time for positive EV, you will _probably_ go bankrupt even though the n=infinity limit of that strategy is positive.

The whole poker thing was merely an analogy in the first place.

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