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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

#121

Post by carlob »

mananaysiempre wrote: post #111
bambax wrote: post #94

Earlier quoted context omitted.

> Expected value is absolutely not a good way to make bets if you value survival Yes! The St. Petersburg "Paradox" shows that we intuitively know that. I put "paradox" in quotes because I don't think it's a paradox, it's just a sane reaction. (Sam Bankman-Fried was a big fan of EV and famously declared that he would toss a coin where heads would double the "value" (?) of the world but tails would destroy it.) In shor…

> It's only a paradox if we think it shows that people are not "rational". But I think it simply shows EV is not a good measure of risk, and everyone knows it. There are standard arguments (e.g. the Von Neumann–Morgenstern utility theorem) that an agent with rational preferences, with remarkably weak definitions of the word “rational”, must have an utility function and a subjective probability function such that thei…

Yeah but that utility function will not be a linear function of money so you can't say EV(u($$)) == u(EV($$)). This is the mathematical formulation that tells you that it is irrational to risk all your money to make an extra dollar even if u(EV($$)) is positive EV(u($$)) can be negative.

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

#122

Post by TheOtherHobbes »

nneonneo wrote: post #118
bambax wrote: post #94

Earlier quoted context omitted.

> Expected value is absolutely not a good way to make bets if you value survival Yes! The St. Petersburg "Paradox" shows that we intuitively know that. I put "paradox" in quotes because I don't think it's a paradox, it's just a sane reaction. (Sam Bankman-Fried was a big fan of EV and famously declared that he would toss a coin where heads would double the "value" (?) of the world but tails would destroy it.) In shor…

The St. Petersburg "paradox" is not a paradox if we consider any real-world implementation of it. The EV accumulates at the rate of $1 per flip. So, if we want to make the EV at least $1,000,000, we must find a counterparty that is willing to pay at least $2^1000000 (or at least 2^1000000 units of "utility" if we're trying to avoid the depreciating utility effect). That's plainly unrealistic. As soon as the counterpa…

It's interesting that in this context the assumption of infinite growth is obviously unrealistic - but in the context of trad econ, infinite growth is considered a bedrock assumption.

Putting them together suggests it's flagrantly irrational to apply naive toy models to the real world. Even if they do have a nice mathy sheen.

Engineers (mostly) know this, but for some reason gamblers and economists (mostly) act as if they don't.

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

#123

Post by quuxplusone »

gavindean90 wrote: post #50

I 100% believe Balmer had an off by one error

From my own blog post (linked from TFA):

> If Ballmer is choosing his secret number uniformly at random, then the expected value of the game is [that you win $0.20]. But, as Ballmer points out in the linked video, if he knows you’re going to do a plain old binary search, then he certainly won’t ever choose 50 as his secret number. In fact, he has no reason to choose 25 or 75 either. Or 12, 13, 37, 38, 62, 63, 87, or 88. If Ballmer avoids those eleven numbers, and chooses uniformly at random from among the rest, that alone is enough to lower the expected value of the game from [$0.20] to about [−$0.0045].

So I think Ballmer was being perfectly honest in what he said: he does know a strategy that makes the expected value of binary search counterintuitively negative, and that strategy is (as he says explicitly) to avoid the first few numbers that you're going to guess. No further speculation about errors or deception on his part is needed.

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

#124

Post by denizener »

gwd wrote: post #86
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.

> The point is if you get _one round_ to play - essentially all or nothing - should you play? No. On the contrary, in general yes you should, because life as a whole will give you a variety of these sorts of risks. Steve Balmer's offer is just one episode in a lifelong series of risks offered you by the universe at large.

It all depends too if the absorbing barrier is a true absorbing barrier like death.

Bankruptcy would suck but it is not like you have no possibility of another chance like death.

I suspect there is much muddled thinking in this area viewing the death of a LLC as equal to the death of a human.

A coin flip for 20 million dollars if tails, physical death if heads is much different than bankruptcy if heads.

One is a stupid gambler with their life and the other is basically a serial entrepreneur taking asymmetrical bets until the coin comes up tails.

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

#125

Post by qarl »

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…

I think you're missing my point. The problem isn't the question - it's the fact that Balmer was objectively wrong about the answer - and he never changed that determination after having conversations about it however many times. ("I asked this question all the time.")

It doesn't matter that it was difficult to prove he was wrong. The issue is that it was impossible to prove he was right. And if anyone ever tried to bring that up to him, he never once heard them.

I believe an interviewer who is wrong and does not listen to you is a perfect example of the broken process. Especially given that he was an industry leader - in this interview he was providing a historical example of the process' merits - all while being entirely incorrect.

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

#126

Post by bee_rider »

trescenzi wrote: post #112
bambax wrote: post #94

Earlier quoted context omitted.

> Expected value is absolutely not a good way to make bets if you value survival Yes! The St. Petersburg "Paradox" shows that we intuitively know that. I put "paradox" in quotes because I don't think it's a paradox, it's just a sane reaction. (Sam Bankman-Fried was a big fan of EV and famously declared that he would toss a coin where heads would double the "value" (?) of the world but tails would destroy it.) In shor…

This is interesting to me in the context of a post[1] yesterday about teaching logical thinking to children. One of the top comments was about how, yes, teach logical thinking but also teach other types too. SBF and those who think with a heavy bias towards EV show an extreme weakness towards reality. Of course SBF himself is a perfect example of this. I won’t pretend to know if his math was always right but one of h…

Does he actually calculate expected values or does he just have a sort of winding way of justifying his gut takes?

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

#127

Post by contravariant »

bambax wrote: post #94
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…

> Expected value is absolutely not a good way to make bets if you value survival Yes! The St. Petersburg "Paradox" shows that we intuitively know that. I put "paradox" in quotes because I don't think it's a paradox, it's just a sane reaction. (Sam Bankman-Fried was a big fan of EV and famously declared that he would toss a coin where heads would double the "value" (?) of the world but tails would destroy it.) In shor…

What idiot wouldn't put destruction of the world as '-infinity' of value?

Equating money with value is a simple trap as well. Who cares if you can win millions when a single loss wipes out all your savings? Since anything below a certain level of money leaves you trapped with no way out it could be argued that the value of being destitute is not 0 but -infinity which makes any risk of losing all money unacceptable. This is especially true in a world where people are willing to offer strange bets with arbitrarily high expected value as long as you have some money.

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

#128

Post by onlyrealcuzzo »

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…

> This sort of misses the forest for the trees, although neat application.

I think people are missing the forest for the trees on it mattering if Balmer was "right" or "wrong".

It's his interview question. He's using it as a way to see your thought process more than the answer you arrive at at the end.

I imagine if interviewees had these thoughtful disagreements, he'd either guide them to the reason he had a different answer or value their input.

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

#129

Post by rini17 »

lucianbr wrote: post #107
fortydegrees wrote: post #95

Earlier quoted context omitted.

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), s…

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.

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

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

#130

Post by chii »

contravariant wrote: post #127
bambax wrote: post #94

Earlier quoted context omitted.

> Expected value is absolutely not a good way to make bets if you value survival Yes! The St. Petersburg "Paradox" shows that we intuitively know that. I put "paradox" in quotes because I don't think it's a paradox, it's just a sane reaction. (Sam Bankman-Fried was a big fan of EV and famously declared that he would toss a coin where heads would double the "value" (?) of the world but tails would destroy it.) In shor…

What idiot wouldn't put destruction of the world as '-infinity' of value? Equating money with value is a simple trap as well. Who cares if you can win millions when a single loss wipes out all your savings? Since anything below a certain level of money leaves you trapped with no way out it could be argued that the value of being destitute is not 0 but -infinity which makes any risk of losing all money unacceptable. T…

> value of being destitute is not 0 but -infinity which makes any risk of losing all money unacceptable.

that's just loss aversion codified.

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