Earlier quoted context omitted.
Many Satyas successes started under Ballmer.
Could you give some examples?
Biggest one: Azure, then Bing
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
#102moral of the story: you might be theoretically correct, but the other dude still has a net worth of 120bn and you don't. so who's the loser now?
not being a billionaire doesn't automatically make you a loser
a better moral of the story would be "a billion dollars does not guarantee that someone is right"
Re: The expected value of the game is positive regardless of Ballmer’s strategy
#103Re: The expected value of the game is positive regardless of Ballmer’s strategy
#104Of all the things that Ballmer was wrong about... I guess this is one of them.
I'd love to be wrong like Ballmer. The net balance of his decisions were billions of dollars.
Re: The expected value of the game is positive regardless of Ballmer’s strategy
#105Earlier 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.
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…
You know that even smart mathematicians got tripped up by the Monty Hall problem, right?
> Even when given explanations, simulations, and formal mathematical proofs, many people still did not accept that switching is the best strategy.[5] Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating Savant's predicted result.
Re: The expected value of the game is positive regardless of Ballmer’s strategy
#106I did a very similar exercise after reading the original post.
You can get the EV a lot closer to the optimal +0.2 (Although I was unable to prove how close) by dropping the requirement "do not increase worst-case complexity for the binary search" as this is lost with initial guesses outside 36-64 anyway. Deviating at a higher depth makes punishing specific guesses in the tails a lot cheaper, only giving up 1-2 cents of EV.
Re: The expected value of the game is positive regardless of Ballmer’s strategy
#107Earlier 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.
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.
Re: The expected value of the game is positive regardless of Ballmer’s strategy
#108Of all the things that Ballmer was wrong about... I guess this is one of them.
I'd love to be wrong like Ballmer. The net balance of his decisions were billions of dollars.
The net balance of his decisions, his circumstances, his random events and who knows what else.
Please please stop with this "if he's rich he must be smart" argument. Please?
Re: The expected value of the game is positive regardless of Ballmer’s strategy
#109Earlier 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.
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…
You think they asked this on the SAT?
Re: The expected value of the game is positive regardless of Ballmer’s strategy
#110When Ballmer said 'adversarial', I considered this strategy: he's not actually required to pick a fixed number at the start at all. He can simply give the answer to each guess which leaves the largest number of possible numbers remaining, guaranteeing a loss regardless of strategy.
This is how it is done in the analysis of competitive ratios of online algorithms. The adversary can change its mind on a whim, it merely has to commit to the decisions it has already made in the past.