Archives, Driving with Mathematicians

Driving with mathematicians

“How many gas stations do you think we’ll pass on the way home?”

“You mean on the side of the road, or at exits?”

“Whichever – places where we’d consider buying gas.”

“I don’t know, six, eight…why?”

“Well, if we pass the first 1/e gas stations and then stop at the first place that offers cheaper gas, then we’ll maximize the chance that we’ll end up buying the cheapest gas. I mean, assuming that gas prices are random and don’t follow any trend with regards to location, which obviously isn’t the case.”

“Oh. Ha! But that’s not the algorithm we want – that one maximizes the probability of getting the cheapest gas; it doesn’t minimize the expected price of the gas we buy, which is what we want.”

“Oh, yeah, you’re right: if we apply that first algorithm, then in the likely event that we don’t get the very cheapest gas, there’s still a reasonable chance that we’ll end up with pretty expensive gas.”

“Right.”

“So what’s the strategy for minimizing the expected price of gas?”

“I don’t know.”

So, is there a probabilist in the house?

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