*I'd be surprised if a cat could do this. But it think it uses the exact same tools as the easy one.*

The eccentric millionaire Oswald Mega walks into a bar and he says:

"This morning, I was showing my newborn about Dungeons and Dragons. We took a couple of six sided dice and rolled them, and wrote the results, which are just numbers from 2 to 12, on a piece of paper with 2D6 written at the top.

Then we took a twelve sided dice, and we wrote 1D12 at the top of a piece of paper, and then we rolled it lots and wrote down the results, numbers between 1 and 12, on the paper.

How she laughed at the difference in the patterns! Truly fatherhood is a joy.

Now, I've brought one of the pieces of paper with me, and if you can tell me which one it is, I'll give you £1000.

How much would you be willing to pay me to know the value of the first number on the sheet?"

*And actually there might be some feline subsystem that solves a problem a bit like this.*

Aye, that's a good lolly of dosh. I'm too faced to bet any folding, but I might lay down a few bob or even a nugget 'cause I am feeling at the moment like a jammy trainspotter.

ReplyDeleteIf the number is a one, I win two monkeys. That's mint.

If the number is a two or a twelve, I'd be a plank to think I knew the answer.

If the number falls between two and twelve, I'd be nutter to bet on anything but 2D6.

You've got a monkey in the bag! Getting a 1 would lock in another. That makes the gen worth an apple on its own!

ReplyDeleteQuestion is, will you go as far as a spit roast?

seems like it'd be equivalent to ask about two lists of flips from a fair coin and a loaded coin.

ReplyDeleteThat would be a good start! This problem turns out to be much harder than I thought it was.

ReplyDeleteAlmost everyone including me initially thinks the answer is £125. But the same reasoning means that if you've already bought several numbers, the next one is absolutely worthless. Which is just silly.

The simplest version I can think of is where you've got a 2:1 heads-biased coin and a 2:1 tails biased coin. But I can't work out what the answer is for that either. Or even work out if there has to be an answer.

the two biased coins thing seems good, too.

ReplyDeletei went ahead and simulated the 1d12 vs. 2d6 version,

using the strategy that seeing 1,2,3,11,12 imply 1d12

and seeing 5,6,7,8,9 imply 2d6,

and got 62.5% correct guesses (out of 10 million trials),

which leads me to agree that it's worth £125.