tag:blogger.com,1999:blog-2800316528417070757.post1850360282210915055..comments2023-04-28T22:14:09.751+01:00Comments on Random Thoughts: A Slightly Harder Problem in Decision TheoryJohn Lawrence Aspdenhttp://www.blogger.com/profile/02587130870181071109noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2800316528417070757.post-57669416665621951212012-09-04T21:00:25.097+01:002012-09-04T21:00:25.097+01:00the two biased coins thing seems good, too.
i wen...the two biased coins thing seems good, too.<br /><br />i went ahead and simulated the 1d12 vs. 2d6 version,<br />using the strategy that seeing 1,2,3,11,12 imply 1d12<br />and seeing 5,6,7,8,9 imply 2d6,<br />and got 62.5% correct guesses (out of 10 million trials),<br />which leads me to agree that it's worth £125.<br />orion elenzilhttp://elenzil.comnoreply@blogger.comtag:blogger.com,1999:blog-2800316528417070757.post-31428305181989259772012-09-04T20:06:24.750+01:002012-09-04T20:06:24.750+01:00That would be a good start! This problem turns out...That would be a good start! This problem turns out to be much harder than I thought it was. <br /><br />Almost 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.<br /><br />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. John Lawrence Aspdenhttps://www.blogger.com/profile/02587130870181071109noreply@blogger.comtag:blogger.com,1999:blog-2800316528417070757.post-76164427331713037952012-09-04T18:54:25.984+01:002012-09-04T18:54:25.984+01:00seems like it'd be equivalent to ask about two...seems like it'd be equivalent to ask about two lists of flips from a fair coin and a loaded coin.orion elenzilhttp://elenzil.comnoreply@blogger.comtag:blogger.com,1999:blog-2800316528417070757.post-77231052383982856222012-08-14T19:57:12.516+01:002012-08-14T19:57:12.516+01:00You've got a monkey in the bag! Getting a 1 wo...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!<br /><br />Question is, will you go as far as a spit roast?<br /><br /><br />John Lawrence Aspdenhttps://www.blogger.com/profile/02587130870181071109noreply@blogger.comtag:blogger.com,1999:blog-2800316528417070757.post-76982445895074754082012-08-14T18:32:11.452+01:002012-08-14T18:32:11.452+01:00Aye, that's a good lolly of dosh. I'm too...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.<br /><br />If the number is a one, I win two monkeys. That's mint.<br /><br />If the number is a two or a twelve, I'd be a plank to think I knew the answer.<br /><br />If the number falls between two and twelve, I'd be nutter to bet on anything but 2D6.Anonymousnoreply@blogger.com