tag:blogger.com,1999:blog-4136837714240263955.post9001855333688414942..comments2016-11-29T12:12:24.606-08:00Comments on Standard Hat Rules Apply: Bit In A BottleKory Stevenshttp://www.blogger.com/profile/12086597476822194991noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-4136837714240263955.post-63129627014301469342010-01-16T11:59:08.391-08:002010-01-16T11:59:08.391-08:00You have $N initially, as stated in the problem.
...You have $N initially, as stated in the problem.<br /><br />If you only have $1, you don't NEED to get the first one right, unless you want to guarantee the money you end with. It is possible to come up with a strategy that simply maximizes the expected money you end with.<br /><br />The strategy that I use for the answer does guarantee the money you end with though, rather than expected value (so, in the N=1 case, it simply asks "is the outcome of the first flip heads?", and plays only that one flip). I am not sure how large the class of strategies that maximizes expected money is.Kory Stevenshttps://www.blogger.com/profile/12086597476822194991noreply@blogger.comtag:blogger.com,1999:blog-4136837714240263955.post-44351555108900674762010-01-15T13:38:27.805-08:002010-01-15T13:38:27.805-08:00How much initial money do you have?
If you only ha...How much initial money do you have?<br />If you only have $1 you NEED to get the first one right... There is a losing condition given, but how much do you need to lose in order to LOSE-lose.McAnerbothttps://www.blogger.com/profile/04363796760400032129noreply@blogger.comtag:blogger.com,1999:blog-4136837714240263955.post-90716777685861925392010-01-14T16:58:58.159-08:002010-01-14T16:58:58.159-08:00I know how to win a dollar! That's good right?...I know how to win a dollar! That's good right? The answer is to ask if the first flip is heads... O_o<br /><br />How about a slightly better bad answer:<br />"Are there more heads than tails in the first N flips?"<br /><br />If yes, say heads every time, if no, say tails every time. At worst you'll break even.<br /><br />You should be able to do better by figuring out when you should quit the game. If there's a critically huge string of victories then I need to stop playing... statistically anyway.<br /><br />Those my initial thoughts. That and the title 'bit in a bottle' is clever.JonBenhttps://www.blogger.com/profile/03435182054451716696noreply@blogger.com