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#11
08-23-2005, 11:47 PM
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Re: Dice Game
Looks like you worked through this a lot like I did, but I like your presentation here, makes it nice and easy to follow. I had it down as a messy recursion type deal, but that last line there
[ QUOTE ] EV(n) = 6 - 0.73*(5/6)^(n-6), for n > 6. [/ QUOTE ] seems to sum it up nicely in the closed form I was looking for. 
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#12
08-23-2005, 11:50 PM
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Re: Dice Game
[ QUOTE ]
Looks like you worked through this a lot like I did, but I like your presentation here, makes it nice and easy to follow. I had it down as a messy recursion type deal, but that last line there [ QUOTE ] EV(n) = 6 - 0.73*(5/6)^(n-6), for n > 6. [/ QUOTE ] seems to sum it up nicely in the closed form I was looking for. [/ QUOTE ] So I get the job?
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#13
08-24-2005, 02:25 PM
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Re: Dice Game
[ QUOTE ]
EV(n) = 6 - 0.73*(5/6)^(n-6), for n > 6 dice. [/ QUOTE ] One-upped again! I swear Bruce, if I wasn't such a nice guy, you'd totally be my arch-nemesis by now. [img]/images/graemlins/tongue.gif[/img]
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#14
08-24-2005, 04:50 PM
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<4.25
For the first situation:
If I roll 1-3, I will re-roll, as my expectation on a random roll (3.5) is higher than 1-3. If I roll 4-6, I will stand, as my expectation on a random roll (3.5) is lower than 4-6. So 50% of the time I will re-roll and stand with that number (on average 3.5), and the other 50% of the time I will stand with 4-6 (on average 5). 50%(3.5) + 50%(5) = 4.25 If I pay $4.25, that's break-even odds. So the gamble is profitable as long as I am paying less than that. (took me a minute and a half, I so could have done that on the spot ^_^)
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#17
08-24-2005, 11:45 PM
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Re: What job does your friend have anyway?
[ QUOTE ]
What job does your friend have anyway? [/ QUOTE ] Its some sort of investment finance stuff but he didnt get too specific, perhaps a back alley dice game manager or something. I havent heard from him since, but it seems that he got called back if they gave him 'homework'...I wonder if answering the first one right was enough to impress them.
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#18
08-24-2005, 11:46 PM
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Re: Dice Game
[ QUOTE ]
So I get the job? [/ QUOTE ] Hired!
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Linear Mode
