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March 15th, 2011, 03:48 AM  #1 
Newbie Joined: Mar 2011 Posts: 2 Thanks: 0  Probability question with dice
Dear all I have a problem which seems very easy, but I still can't wrap my head around the math of it. If I roll a large series of 6sided dice, the average should be ca. 3.5. So far, so good. However, if I were allowed to always roll two dice, and pick the highest for each cast, what would be the new average? Surely, this isn't the same as rolling a certain amount of dice and simply crop the higher half of the results  or is it? I may be confusing myself with the procedure. Looking forward to your help! 
March 15th, 2011, 04:23 AM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Probability question with dice
Throwing two dice and taking the maximum: Each entry in the table has the same probability, so sum them and take the average. The array is symmetrical. Twice the upperright triangle + the leading diagonal = 2 (1.2 + 2.3 + 3.4 + 4.5 + 5.6) + (1+2+3+4+5+6) = 161 161 / 36 = 4.47222... 
March 15th, 2011, 04:55 AM  #3 
Newbie Joined: Mar 2011 Posts: 2 Thanks: 0  Re: Probability question with dice
Thanks, aswoods, it's quite clear now 

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