Quote:
Originally Posted by David Sklansky
But your words were essentially true. Markov chains? Power series? Cmon.
hey, some like heavy artillery. nothing wrong with that!
Oh, I see now
being funny
LOL
*****
the basic math
*****
1s and 6s (as the other faces are not relevant)
the probability of one or the other would be 1/6 + (1/6 + 1/6) = 1/2 = p
the craps principle there
the winning sequences
111 = p^3 = 1/8
6 = p^1 = 1/2
16 = p^2 = 1/4
116 = p^3 = 1/8
for the mean # of total rolls for either face1 wins or face6 wins
3* 1/8 + 1* 1/2 + 2* 1/4 + 3* 1/8 = 3/8+4/8+4/8+3/8 = 14/8=1.75
the average # of rolls to see either face1 or face6 = 6/2 = 3
3*1.75 = 5.25
for the mean # of total rolls given face1 wins =
3* (6/2) = 9
for the mean # of total rolls given face6 wins =
we have to normalize here (left to the reader as a fun exercise)
1.571428571*3=4.714285714 (rounded)
fun is fun
math is fun!