[GZG] lessons in dice

One quick point: 

Rolling 1 dice for 2 sixes or 3 sixes versus rolling 2 or 3 dice for the
same result -
equal probability! 

Proof: 

1 dice for two sixes in 2 rolls: 
Chance of getting a 6: 1/6. 
Change of getting 2 in a row: 1/6 * 1/6 = 1/36

2 dice for two sixes in one roll:
Chance of getting a single 6 on one die: 1/6
Chance of getting both dice as sixes: 1/6 * 1/6 = 1/36

Expand this to three dice, and you have:
1 dice, rolled 3 times, for 6, 6, 6: 1/6 * 1/6 * 1/6 = 1/216
3 dice, rolled once, for 6, 6, 6: 1/6 * 1/6 * 1/6 = 1/216

I figured most of us know that rolling two dice yields 36 possible
combos, only one of
which is double six. Similarly, roling 3 dice yields only one way to
generate an 18 for
your AD&D character's strength, one way out of 216 possibilities. That
works out to be
just the same as the odds of rolling 1 die for two sixes in a row or for
three sixes in a
row (respectively). So it doesn't matter if you throw Nd6 or d6 N times
to generate X
number of sixes. This logic applies beyond the number of dice = 3. 

Tom B
(just to settle that side point)
(Can we stop now, BTW, or do we need to open a new
gzg-math@csua.berkeley list...?)

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