[GZG] Re: laser classes

I respectfully disagree.

Tell you what, we each roll some dice 10,000 times (rerolling 6's). I'll roll
mine in chunks of 4, you'll roll yours as individuals (so I'm only going to
roll 2,500 times). Everytime we roll EXACTLY 4 6's, we pay the other guy a
dollar. I'll guarantee you I'll end up on top. Everytime we do it, I'll end up
paying you about 50 dollars, you'll end up paying me about 300.

The mistake you're making is that you're assuming independence between dice
rolls. There IS dependence between set of rolls (within a set of rolls it's
independent). Where I'm defining a set as a fistful of dice (4 in this case
versus 1). The dependence between sets of rolls is that you don't get to roll
that dice again if you don't roll a 6!

Or to use your example from below (hopefully I get all the numbers correct):

Probability of rolling EXACTLY 4 6's when rerolling 6's (everthing in a
parathensis can be viewed as one "roll (of potentially multiple dice)")

1 dice:
1st   2nd   3rd   4th	5th
(1/6) * (1/6) * (1/6) * (1/6) * (5/6) = 0.00064

2 dice:
(1/6 * 1/6) * (1/6 * 1/6) * (5/6 * 5/6) +
(1/6 * 1/6) * 2(1/6 * 5/6) * (1/6) * (5/6) +
2(1/6 * 5/6) * (1/6) * (1/6) * (1/6) * (5/6) =
5 * (1/6)^4 * (5/6)^2 = 0.002679

3 dice
(1/6 * 1/6 * 1/6) * 3 (5/6 * 5/6 * 1/6) * (5/6) +
3 (1/6 * 1/6 * 5/6) * (1/6 * 1/6) * (5/6 * 5/6) +
3 (1/6 * 1/6 * 5/6) * 2 (1/6 * 5/6) * (1/6) * (5/6)
3 (1/6 * 5/6 * 5/6) * (1/6) * (1/6) * (1/6) * (5/6) =
20 * (1/6)^4 * (5/6)^3 = 0.0089

4 dice
(1/6 * 1/6 * 1/6 * 1/6) * (5/6 * 5/6 * 5/6 * 5/6) +
4 (1/6 * 1/6 * 1/6 * 5/6) * 3 (1/6 * 5/6 * 5/6) * 5/6 +
6 (1/6 * 1/6 * 5/6 * 5/6) * (1/6 * 1/6) * (5/6 * 5/6) +
6 (1/6 * 1/6 * 5/6 * 5/6) * 2 (1/6 * 5/6) * (1/6) * (5/6) +
4 (1/6 * 5/6 * 5/6 * 5/6) * (1/6) * (1/6) * (1/6) * (5/6) =
35 * (1/6)^4 * (5/6)^4 = 0.013

Hopefully this makes some sense,

Daryl

> On 10/24/05, B Lin <lin@rxkinetix.com> wrote:
For
> a total of 2 in 18 or 1 in 9.
gzg-l-bounces+tom.mccarthy=xwave.com@lists.csua.berkeley.edu
> ]

<sotto voce> boy, that horsemeat must be pretty well tenderized now
....

_______________________________________________
Gzg-l mailing list
Gzg-l@lists.csua.berkeley.edu
http://lists.csua.berkeley.edu/mailman/listinfo/gzg-lMuch better morally
to beat a dead horse than a live one.

Roger

> On 10/25/05, Laserlight <laserlight@quixnet.net> wrote:

It's not a horse, it's an alien, and we're practicing to be on the Narn Bat
squad....

;)

--Binhan

[quoted original message omitted]