pair o' dice no paradox, men

Michael Andre-Driussi · 15 Dec 2001, 15:43 · from urth-v0031.mbox · original

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From: Michael Andre-Driussi <mantis at siriusfiction.com>
Subject: (urth) pair o' dice no paradox, men
Date: Sat, 15 Dec 2001 07:43:35 -0800
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Thanks Sunanda!

Joel Sieh also caught this and I thought he and I had posted to the list!
Here is my quote and response to him.

Joel Sieh wrote:
>>6 different throws on each of two sided dice gives us 36 possible throws.
>>
>>Possible combinations equalling 7:
>>
>>Die 1	Die 2
>>1	6
>>2	5
>>3	4
>>4	3
>>5	2
>>6	1
>>
>>Total combinations:  6
>>Probability =3D combinations equalling 7 / all possible combos
>>=3D 6 / 36 =3D 1 / 6 =3D 16.6%.
>>
>>Following these calculations, rolls of 2 or a 12 would each have a
>>probability 1 / 36.  I agree that these are much less probable than
>>rolling a 7 (the most probable roll with two six sided dice), but it seems
>>that 1 / 6 is still against the odds, if you consider "against the odds"
>>to mean less than 50%.
>
>Wow, you are right!
>
>What was I thinking?
>
>Well, I was working off the fact that in games involving two dice, 7 is
>the middle of the bell curve.  I was erroneously thinking in terms of the
>odds of rolling >=3D 7 or <=3D 7 (which is a 58% probability), rather than
>just 7.
>
>With regard to the text I was also puzzled as to why a 7 would mean death,
>when, for example, there are 10 men.  Up until the moment I typed it in, I
>sort of thought there were only 7 men, and the dice were saying how many
>would die (all, in this case); but the dice tell a group fate, not a
>fractional amount (all die or none die).  On my first reading I thought he
>was supposed to roll a number related to the number of crewmen, like, say
>>=3D 8 (42% chance).
>
>Even as I was typing it in this evening, and there was a glimpse of the
>truth (that rolling a 7 really is a 1/6 chance), I veered away from this
>and into the notion "Why not just use one die, if one-in-six is the
>desired probability -- then the roll of a =3D1=3D would make the whole thi=
ng
>quite obvious."  And the waste of a perfectly nice bellcurve (as opposed
>to the "flat" curve of a single die)!
>
>(The reason why one-in-six is important is made clear in the text: that is
>the fatality rate for sunmen.)
>
>The reason why a 7 means death is because that is the only way to squeeze
>out a 1 in 6 chance out of two dice!
>
>Anyway, I was wrong.  Thanks for correcting me! (I still wonder why
>Harness would choose to use =3Dtwo=3D dice when one die would work better.
>Well, work better for =3Dme=3D, at least!)
>

Addendum: we both arrived independently at the notion that Harness is
probably talking about the dice game "craps," which, in the
pre-wargaming/pre-rpg world, was the most common exposure to dice games.

=3Dmantis=3D


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