ASL and the joy of mathematics

Hi,

last week-end I and 15 other guys met in Lyon, France, for a small
tournament that's been happening for several years now. The attendance
was mostly French (obviously) with people from Lyon, Marseille and
Lille. But there was an international element with yours truly from
nearby Switzerland, as well as Tim "American by birth, French by heart"
Hundsdorfer - who, I was very pleased to learn, doesn't live all that
far from my place. Great fun and excellent food was had by all :-) Many
thanks to Lionel Dondé and his team for organizing this.

I will not go too much into the details of the tournament, let's just
say I finished at rank 12 out of 16, my best performance so far. For
more details, use either your highschool French skills or Google
Translate on the French ASL forum:

http://aslforum.histofig.com/smf/index.php?topic=9615.0

During the one game I won (ESG91 It's not over, with me as the French),
a most unlikely thing happened:

- my opponent easily passed a MC, but triggered my sniper (nothing
incredible so far)
- the Sniper rolled a 1 (rare, but OK, such things happen)
- after moving the Sniper, the nearest enemy stack was a Melee
containing a very scared HS on my side, a 9-2 Leader + 2 squads + the
enemy Sniper (you don't get such targets everyday, right?)
- I decided not to target the Axis Sniper and rolled for Random
Selection; guess what, I got the Leader!
- both Squads rolled boxcars for their LLMC!

Needless to say, this cleared up the situation quite a bit for me. I
mean, what were the odds?

WHAT WERE THE ODDS? I couldn't leave this question unanswered and
decided to investigate.
Here are the steps we can use to calculate the final probability:

1) Sniper rolls 1, easy, that's 1/6 = 16.67%
2) both squads roll boxcars, easy too, that's 1/36 times 1/36 = 0.077%
3) Random selection hitting the Leader, this is more complicated:
 - the Leader dr could be 6, and he would be hit in all cases (100%, or
216/216 as we'll use it here);
 - it could be 5, and all other drs should be 5 or less, with odds of
5/6 * 5/6 * 5/6 = 25/216;
 - it could be 4, and all other drs should be 4 or less, with odds of
4/6 * 4/6 * 4/6 = 64/216;
 - and so on until Leader dr = 1 and odds of 1/6*1/6*1/6 = 1/216;
 - now we add all these odds multiplied by 1/6 (probability of each
possible Leader dr) for a total of
   1/6 * 395/216 = 30.48% (I was surprised by this rather high number

So the final probability of this result (neglecting the original MC,
which we could evaluate easily
if needed, and Sniper direction, which is almost impossible to determine
in my opinion) is

16.67% * 0.077% * 30.48% = 0.0039%

I feel even luckier now that I know the number :-)

Alain Borel
Switzerland

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