Re: [FT] OFFICIAL RULING REQUEST (was Re: Couple of questions)

On Wed, 3 Feb 1999, Laserlight wrote:
[snip]
> >salvo @ 3.5 missiles vs 0 PDS = (3.5 - 0) * 3.5 = 12.25 points
> >salvo @ 3.5 missiles vs 1 PDS = (3.5 - 0.8) * 3.5 = 9.45 pts
> >salvo @ 3.5 missiles vs 2 PDS = (3.5 - 1.6) * 3.5 = 6.65 pts
> 
> Your example here is not exactly right because you neglected the
possibility
> of PDS killing more missiles than are on target, which when taken into
> effect increases the	average damage.  No time to work out the figures
right
> now but the effect should be fairly small.

You're right, but the effect is larger than I would have thought. Using
a
matrix sum to work out the figures manually, a salvo missile against 1
PDS has
an actual average damage of 3.078 dice for 10.77 points of damage -
instead of
the 2.7 dice/points I originally estimated. This is an increase of +14%
over
my original figure.

Here's the matrix I used - at least this time I know the figures are
correct.
:)

S/P| 1	2  3  4  5  6
---+-----------------	
 1 | 1	1  1  0  0  0
 2 | 2	2  2  1  1  0
 3 | 3	3  3  2  2  1, reroll PDS
 4 | 4	4  4  3  3  2, reroll PDS
 5 | 5	5  5  4  4  3, reroll PDS
 6 | 6	6  6  5  5  4, reroll PDS

The row header represents the die roll of the PDS, the column header
represents the salvo missile number roll, while the table contents
represent
the number of missiles that make it through the PDS fire (vs 1 PDS). 
Recurse
the table on rerolls.  The proper probability is therefore expressed by
the
following:

Average number of salvo missiles vs 1 PDS =

    ( 3/6 + 8/6 + (14/6 + (3/6 * 1/6)) + (20/6 + (8/6 * 1/6)) 
      + (26/6 + (14/6 * 1/6) + (3/6 * 1/6 * 1/6))
      + (32/6 + (20/6 * 1/6) + (8/6 * 1/6 * 1/6)) ) / 6 = 3.078 missiles

Average damage = 3.078 * 3.5 = 10.77 points

===================================================================
Mark "Hauptmann" Shurtleff
  email: hauptman@sfcmd.com -or- hauptman@concentric.net
  visit the Gear Locker at http://www.sfcmd.com/HeavyGear/

 Finagle's Law:
   The perversity of the Universe tends towards the maximum.
===================================================================