Re: Shields, was Re: Armor (long)

At 12:21 PM 11/8/96 EST, Brian Bell wrote:
>Below are some stats that take into account losses to threshold rolls.
<<snip>>
>Chance to reduce screens at 1st threshold roll:
>  no reduction:	    83% (5/6,10/12,15/18) (.833333)
>  loose at least 1 level:  17% (1/6, 2/12, 3/18) (.166666)
>  loose at least 2 levels: 8-11% (1/12,2/18) (.083333-.111111)
>  loose all screens:	     6% (1/18)		  (.055555)
>  *NOT cumulative! 17% contains the 8-11% which contains the 6%

I don't think your stats are correct. Take the "no reduction" line
above.
With one shield there is a 5/6 chance that the ship will not lose a
shield.
However, with 2 shields, the possibility of not losing a shield is not
10/12, it is 25/36. With two shields you roll two dice (one per shield)
meaning that there are 36 possible dice combinations. You lose one
shield in
any of the following combinations: 1,6; 2,6; 3,6; 4,6; 5,6; 6,1; 6,2;
6,3;
6,4; 6,5. You ALSO lose two shields with a 6,6. Out of 36 possible dice
combinations, 11 of them result in at least one shield dropping. (Or,
there
is a 5/6 chance of not losing a shield in a level 1 ship, and a 5/6 *
5/6
chance of not losing a shield in a level 2 ship.)

It's even more pronounced with 3 shields. There are 216 combinations.
There
are 91 shield dropping combinations out of 216 (if I've done the math
correctly) for three shields, or a 42.13% chance that NO SHIELD will be
dropped when checking three shields. You lose 2 shields in 15/216
combinations, and three shields in 1/216 combinations.

So the loses are: 
no reduction:	 5/6 for L1 ship, 25/36 for L2 ship, 125/216 for L3 ship
lose at least 1 level: 1/6, 12/36, 91/216
lose at least 2 levels: 0/6, 1/36, 16/216
lose 3 levels: 0/6, 0/6, 1/216

This error gets bigger at the second threshold. For ships with 2
shields,
there are 16 combinations of 36 that result in the loss of one shield,
and 4
that result in the loss of two shields. This means that there is a 16/36
chance that a level 2 ship will not lose a shield. For level 3 shields,
the
chance of not losing a shield is 64/216.

Unfortunately, this error makes the rest of your analysis inaccurate.

Allan

Allan Goodall:	agoodall@sympatico.ca 
"You'll want to hear about my new obsession.
 I'm riding high upon a deep depression. 
 I'm only happy when it rains."    - Garbage