Scott Turner (srt@sun-dimas.aero.org)
Fri, 23 Sep 1994 08:08:01 -0700

In message <9409231139.AA10908@capitalist.princeton.edu>you write:
>An "average AF" of a stack is just not a meaningful concept in
>Olympian combat.

It's not? All other things being equal, a stack with a higher AAF will
beat a stack with a lower AAF. But I think what you're saying is that
AAF alone isn't a good predictor of outcome. Of course I agree with
that.

>If you don't believe that a stack with a peasant leader and a dragon is
>stronger against any enemy than a dragon alone, imagine that the peasant
>misses whenever it gets to attack... But if the peasant never hits and can
>never be hit, the combat proceeds as if he wasn't there.

No. Even if the peasant has a zero attack value, he definitely has an
effect on the battle. The peasant is making some attacks which the
dragon would be making if the peasant wasn't there.

Consider 1 dragon vs. 2 knights. The dragon makes 1/3 of the attacks
and the other 2/3 are by the knights against the dragon. Add a
peasant to the dragon's side, and now the dragon is only making 1/4 of
the attacks (the peasant is making 1/4 and the knights are making 1/2
the attacks against the dragon).

To look at it another way, without the peasant the dragon stack got
1/3 of the attacks at an AAF of 500 and receives 2/3 of the attacks at
the AAF of a knight. With the peasant, the dragon stack gets 1/2 the
attacks at an AAF of 250 and receives 1/2 the attacks at the AAF of a
knight.

So it isn't as if the peasant isn't there. His presence changes the
balance of attacks between the two sides. Whether he weakens the
stack overall or strengthens the stack overall depends upon the
balance between the benefit of fewer attacks *against* the dragon and
the disadvantage of fewer attacks *by* the dragon.

But as I say, it appears that this balance is always in favor of
adding the peasant to the stack. (Actually, in at least one case it
is a wash. Adding a peasant to a 1 vs. 1 battle is a wash.)

-- Scott T.

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