# Re: Pathological combat examples

Scott Turner (srt@sun-dimas.aero.org)
Thu, 22 Sep 1994 12:08:16 -0700

Ed has been attempting to come up with 4:1 counterexamples using
archers. This is a little bit problematic. Missile combat isn't
really handled realistically in Olympia right now. Missile combat is
one area where you should be able to get more than 4:1 ratio on a
defender -- especially against a large defender like a dragon. But
anyway...

>4-in-1 rule, no breaking
>========================
>Side A: L lions (100 att/defense)
>
>Side B: 1 super-dragon (1000 attack/defense)
> M blowpipers (2 attack & defense, 25 missle), behind 9
>
>You want M/L to be large enough so that the 4-in-a-row rule is fairly common.
>M/L ~= 4-6 should do it.
>
>Choose values of L & M such that M blowpipers are a near-even match
>to L-11 lions.

I'm not sure how to choose M and L given these two conditions. Maybe
you can give me some actual numbers (I know you mathematicians hate
that, but my simulator insists on it :-). Certainly in all the
battles I ran, if M/L > 4, the archers win easily. But here are some
examples for N archers + 1 (5000,5000) dragon vs. 10 lions and N
archers + 1 rockthrower, no breaking:

wins for archers (%), 1000 trials
N -rock +rock
1 54 51
2 60 58
3 60 61
4 68 66
5 71 69
6 74 69
7 75 71
8 76 77
9 80 80
10 82 82
11 84 83
12 88 86
13 87 89
14 89 92
15 91 92
16 94 95
17 95 95
18 95 97
19 97 97
20 99 98

Some of the differences are likely to be statistical abberations, but
at least at the low end there is a real loss of effectiveness by
adding the rockthrower. In 10K trials, -rock 54%, +rock 52%. The
weird thing here is that the 4:1 rule in this case is applying to the
*other* side. The addition of the rockthrower reduces the attack
effectiveness of archer stack, but this doesn't overwhelm the defense
bonus until the archer stack gets a lot of attacks -- which doesn't
happen unless the other side is limited by the 4:1 rule! Strange.

I can try to make this more apparent by beefing up the lions side (to
give the attackers more attack chances). Fighting 25 lions, -rock:
7.76% +rock: 6.33%.

So there you go. There is an extreme case under the 4:1 rule where
adding a certain kind of unit to a stack can make it less effective.

-- Scott T.

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