Complete.Org: Mailing Lists: Archives: freeciv-ai: April 2002: [freeciv-ai] Re: Approximate win_chance

# [freeciv-ai] Re: Approximate win_chance

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 To: "Ross W. Wetmore" Cc: Gregory Berkolaiko , Raahul Kumar , freeciv-ai@xxxxxxxxxxx Subject: [freeciv-ai] Re: Approximate win_chance From: Raimar Falke Date: Tue, 23 Apr 2002 21:41:53 +0200 Reply-to: rf13@xxxxxxxxxxxxxxxxxxxxxx

```On Fri, Apr 19, 2002 at 04:28:35PM -0400, Ross W. Wetmore wrote:
> At 12:57 PM 02/04/19 +0100, Gregory Berkolaiko wrote:
> >On Thu, 18 Apr 2002, Raahul Kumar wrote:
> >
> >> > Power 5 works best (better than 4 or 6).  Not very often.  You can
> >> > experiment with the code I attached.
> >>
> >> That's what I don't understand. I assume higher powers should always work
> >> better. More precision, less errors. Yet your results show differently.
> I am
> >> suspicious. I demand an explanation.
> >
> >I have no explanation.  This is the way things are.  In principle it is
> >possible to play with the win_chance formula (which is essentially
> >hypergeometric function) and maybe do some expansions and show why 5 is
> >the best, but I'm not interested in doing it.
>
> I suspect you will find that most battles are decided in multiples of 5
> rounds, i.e. 10, 20, 30 hitpoints with firepower of 1 or 2. On a wild
> hunch, this may make the 5th power term of any full expression dominant.
>
> If you restrict cases used to fp = 3, you might find 20 hp and 6/7 power,
> or generally an ~3rd power multiple shows up slightly better.
>
> That might at least indicate whether the number of rounds has something
> to do with it.

I have done some changes and factor (10.0 in the original test.c) is
indeed important. I have attached another version which shows the
quality of the approximation for various factors.

It turns out that the power of 5 minimized the error for the factor
8. A power of 6 prefers the factor 12. A power of 5.5 really make the
factor 10 the one with the minimum error.

Bottom line for me: the proposed approximation is much to fragile.
Bottom line 2: we have to carefully select the set of values we test
the approximation against. Best would be the whole possible set of
values. Or a real (not by simulation) mathematical calculation of the
errors we have to expect.

Raimar

--
email: rf13@xxxxxxxxxxxxxxxxx
"When C++ is your hammer, everything looks like a thumb."
-- Steven M. Haflich
```

test.c
Description: Text document