[freeciv-ai] Re: Approximate win_chance

["Ross W. Wetmore" <rwetmore@xxxxxxxxxxxx>]

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.

>G.
>
>
>Attachment Converted: "c:\program files\eudora\attach\test1.c"

Cheers,
RossW
=====