[freeciv-ai] Re: Approximate win_chance

[Gregory Berkolaiko <Gregory.Berkolaiko@xxxxxxxxxxxx>]

On Fri, 19 Apr 2002, 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.

Too wild a guess.  I am giving this question as a degree project, I'm sure 
some poor student will decide to go for it, so if he succeeds we'll know 
the answer in a year's time.

G.