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[freeciv-ai] Re: Approximate win_chance

[freeciv-ai] Re: Approximate win_chance

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To: Gregory Berkolaiko <Gregory.Berkolaiko@xxxxxxxxxxxx>
Cc: freeciv-ai@xxxxxxxxxxx
Subject: [freeciv-ai] Re: Approximate win_chance
From: Raahul Kumar <raahul_da_man@xxxxxxxxx>
Date: Thu, 18 Apr 2002 18:54:56 -0700 (PDT)

--- Gregory Berkolaiko <Gregory.Berkolaiko@xxxxxxxxxxxx> wrote:

I like your approximation better than the current system. You have me convinced
that your way is better. 

> Current system:
> A_rating = A_strength * A_HP * A_FP;
> D_rating = D_strength * D_HP * D_FP;
> chance = A_rating^2 / ( A_rating^2 + D_rating^2 )
> My formula:
> chance = A_rating^5 / ( A_rating^5 + D_rating^5 )
> I believe diminishing returns kick in sharply. Would using the formula 
> chance = A_rating^6 / ( A_rating^6 + D_rating^6 )
> fix the problem of absolute error sometimes being 15%. You should have
> mentioned how often those values crop up. 
> 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.

> This performs way better but for some weird cases it still gives an 
> absolute error of about 15%.
> Is there any way we can avoid calling approx win_chance when that happens?
> The problem is that I don't know beforehand when such thing would happen.  
> But I am still thinking about it...

There must be a range of some weird values. 


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