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[freeciv-ai] Re: Approximate win_chance

[freeciv-ai] Re: Approximate win_chance

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To: "Ross W. Wetmore" <rwetmore@xxxxxxxxxxxx>
Cc: Raahul Kumar <raahul_da_man@xxxxxxxxx>, Gregory Berkolaiko <Gregory.Berkolaiko@xxxxxxxxxxxx>, freeciv-ai@xxxxxxxxxxx
Subject: [freeciv-ai] Re: Approximate win_chance
From: Raimar Falke <hawk@xxxxxxxxxxxxxxxxxxxxxxx>
Date: Thu, 25 Apr 2002 09:52:49 +0200
Reply-to: rf13@xxxxxxxxxxxxxxxxxxxxxx

On Wed, Apr 24, 2002 at 08:17:47PM -0400, Ross W. Wetmore wrote:
> At 02:02 PM 02/04/24 +0200, Raimar Falke wrote:
> >On Wed, Apr 24, 2002 at 04:08:41AM -0700, Raahul Kumar wrote:
> >> 
> >> <snip>
> >> > Bottom line for me: the proposed approximation is much to fragile.
> >> 
> >> I'm not with you on the logic train. Let's slam the brakes. Greg's
> >> approximation is far better than the current one, which just squares the
> >> results.
> >
> >AFAIK the current win_chance isn't an approximation but returns the
> >exact value. Or do I'm mistaken about that?
> If I am not mistaken, you cannot compute the exact value since that is
> determined randomly. 

> And if you are only estimating the chance

This is what is done.

> , then "exactness" is not a particularly hard criteria - certainly
> not the determining one.

Yes the wording was bad.

> >> It has a much smaller absolute error and and the error occurs fewer
> times than
> >> the current implementation. That's good enough for inclusion.
> This is a more sensible way to approach this kind of thing.
> The only thing to add is maybe some "risk" assessment that it won't be bad
> in a particularly sensitive area.
> [...]
> >> > 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.
> >> 
> >> Not asking for much are you?
> >
> >As I said this would be the ideal solution. If the current win_chance
> >returns the correct value we have to have an estimation of the error
> >which a new win_chance will produce.
> I think the estimations have been done. They seem to indicate that the
> 5th power solution is better than the current 2nd power one and almost
> indistinguishable from the more explicit estimation of chances.

> Since none of this really affects anything critical in the game, the 

And this is a question which is still unanswered for me: How do you
(the ai developers) that a particular code construct needs the "exact"
value (as returned by win_chance) and when does it can cope with an
approximation (which has an average/maximal error of something)? I
suspect that you don't do this decision based on hard facts.

> speed differential should seem to be the overwhelming consideration.

So what is the speed difference between x^2 and the new x^5?

> Even the explicit win_chance() computation is probably worth throwing 
> out when it is that expensive in comparison for no significant increase
> in benefit.

How do you estimate the benefit?


 email: rf13@xxxxxxxxxxxxxxxxx
 "Premature optimization is the root of all evil."
    -- D. E. Knuth in "Structured Programming with go to Statements"

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