RE: [Bug-gnubg] Analysis of race rollouts

[Ian Shaw]

> From: Joseph Heled [mailto:address@hidden
> Sent: 29 October 2002 16:55
> 
> I am still working on analyzing and thinking about the races results. 
> 
> Ian Shaw wrote:
> > 
> 
> > As Joseph notes, the rollout might be wrong. With 97507 
> positions, we can expect some of them to produce results 
> outside the 95% CI. Would comparing the rollout to Sconyers' 
> or Trice's databases prove anything?
> > The OSRDB might be wrong in positions where two sided 
> database might get it right. E.g. desperate situations where 
> you need to play to take advantage of specific doubles. I 
> guess it's not surprising if 2-ply gets some of these but 
> OSRDB can't. Is it possible to find the error rate for OSRDB 
> supplemented by the two sided database when the position 
> falls within the scope of the latter?
> > Jørn's been slaving away at extending the OSRDB, but are we 
> getting anything extra from it if 2-ply is just as good/better?
> 
> It is much faster, and it works for any position, but I think 
> the point is
> valid. That is why making this "unbiased benchmark" is so 
> important. Now we will
> be able to make informed decisions.
> 

The OSRDB makes the play that bears off in fewest average moves. The real 
objective is to bear off in fewer moves than your opponent. Usually these are 
the same thing, but not always, as we discussed above. Many of the times when 
one needs to make desperation  plays would be included in the two-sided 
database, so we can forget about them. There are still times in longer races 
when it is right to make a desperation play, either pull off a miracle win or 
to improve your gammon chances when the win is certain. I'm wondering whether 
there is a way to take account of these factors while using the OSRDB.
The distribution of rolls required to bear off for either side is appromimately 
normal, and Jorn is already thniking about including this in the database.
Is there some algorithm that compares two independent normal distributions, and 
which can maximize P(Ra < Rb) where Ra and Rb are the number of rolls each side 
requires to bear off? This sounds like the sort of thing that statisticians 
would have got nailed by now.
-Ian