Re: [Bug-gnubg] Match math mysteries

[Joern Thyssen]

On Sun, Dec 14, 2003 at 06:13:36PM +0100, Petr Kadlec wrote
> 
> Now you may ask, where I see any problem? The problem is that according to 
> gnubg analysis, the situation is "Optional double, take". OPTIONAL? HOW SO?

gnubg reports the cube as optional when there are no market losers.

> I have tried more positions, and even when gnubg says the position is 
> "double, take", the difference between this and "no double" is very small. 
> I would expect the difference to be equal to (1 - C) * Ps, for C = 0.7 it 
> is 0.3 * Ps. For example, in position 3N0BAIB77wEAAA, gnubg reports 
> P(win)=0.227, with double/take MWC (correctly) equal to that, but no-double 
> MWC is reported to be also equal to 22.67%, although I would expect it to 
> be 0.7 times smaller (ca 16%). But a rollout result is the same -- no 
> difference...

The cubeful MWC is 22.7% (I'll explain below) but you're right that the
cubeless MWC is 16%. However, gnubg uses cubeful equities for cube
decisions, and as the equity for "no double" is equal the equity for
"double, take" the decision is reported as "optional double".

Your opponents drop point is 30%, and gnubg finds no sequence that
gives you more than 70%, so you might as well wait with the double. The
idea is to double closer to 70% and hope the opponent makes a mistake.

The same delay technique is often used at -1,-3 post crawford where the
gammonless take point is below 2% for the leader. The first rolls the
mandatory "double" is optional.

Jørn

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