> Here's something very odd:
> I rolled out Achim's first position, interrupting after 581 games
and
> saved it as an .sgf file. At that time, the rollout window was showing
> a cubeful equity of +1.01988 with a standard error of 0.56934. But
in
> the .sgf file, we find the following data:
>
> ;W[double]
> DA[X ver 3 Eq Trials 581
> NoDouble Output
> 0.7799348235 0.01718181372 0.0001586886356 0.007273085415
> 9.895129915e-05 0.5677405596 0.7075381875
> StdDev
> 0.02783757448 0.0009133279673 1.405134844e-05 0.0005356273614
> 2.413918082e-05 0.02059437521 0.0252378732
> DoubleTake Output
> 0.7841442227 0.0157496836 0
0.006656042766
> 0.0001128451986 0.5762649775 0.7096174955
> StdDev
> 0.001400601584 0.0009878044948 9.480622248e-05 0.0005143946619
> 2.456640868e-05 0.00280232681 0.000292532146
>
> wheras an export to text of the match says:
>
> Cubeful equities:
> 1. No double +1.01988
> 2. Double, take +1.06679 ( +0.04691)
> 3. Double, pass +1.00000 ( -0.01988)
> Proper cube action: Too good to double, pass (29.8%)
> Rollout details:
> Centered 1-cube:
> 0.77993 0.01718 0.00016 - 0.22007 0.00727 0.00010 CL +0.56774
CF +1.01988
> [0.02784 0.00091 0.00001 - 0.02784 0.00054 0.00002 CL
0.02059 CF 0.56934]
> Player bert owns 2-cube:
> 0.78414 0.01575 0.00000 - 0.21586 0.00666 0.00011 CL +1.16871
CF +1.06679
> [0.00140 0.00099 0.00009 - 0.00140 0.00051 0.00002 CL
0.00534 CF 0.00660]
>
> In the .sgf file, the NoDouble Output is the probability of win,
> win gammon, win backgammon, lose gammon, lose backgammon, cubeless
> equity, and cubeful equity, the StdDev just after is the Standard
> error for the above values in the same order.
>
> Ahs - I found where it happens, but I'm not sure it's wrong
>
> the last value in the NoDouble Output and DoubleTake Output is treated
> as match winning chance. For cubeless equity, the routine mwc2eq in
> eval.c is called. It takes the values from the MET for winning or
> losing and considers the equity to be a straigtline function from
> equity = -1 for the MET value of losing, +1 for the MET value of
> winning and finds the corresponding equity value for the MWC which
is
> input:
>
>
> * 2 * rMwc - ( rMwcWin + rMwcLose
)
> * rEq = ---------------------------------
> * rMwcWin -
rMwcLose
>
> (where rEq is the equity to be determined, rMwc is the rollout
> estimate of the match winning chance and rMwcWin and rMwcLose are
the
> Met mwc's for winning or losing this game at this cube value. This
all
> seems reasonable.
>
> For the std error, the caculcation done is:
>
> * 2.0 * rSeMwc
> * rSeEQ = ------------------
> * rMwcWin - rMwcLose
>
> where rSeMwc is the standard error of the MWC from the rollout
>
> This is what you'd get if you used the first formula with the rollout
> mwc and subtracted the result of using that formula with the rollout
> mwc minus one standard error.
>
> In the case of Achim's game,
>
> rMwc - 0.707538188
> rMwcWin = 0.706656933
> rmwcLose = 0.617999971
> rSeMwc = 0.0252378732
>
> the cubeful equity then comes out as 1.01988...
> but if rMwc is reduced by 1 std error so it becomes 0.6823003148
> then the cubeful equity becomes .45054245824484714466
> and similarly, if it's increased by 1 std error, it becomes 0.7327760612
> and then the cubefule equity becomes 1.58921775821734112657
>
> so plus/minus one std error in the rollout mwc really does appear
to
> correspond to plus minus 0.56933764998624699095 in equity.
The only strange thing to me here is the stderr in
the rollout result (in MWC) in the two cases (no double and double/take). I report the output here for clarity: