JF Cube strategy:
It does not do any volatility analysis, but that we may try to
get into a later version.
It first estimates the value of the cube for the take side
by multiplying his winprob by a factor 0.15, giving an eq-estimate E.
If E<0.5 it takes.
If E>L it doubles, only I don't quite remember the number.
Think L was set to about 0.32.
Note that the cube action from this alg. is not a function of equity only!
In a gammonish position, the underdog will win more games (cubeless)
than in a race, assuming identical equities,
and therefor he will have more use of the cube.
From rollouts I have gotten the impression that 0.15 is a bit low,
and maybe should be about 0.2.
It first calculates recube potental from the score as the fraction of extra
points from recube usefull (R). If the recube will be to 8, for example,
and it only needs 6 more points, only 2 of the 4 extra points put on the
line are usefull, so the recube potential from the score (R) = 0.5. It
estimates the cube value for the taker by multiplying his win prob by the
(1+0.15*R). It then checks if the matcheq gotten by immediately redoubling
is higher than the one the preceeding calculations give, and in that case
disregards the R.
Then it calculates the matcheq according to the corrected probabilities
using Kits table to get the double-take match eq (DT).
It then calculates the matcheq gotten from never cubing (N).
It then tabulates the matcheq from double-pass (DP).
If N>DP, it plays on automatically.
The intervall [N,DP] is the doubling window,
and it doubles if DT is bigger than a*N+(1-a)*DP.
We currently use a=0.4, which means that it doubles in the upper 40%
of the doubling window.
When either player needs more than 11 points we don't use eq charts,
but simply assume that each point is equally valuable,
and truncate the payoff when it exceeds the number of points needed.