On Mar 26, 4:49*pm, (Torben Ægidius Mogensen)
wrote:
...

The doubling cube is normally limited to 7 possible positions (absent
or 2, 4, ..., 64), ....

This is completely false. There is nothing wrong or problematic with
a double to 128. Admittedly, this can't be recorded on a normal
doubling cube but players can just write it down. Also, doubling
"cubes" are available which reach a max value of 256. Doubles beyond
64 are rare among good players, but if you're talking about what is
rare rather than what is legal, you shouldn't include 64 since good
players don't often let the cube get even that high.

Paul Epstein