> I understand that, when 2-away, 2-away, one ought to double as soon as
> one has an advantage. If this is to be taken literally, should the cube
> always be turned on the 3rd or 4th move?
The short answer is "yes". This has been discussed at length
previously, so I will try to be brief.
It can be shown that it is always theoretically correct to double at
2-away 2-away (assuming the two players are of comparable strength).
It can be proven mathematically, and is almost immediately obvious to
those familiar with game theory.
In practice, one need not double if there are no market losers
(sequences leading to a correct double/drop). If there is even one
sequence (of the 21*21 roll combinations) where your advantage could
grow to the point where your opponent has a valid drop, then you must
double, or risk a "mathematical disaster".
Strong players will often delay doubling in the hope that the weaker
opponent will incorrectly drop when doubled in a position that is
difficult to assess. This is a valid tactic, in practice.
There is also some theoretical justification for the stronger player to
delay doubling until her advantage is somewhat greater than a 50% chance;
but in that case, the weaker side should be doubling sooner (even when
at a slight disadvantage). So it could be argued that other factors may
warrant not doubling, even if there are a few market losers, but this
is usually a specious way of thinking.
Doubling at 2-away 2-away is almost never wrong, whereas not doubling
could be an enormous error. So unless you have no respect at all for
your opponent, just turn the cube and concentrate on more important
things, like correct checker play.
> For example, if I start with 1 3 and my opponent follows up with a
> mediocre roll like 5 1, should I double?
Absolutely. If you roll 66, for example, your opponent could have a
legitimate drop next turn. This would constitute a potentially large
loss in terms of expected value. That risk is much higher than any
possible gain from waiting, so you must double immediately.
Cheers, - Darse.