24 23 22 21 20 19 18 17 16 15 14 13
| O O X O | | O O X |
| X O | | O O X |
| X | | O X |
| | | |
| | | |
| | | |
| | | |
| | | |
| O X | | |
| O O X X | | X X |
| O O O X X | | X X |
1 2 3 4 5 6 7 8 9 10 11 12
X needs 5, O needs 6. Centered cube. Cube action?
Thanks to Michael J. Zehr, Barry Miller and Kit Woolsey for giving
their comments on this position. Both Michael and Barry think
that it is not a double and a take. Kit passes against a strong
opponent, and would try to tailor his doubling decision to
The position came up in a recent FIBS match between me and
Rick (rikjan) Janowski. I doubled and Rick passed. I think
I would still double, but I have no idea whether or not it's
Michael and Kit both made a point that was educational for
me: in a low variance position, if the opponent is currently
passing, then the opponent will probably be passing next roll.
I am used to thinking about low variance in terms of taking: if
the opponent is currently taking, and the position is low variance,
then doubling is often incorrect because the opponent will
still have a take (or will still mistakenly take) next roll.
But the same reasoning applies to passing, which I hadn't
really thought about.
I think most backgame positions are low variance positions,
at least until the non-backgame player is or is near bearing
off. The backgame player typically has a strong defense, and
so cannot be blown off the board in a single roll. If the
backgame player has timing sufficient for the near term, and few
rolls force the backgame player to crash or give up some substantial
asset, then probably relatively little will happen over the
next two ply.
So when do you double? For a deep backgame with sufficient
timing, Robertie provides the heuristic of doubling when about
to clear the third point in front of the two anchors. But
most backgames are not well timed, so the non-backgame
player has a significant edge long before he or she starts
It is my belief that most players do not have a good grasp of the
proper dropping or taking action when playing a backgame with what is
somewhat inadequate timing and still many rolls before the bearin.
I know that I do not. If this belief is true, then one can expect
one's opponent to make a mistake often when doubled as the backgame player,
and so one should be more inclined to double.
So there are conflicting heuristics: as the defender against
the backgame, one has a low variance position, and so generally
should not double, but the player with the backgame may be more likely
than normal to make a mistake, and so perhaps the defender should double.
Kit points out, as was pointed out by others on earlier problems, that
for many backgame problems, the strengths and inclinations of the players
is a very important consideration.
> if I were doubled as O, I would probably pass against a
> strong player but take against a weaker player, since X's skill in
> playing the position will have a big effect on my equity.
Kit goes on:
> Similarly, knowing the opponent makes a big difference in determining
> whether or not to double a back game. [...] if I were X and I
> was pretty sure my opponent would take [...] then I would not double,
> since [...] if he is taking now he will almost certainly take after the
> next exchange [...]. On the other hand, if I thought there was a good
> chance my opponent would pass, then of course I would double.
Putting this together, it seems that Kit believes that the low volatility
of the position is the more significant characteristic of the position.
Kit thinks that the position is probably a pass, when X is a strong
player, but he still would not double if he felt his opponent was taking,
since his opponent would still be taking next turn.
This makes sense, but now lets say you are playing someone, and you
have no idea of whether or not they will take or pass. I think this is a
very common situation. If you think the position is a pass, should you
double? I think you generally should. There are four possibilities:
Position is a Opponent will
1. take take
2. take pass
3. pass take
4. pass pass
First, consider possibilities 3 and 4, since you think the position
is probably a pass. First, if the reality is possibility 4, then
doubling is almost certainly the right way to go (I assume that you
are not too good to double). By the next roll, your position might
have gotten weaker so that your opponent will have a take, so its
best to claim the point now.
With possibility 3, you have clearly picked up some equity, since
the opponent made a mistake. Might you have picked up more by waiting?
Well, maybe. But on the other hand, among the successor positions
will be some which are weaker for you, perhaps making the take correct,
and there will be others which are stronger for you, perhaps enough
stronger that the opponent will now correctly decide to pass. So
my guess is that in general you gain from doubling with possibility 3.
With possibility 2, you again have gained since your opponent made
a mistake. As with possibility 3, it is possible that waiting
might gain more, but I suspect that more often you are better off to
get your opponent to make a mistake now, while you can.
Only with possibility 1 is there much chance of losing equity.
And if the position is really strong enough that you think it is
probably a pass, then to me it seems unlikely that you will give up
much equity by doubling, even if the position turns out to be a take.
In summary, if you have a strong position (say strong enough that you
think the position may be a pass), and you don't have any idea whether
your opponent will take or drop, then you should probably double, even
if the position is not very volatile. This is essentially Woolsey's
doubling rule, except that instead of considering whether you think the
position is a drop or a take, you are considering what your opponent
is likely to do.
Kit also wrote:
> For these reasons, I don't find analyzing cube decisions involving back
> games particularly interesting. The correct cube action is generally
> much more a function of your opponent than the actual position.
Decisions to double or not are always to some degree a function of
the opponent's characterstics, more so than taking decisions. And
I would agree with Kit that the double-no double decision in
backgames is less interesting than in most positions. Since in most
non-backgame positions players have a better sense of the correct
drop-take action than in many backgames, determining the technically
correct double-no double decision against an optimal opponent has more
value (than in a backgame problem).
However, taking decisions are much less a function of the opponent
than the double-no double decision. The strength of the opponent is
important, of course, but for weak players (like myself), one way to
improve is to find out what the correct taking decision should be
against a strong opponent. Although this may not optimize my winnings
when playing against a weak opponent, it will ensure that I lose less
to those strong players which I hope to join. Eventually I may even
learn to adjust my play based on the strength of the opposition, but
as a starting point, the best approach is to learn the correct cube
actions assuming reasonably strong opposition.
It is primarily with hope of learning something about the drop-take
decisions in backgames, assuming reasonably strong opposition, that
I am posting these problems. I am less interested in the
double-no double decision, for the reasons Kit describes. For myself,
I have no idea whether many early backgame positions are drops or takes.
For many other kinds of positions, I can just have a computer program
roll out the position, and determine relatively accurately whether
I should drop or take. But with the currently available backgammon
programs, backgame problems are not so easily solved.
This position is one where I think many players definitely have something
to learn (although I still don't know what it is). I have no idea
whether the position is a drop or a take against, say, your typical
1800-level FIBS player. My first impression was that it was a take.
Rick Janowski (FIBS rating 1834) dropped. Michael J. Zehr (rating 1845)
and Barry Miller (rating 1630) think it's an easy take. Kit
Woolsey (rating 1832) says its probably a pass. Who knows?
monty on FIBS