The document discusses various cube action scenarios in backgammon during the bear off phase, emphasizing the importance of decision-making in high-stakes situations where equity differences are significant. It presents multiple problems involving cube actions with the correct answers, detailing the implications of doubling and passing based on the game's positions and probabilities. Key strategies are also outlined, such as the optimal approach to bearing off and the significance of not placing checkers on the same point.

1. Bear off cube action
by mochy
@ Merit Backgammon Open 2013

2. Today’s agenda
1) N roll vs N roll
2) Two men bear off

3. Why Important?
Each decision in the bear off is CRITICAL
as Equity difference is usually very large.
Cube gets high in the end game much
more often.
It shows the nature of the game. You
can’t win without taking a risk.

4. True N roll vs N roll
1) All checkers
are piled on the
low points.
2) You never miss.
3) All doublets
should work.

5. Problem 1
White on roll. Cube action?
1) No double
& Take
2) Double &
Take
3) Double &
Pass

6. Problem 1 answer
3) Double & Pass
Red has only
21%.
Much lower
than 25%.

7. Correct Cube Action
2 roll vs 2 roll = Double / Pass
14%
3 roll vs 3 roll = Double / Pass
21%
4 roll vs 4 roll = (Re)Double / Take 25.5%
5 roll vs 5 roll = Double / Take 28%
(No redouble)

8. Problem 2
White on roll. Cube action?
1) No double
& Take
2) Double &
Take
3) Double &
Pass

9. Problem 2 answer
2) Double & Take
White loses
with 21.
(Red redoubles
and white must
pass)
5.5% + 21% > 25%

10. Problem 3
White on roll. Cube action?
1) No double
& Take
2) Double &
Take
3) Double &
Pass

11. Problem 3 answer
2) Double & Take
32, 31, 21 are
misses.
6/36 = 17%
17% + 14% > 25%

12. Problem 4
White on roll. Cube action?
1) No double
& Take
2) Double &
Take
3) Double &
Pass

13. Problem 4 answer
2) Double & Take
1) 11, 22 don’t
work.
2)Rolling an
ace three
times!
3)21, 21 makes
red redouble!

14. Problem 5
White on roll. Cube action?
1) No double
& Take
2) Double &
Take
3) Double &
Pass

15. Problem 5 answer
3) Double & Pass
Both sides have
non working
doublets. (11, 22,
33)
It hurts Red
much more !
Red needs to roll
doubles, White
doesn’t.

16. Two men bear off

17. Problem 6
White to play 21.
1) 6/3
2) 5/2
3) 6/4
5/4

18. Problem 6 answer
1) 6/3
5&3
14 numbers
6&2
13 numbers
4&4
11 numbers

19. The rule
1 ) If you can bear off, do so.
2) Never put checkers on the same point
3) Magic Number “31524”
It is the ranking of the gap between two
checkers.
3 pips apart is the best, 1 pip apart is the
second… and so on.

20. Problem 7
1) 6/2
2) 5/1
3) 6/3
5/4

21. Problem 7 answer
1) 6/2
5 & 2 – 19 numbers
(3 pips apart)
4 & 3 – 17 numbers
(1 pip apart)
6 & 1 – 15 numbers
(5 pips apart)

22. Problem 8-1
White on roll. Cube action?
1) No double
& Take
2) Double &
Take
3) Double &
Pass

23. Counting
1) Count the lesser!
2) Count them in order. (from big to small
or vice versa)
3) Count non-doublet first, multiply by 2,
then go for doublet.
- 65, 64, 63, 62, 61, 54,,,,21. (multiply by 2)
- 66, 55, 44, 33, 22, 11

24. Problem 8-1 answer
2) Double & Take
19 numbers are
little more than
18.
You are a tiny
favorite.

25. Flip a coin?

26. Problem 8-2
White on roll. Cube action?
1) No double
& Take
2) Double &
Take
3) Double &
Pass

27. Problem 8-2 answer
2) Double & Take
White would miss
with any 1 except
11. (10 numbers)
10 numbers is
more than 9.
(9/36 = 25%)

28. 2 & 2 is a STRONG double

29. Problem 9
White on roll. Cube action?
1) No
redouble
& Take
2) Redouble
& Take
3) Redouble
& Pass

30. Problem 9 answer
1) No Redouble & Take
White is only a tiny
favorite (flip a coin!)
Don’t give red a
chance to offer a
very strong
redouble!
Also known as
“Jacoby Paradox”

31. Problem 10
White on roll. Cube action?
1) No double
& Take
2) Double &
Take
3) Double &
Pass

32. Problem 10 answer
3) Double & Pass
To take, your
position needs to
be better than
your opponent.
Or you must have
an instant
redouble if he
misses.