Bear off cube action

by mochy @ Merit Backgammon Open 2013

1) N roll vs N roll

2) Two men bear off

Today’s agenda

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.

Why Important?

True N roll vs N roll1) All checkers are piled on the low points.

2) You never miss.

3) All doublets should work.

1) No double & Take

2) Double & Take

3) Double & Pass

Problem 1White on roll. Cube action?

Red has only 21%.

Much lower than 25%.

Problem 1 answer3) Double & Pass

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)

Correct Cube Action

1) No double & Take

2) Double & Take

3) Double & Pass

Problem 2White on roll. Cube action?

White loses with 21. (Red redoubles and white must pass)

5.5% + 21% > 25%

Problem 2 answer2) Double & Take

1) No double & Take

2) Double & Take

3) Double & Pass

Problem 3White on roll. Cube action?

32, 31, 21 are misses. 6/36 = 17%

17% + 14% > 25%

Problem 3 answer2) Double & Take

1) No double & Take

2) Double & Take

3) Double & Pass

Problem 4White on roll. Cube action?

1)11, 22 don’t work.

2)Rolling an ace three times! 3)21, 21 makes red redouble!

Problem 4 answer2) Double & Take

1) No double & Take

2) Double & Take

3) Double & Pass

Problem 5White on roll. Cube action?

Both sides have non working doublets. (11, 22, 33) It hurts Red much more !

Red needs to roll doubles, White doesn’t.

Problem 5 answer3) Double & Pass

Two men bear off

1)6/3

2)5/2

3)6/4 5/4

Problem 6 White to play 21.

5 & 3 14 numbers

6 & 2 13 numbers 4 & 4 11 numbers

Problem 6 answer1) 6/3

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.

The rule

1)6/2

2)5/1

3)6/3 5/4

Problem 7

5 & 2 – 19 numbers (3 pips apart)

4 & 3 – 17 numbers

(1 pip apart)

6 & 1 – 15 numbers

(5 pips apart)

Problem 7 answer1) 6/2

1) No double & Take

2) Double & Take

3) Double & Pass

Problem 8-1White on roll. Cube action?

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

Counting

19 numbers are little more than 18.

You are a tiny favorite.

Problem 8-1 answer2) Double & Take

Flip a coin?

1) No double & Take

2) Double & Take

3) Double & Pass

Problem 8-2White on roll. Cube action?

White would miss with any 1 except 11. (10 numbers)

10 numbers is more than 9.(9/36 = 25%)

Problem 8-2 answer2) Double & Take

2 & 2 is a STRONG double

1) No redouble & Take

2) Redouble & Take

3) Redouble & Pass

Problem 9White on roll. Cube action?

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”

Problem 9 answer1) No Redouble & Take

1) No double & Take

2) Double & Take

3) Double & Pass

Problem 10White on roll. Cube action?

To take, your position needs to be better than your opponent.

Or you must have an instant redouble if he misses.

Problem 10 answer3) Double & Pass