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Bad-Beat PUZZLE: Five checker bar-gammon - SOLUTION

Posted By: Nack Ballard
Date: Thursday, 6 August 2026, at 7:57 p.m.

In Response To: Bad-Beat PUZZLE: Five checker bar-gammon (Nack Ballard)

Backgammon puzzles attracted a lot of interest and responses here several years ago. Now, not so much. However, given that I worked on and posed this one, I may as well publish the solution.





White is Player 2

score: 0
pip: 168
Unlimited Game
Jacoby Beaver
pip: 96
score: 0

Blue is Player 1
XGID=cBBBB-B--AAAbA---ccbbA----:1:-1:1:00:0:0:3:0:10
Initial position: Blue to roll, White wins backgammon!

Bad-beat story alert.

Stick: "In the position [above] I'm Blue and on roll. From this position I lose a backgammon after taking a recube!!!" XG shows my opponent's backgammon chances to be 0% in the display panel. And no, no double fives were thrown. The game was played out perfectly" (according to XGR++).

Nack: The idea of my proposed puzzle is to figure out the minimum number of rolls (for each side) that satisfies the conditions indicated in boldface font above.

I added two extra credit nuances (the first of which probably happened to Stick but the second of which didn't happen to him):

(1) White closes out Blue.
(2) White bears off her last checker off when Blue still has five checkers on the bar.

The shortest sequence that meets all elements of Stick's bad beat plus my added conditions above is eleven rolls (each). Here is the solution (in traditional notation), with some intermittent diagrams beneath it:

-----------------------------------------------------------
11: 9/7 6/5(2)........... ....66: Bar/19(2) bar/13 [diag 1]
65: 21/10.................... 61: 19/18*/12*
21: Bar/24 bar/21.[diagram 2].....[Redouble]
....[Take] ...................44: 13/9(2) 13/5
43: 24/21 10/6* ..[diagram 3].66: bar/19* 12/6 8/2*(2)
63: bar/22................... 44: 19/15* 9/5 7/3*(2)
66: Fan...........[diagram 4] 11: 15/14*/13 5/4*(2)
66: Fan.......................66: 13/1 7/1 9/3
11: Fan.......................66: 8/2 6/off(3)
11: Fan.......................55: 5/off(2) 4/off(2)
11: Fan.......................33: 3/off(3) 2/off
11: Fan.......................22: 2/off(2) 1/off(2) [diag 5]
------------------------------------------------------------

Poor Blue. White doesn't even leave a shot in the bearoff.

Below are (the intermittent) diagrams 1 to 5.

Nack





White is Player 2

score: 0
pip: 144
Unlimited Game
Jacoby Beaver
pip: 92
score: 0

Blue is Player 1
XGID=-BBBBBbA--AAcA---ccbbA----:1:-1:1:65:0:0:3:0:10
DIAGRAM 1: 11-66, now Black to play 65

1.XG Roller++21/10eq: -0.089
Player:
Opponent:		51.83% (G:13.17% B:0.12%)
48.17% (G:6.65% B:0.27%)
2.XG Roller++21/16 13/7eq: -0.175 (-0.087)
Player:
Opponent:		48.19% (G:14.39% B:0.10%)
51.81% (G:8.15% B:0.34%)
3.XG Roller++13/7 10/5eq: -0.287 (-0.198)
Player:
Opponent:		43.33% (G:13.46% B:0.07%)
56.67% (G:6.89% B:0.23%)
White is Player 2

score: 0
pip: 137
Unlimited Game
Jacoby Beaver
pip: 108
score: 0

Blue is Player 1
XGID=-BBBBBa---BAca---ccbb--AA-:1:-1:1:00:0:0:3:0:10
DIAGRAM 2: 11-66-65-61-21,
White correctly redoubles and rolls 44
White is Player 2

score: 0
pip: 127
Unlimited Game
Jacoby Beaver
pip: 101
score: 0

Blue is Player 1
XGID=aBBBBBA---AA-a--bccbcA-A--:2:1:1:00:0:0:3:0:10
DIAGRAM 3: 11-66-65-61-21-[R-T]-44-43,
White to play 66





White is Player 2

score: 0
pip: 87
Unlimited Game
Jacoby Beaver
pip: 137
score: 0

Blue is Player 1
XGID=-BBBBB----aA----aaacdAbb-C:2:1:1:00:0:0:3:0:10
DIAGRAM 4: 11-66-65-61-21-[R-T]-44-43-66-3-44-F,
White to play 11, then bears off in five
White is Player 2

score: 0
pip: 0
Unlimited Game
Jacoby Beaver
pip: 155
score: 0

Blue is Player 1
XGID=-BBBBB-------------------E:2:1:1:00:0:0:3:0:10
DIAGRAM 5 (final): 11-66-65-61-21-[R-T]
-44-43-66-3-44-F-11-F-66-F-66-F-55-F-33-F-22

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