position 303 from Advanced Backgammon - as tough now as in 1991?

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position 303 from Advanced Backgammon - as tough now as in 1991?

Posted By: Taper_Mike
Date: Tuesday, 30 April 2013, at 8:49 a.m.

In Response To: position 303 from Advanced Backgammon - as tough now as in 1991? (Timothy Chow)

Advanced Backgammon, Position 303
The following data show that after White cracks, Blue has a slightly better chance to hit if he plays 16/15 rather than 22/21. He trades 0.5 single hits in order to pick up 0.5 triple hits. He also picks up a second checker an extra 0.5 times.
The downside Timothy mentions is that playing 16/15 leaves Blue more prone to being hit himself. White could hit on the 15pt with 54 or 63 (but not 33). He could hit on the 16pt with 55 or 64.
If Blue is hit on the 15pt, he can hit back with 44 or 64 (but not 55). Hit on the 16pt, Blue has a direct return shot. He can hit with most any 5 or 9: 33, 52, 53, 54, 63, and 65. In 1296 trials, Blue hits 35 more return shots when he plays 22/21. That’s not quite 1 time in 36. Furthermore, even when Blue misses the return shot, he usually gets more chances, often on the next throw.
Which play is right? After looking at all these numbers, I am inclined to agree, at least in part, with Timothy.
I’m not quite sure how to choose between the two.
Mike

Blue on roll
Position ID: kwAEwLchGAESAA Match ID: UQkAAAAAAAAA

After Blue plays 17/12, 16/15
White rolls 42, playing 19/15, 5/3*

On Blue’s Turn Specific Rolls Rolls in 36

Blue can hit a “second checker” with 3 or 5 from the bar.
Blue can also hit a “second checker” with 1 or 3 from the 23pt. any 1, 3, or 5, except 11 26

Blue can miss inside, and still hit outside with a 2. 22, 42, 62 5

Air balls 11, 44, 46, 66 5

Single hits — 24

Double hits 32, 52, 53, 55 7

Total hits — 31

Blue on roll
Position ID: kwAEwLchGIIEAA Match ID: UQkAAAAAAAAA

After Blue plays 22/21, 17/12
White rolls 42, playing 19/15, 5/3

On Blue’s Turn Specific Rolls Rolls in 36

Blue can hit a “second checker” with a 1 from the 21pt.
Blue can also hit a “second checker” with 1 or 3 from the 23pt. any 1 or 3 20

Blue can miss inside, and still hit outside with 2 or 6. 22, 42, 52, 62, 64, 65, 66 12

Air balls 44, 45, 55 4

Single hits — 23

Double hits 11, 21, 32, 33, 61, 63 10

Total hits — 32

Blue on roll
Position ID: owACwLchGAEFAA Match ID: UQkAAAAAAAAA

After Blue plays 17/12, 16/15
White rolls 51, playing 19/14, 5/4

On Blue’s Turn Specific Rolls Rolls in 36

Blue can hit a “second checker” with 1 or 2 from the 21pt.
Blue can also hit a “second checker” with 2 or 3 from the 23pt. any 1, 2, or 3 27

Blue can miss inside, and still hit outside with a 4, 11, or 12. 44, 54, 64, 65, 66 8

Air balls 55 1

Single hits — 24

Double hits 21 31 33 41 42 43 11

Triple hits 11 1

Total hits — 35

Blue on roll
Position ID: owACwLchGAISAA Match ID: UQkAAAAAAAAA

After Blue plays 22/21, 17/12
White rolls 51, playing 19/14, 5/4*

On Blue’s Turn Specific Rolls Rolls in 36

Blue can hit a “second checker” with 4 or 5 from the bar.
Blue can also hit a “second checker” with 2 or 3 from the 23pt. any 2, 3, 4, or 5 32

Blue can miss inside, and still hit outside with a 1 or 12. 61, 66 3

Air balls 11 1

Single hits — 27

Double hits 41, 44, 51, 54, 55 8

Triple hits — —

Total hits — 35

On average, after White cracks

In 36 tries After Blue plays 16/15 After Blue plays 22/21

Blue picks up a second checker 26.5 26

Blue hits at least once 33 33.5

Blue hits exactly twice 9 9

Blue hits three times 0.5 —