A) Double or no double for O from the bar?
B) If O dances, what should O do when X doubles?
Money session. Score X-O: 0-0
O on roll, cube action
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
| O O O | | O X O X |
| O O O | | O O X |
| O | | | S
| O | | | n
| | | | o
| |BAR| | w
| X | O | | i
| X | | | e
| X | | |
| X X X | | O |
| X X X X | | X X O |
+24-23-22-21-20-19-------18-17-16-15-14-13-+
Pipcount X: 99 O: 129 X-O: 0-0/Money (1)
CubeValue: 1
B) Pass. X will probably make one more point in his home board next
turn, and is ahead in the race.
B) I agree with jckz that 0 passes in this scenario. Even if X fails
to make another point, X can safety the blot on the 3 point. Then X
wins the race when 0 enters. X doesn't have enough contact
possibilities to justify a take.
Paul Epstein
>A) I don't understand jckz saying "only 5 numbers hit". I counted 20
>hitting numbers. But jckz is right that it's no double. The hits are
>not devastating and X is well ahead in the race if 0 misses and
>slightly ahead if 0 hits. If 0 blunders and doubles, X should not
>beaver.
>
>B) I agree with jckz that 0 passes in this scenario. Even if X fails
>to make another point, X can safety the blot on the 3 point. Then X
>wins the race when 0 enters. X doesn't have enough contact
>possibilities to justify a take.
Assuming that the last sentence was a typo, this all seems
right to me. Actually this seems like the easiest one so far.
(But what do we know?)
>Paul Epstein
>
>
>
>
>jckz wrote:
>> A) No double. 9 numbers don't enter, only 5 numbers hit, and X is way
>> ahead in the race.
>>
>> B) Pass. X will probably make one more point in his home board next
>> turn, and is ahead in the race.
************************
David C. Ullrich
Paul
B) That 25% are *big* cashes for X.
C) We can add a third question, making it problem 12bis:
If O doubled and then danced, it's not obvious at all that X should
redouble -- should X play on for a gammon instead ?
X is nowhere near good enough to play on for a gammon. The number of
losses for X are far more than 1/2 X's gammons and there are lots of
ways for X to lose if X plays on. Playing on for the gammon is a huge
blunder.
Even if X achieves the closeout without 0 moving at all (surely a great
deal to hope for), 0 retains significant gammon-saving chances.
Paul Epstein
A:
3-ply instant evaluation:
Money session. Score X-O: 0-0
O on roll, cube action
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
| O O O | | O X O X |
| O O O | | O O X |
| O | | | S
| O | | | n
| | | | o
| |BAR| | w
| X | O | | i
| X | | | e
| X | | |
| X X X | | O |
| X X X X | | X X O |
+24-23-22-21-20-19-------18-17-16-15-14-13-+
Pipcount X: 99 O: 129 X-O: 0-0/Money (1)
CubeValue: 1
3-Ply Money equity: 0,216
1,1% 21,7% 55,7% 44,3% 12,1% 0,3%
1. No double 0,171
2. Double, take 0,107 (-0,064)
3. Double, pass 1,000 (+0,829)
Proper cube action: No double, take 7%
------------------------------ End ----------------------------------
3-ply rollout:
Money session. Score X-O: 0-0
O on roll, cube action
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
| O O O | | O X O X |
| O O O | | O O X |
| O | | | S
| O | | | n
| | | | o
| |BAR| | w
| X | O | | i
| X | | | e
| X | | |
| X X X | | O |
| X X X X | | X X O |
+24-23-22-21-20-19-------18-17-16-15-14-13-+
Pipcount X: 99 O: 129 X-O: 0-0/Money (1)
CubeValue: 1
Rollout Money equity: 0,218
1,4% 21,6% 55,4% 44,6% 11,8% 0,3%
95% confidence interval:
- money cubeless eq.: 0,218 ą0,024,
- live cube no double: 0,179 ą0,044,
- live cube double take: 0,174 ą0,066.
Rollout settings:
Full rollout,
324 games (equiv. 13764 games),
played 3-ply (standard), cube 3-ply,
settlement 0,550 at 16 pts,
seed 1, without race database.
Evaluations
1. No double 0,171
2. Double, take 0,108 (-0,063)
3. Double, pass 1,000 (+0,829)
Proper cube action: No double, take 7%
Live cube
1. No double 0,179
2. Double, take 0,174 (-0,005)
3. Double, pass 1,000 (+0,821)
Proper cube action: No double, take 1%
------------------------------ End ----------------------------------
3-ply instant evaluation:
Money session. Score X-O: 0-0
X on roll, cube action
+24-23-22-21-20-19-------18-17-16-15-14-13-+
| O O O | | O X O X |
| O O O | | O O X |
| O | | | S
| O | | | n
| | | | o
| |BAR| | w
| X | O | | i
| X | | | e
| X | | |
| X X X | | O |
| X X X X | | X X O |
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
Pipcount X: 99 O: 129 X-O: 0-0/Money (1)
CubeValue: 1
3-Ply Money equity: 0,459
0,4% 19,3% 66,5% 33,5% 6,5% 0,2%
1. Double, take 0,675
2. No double 0,626 (-0,048)
3. Double, pass 1,000 (+0,325)
Proper cube action: Double, take
------------------------------ End ----------------------------------
3-ply rollout:
Money session. Score X-O: 0-0
X on roll, cube action
+24-23-22-21-20-19-------18-17-16-15-14-13-+
| O O O | | O X O X |
| O O O | | O O X |
| O | | | S
| O | | | n
| | | | o
| |BAR| | w
| X | O | | i
| X | | | e
| X | | |
| X X X | | O |
| X X X X | | X X O |
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
Pipcount X: 99 O: 129 X-O: 0-0/Money (1)
CubeValue: 1
Rollout Money equity: 0,505
0,2% 19,0% 68,8% 31,2% 6,0% 0,2%
95% confidence interval:
- money cubeless eq.: 0,505 ą0,018,
- live cube no double: 0,652 ą0,026,
- live cube double take: 0,797 ą0,046.
Rollout settings:
Full rollout,
324 games (equiv. 14381 games),
played 3-ply (standard), cube 3-ply,
settlement 0,550 at 16 pts,
seed 1, without race database.
Evaluations
1. Double, take 0,783
2. No double 0,663 (-0,121)
3. Double, pass 1,000 (+0,217)
Proper cube action: Double, take
Live cube
1. Double, take 0,797
2. No double 0,652 (-0,144)
3. Double, pass 1,000 (+0,203)
Proper cube action: Double, take
------------------------------ End ----------------------------------
Paul Epstein
/Micke
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