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Robertie: 501 Essential Backgammon Problems #75
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After reading Robertie's "501 Essential Backgammon Problems" randomly,
some problems each night, I now started to work my way through the book
more systematically :)
Problem #75 contains an error in the text:
GNU Backgammon Position ID: bHcwAyC22U4AIA
Match ID : cIkEAAAAAAAA
+24-23-22-21-20-19------18-17-16-15-14-13-+ O: WHITE
| X O O O O | | O |
| O O O O | | O |
| O O | | |
| | | |
| | | |
| |BAR| |v (Cube: 1)
| | | |
| | | |
| | | X |
| X X X X | | X X O |
| O X X X X | | X X X O |
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: BLACK
Pip counts: O 119, X 102
Black (X) rolls 1-1.
Robertie comments:
"This is a great shot, and three of the aces are very clear: 24/23 (to
escape) and 2/1* (2), putting White on the bar. How about the last ace?
A prosaic player would try either 8/7 or 10/9, both of which leave
Black with three builders for the open 5-point, at a cost of one or two
shots from the bar. The ingenious player, however, notices that
duplication allows him to play 8/7! [HE PROBABLY MEANS 7/6 HERE!] At a
cost of three shots (52 and 55) instead of two, Black gets four builders
for the 5-point and three builders for the 2-point, with complete
diversification of point-making numbers. A great play."
1) It should be noted, that Robertie actually recommends 7/6, while 8/7
is printed. (Otherwise 52 would not be a shot and there were no 3
builders for the 2-point.)
2) While Robertie's play is actually very bold, I am not sure whether I
would play 7/6. Rollouts (1296, cubeless, with variance reduction)
seem to indicate, that 7/6 only wins few gammons more than 8/7, while
winning less often and losing more gammons. How would you play the last
ace?
1. Rollout 24/23 8/7 2/1*(2) Eq.: +0,214
0,560 0,193 0,002 - 0,440 0,099 0,003
2. Rollout 24/23 7/6 2/1*(2) Eq.: +0,171 *(-0,043)*
0,549 0,210 0,002 - 0,451 0,132 0,007
Hardy ;-)
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Raccoon writes:
With 24/23 2/1*(2), I'd have played the "prosaic" 8/7. Although
Robertie writes (correctly) that
> three of the aces are very clear
2/1*(2) 8/6 also gives 3 builders for the 2 point and 4 builders for
the 5 point. Perhaps that is the prozac play, but it's not a terrible
play. I do agree that 24/23 is "clear."
8/7 and 10/9 both give X three builders for the 5 point, but 8/7 is
better because X can use the spare without giving up the bar point. The
duplication of 54 (bar/20/16* or bar/20 6/2*) after 10/9 is illusory;
with 54, O will simply play bar/16*, and 55 is still a great number.
After X's play O is 16/36 to fan. When he does X has a
stronger double after Robertie's suggested play, 24/23 2/1*(2) 7/6. I
recollect that there isn't much discussion in "501" in the checker play
problems about anticipated cube action but perhaps that is key to
finding the correct play in problem 75. 7/6 also gives X a few more
returns in response to O's 23 22 24 53 and 54, and is probably better
if O rolls 25 26 21 or 51.
24/23 2/1*(2) 7/6 seems to gain a little on a lot of O's rolls.
Your rollout was cubeless; I'll run a couple of cubeful rollouts and
post them by and by.
----
GNUBG 0-ply (2-ply cube)
rollout at match score 0-0/17 (7776 games):
1. Rollout 8/6 2/1*(2) Eq.: +0.3195
0.5546 0.1908 0.0024 - 0.4454 0.0864 0.0037
2. Rollout 24/23 8/7 2/1*(2) Eq.: +0.3184 ( -0.0011)
0.5608 0.1931 0.0024 - 0.4392 0.0981 0.0037
3. Rollout 24/23 7/6 2/1*(2) Eq.: +0.3127 ( -0.0069)
0.5457 0.2113 0.0024 - 0.4543 0.1340 0.0067
4. Rollout 24/23 10/9 2/1*(2) Eq.: +0.3105 ( -0.0090)
0.5577 0.1852 0.0024 - 0.4423 0.0942 0.0037
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