{"id":107,"date":"2017-06-25T00:21:15","date_gmt":"2017-06-25T00:21:15","guid":{"rendered":"http:\/\/pdxbg.club\/?p=107"},"modified":"2017-06-25T00:21:36","modified_gmt":"2017-06-25T00:21:36","slug":"man-versus-machine","status":"publish","type":"post","link":"http:\/\/pdxbg.club\/?p=107","title":{"rendered":"Man versus machine"},"content":{"rendered":"

Not surprisingly, I was playing some backgammon against the computer today. What was surprising, to me at least, was the following position came up that got marked as “doubtful” by GnuBG:<\/p>\n

\"gnubg-danbu_7p_2017-06-24\"<\/p>\n

Now, I didn’t even think about this one, clearly the right move is 11\/7,10\/7\u00a0and making the 6 prime. But GnuBG said no, 10\/6, 9\/6 is better. Huh?<\/p>\n

GnuBG says 10\/6, 9\/6 has equity +0.788, 11\/7, 10\/7 has equity +0.715; a difference of -0.073 and so a blunder!\u00a0Extreme gammon rates it similarly, 10\/6, 9\/6 gets +0.797 while 11\/7, 10\/7 gets +0.736, a difference of -0.061 and again\u00a0a blunder!<\/p>\n

It gets worse for me. After the next exchange of rolls, I was at the following position:<\/p>\n

\"gnubg-danbu_7p_2017-06-24b\"<\/p>\n

D’uh – clearly 9\/2\u00a0is the right move. But no, GnuBG says 7\/2, 5\/2!!! 9\/2 has +0.728\u00a0equity, versus +0.792 for 7\/2, 5\/2, a difference of -0.064 and so another blunder! Extreme gammon agrees again.<\/p>\n

The key here is\u00a0the cube. With the cube in the middle, the moves I actually made are the correct moves. But the cube has already been offered and taken, and that makes a difference. I no longer have the option to double red out after a rough roll, I have to take what I get – and if I get something bad red has the redouble.<\/p>\n

As it happens, what I got was a 5-6 on the first roll bearing in against the men still on my one point, forcing me to leave two blots. Red rolled a 5, putting me on the bar, I danced, and then got redoubled out. So it really could have worked out better for me. But the main thing was these back-to-back positions where the difference in correct play depends so much on the cube position.<\/p>\n

This table shows the winning chances for each move for the first position, per GnuBG:<\/p>\n\n\n\n\n<\/colgroup>\n\n\n\n\n
<\/td>\nWin<\/td>\nW g<\/td>\nW bg<\/td>\nLose<\/td>\nL g<\/td>\nL bg<\/td>\n<\/tr>\n
11\/7, 10\/7<\/td>\n0.811<\/td>\n0.129<\/td>\n0.005<\/td>\n0.189<\/td>\n0.005<\/td>\n0.000<\/td>\n<\/tr>\n
10\/6, 9\/6<\/td>\n0.835<\/td>\n0.146<\/td>\n0.005<\/td>\n0.165<\/td>\n0.005<\/td>\n0.000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

And this is the equity, depending on who owns the cube:<\/p>\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n
<\/td>\nEquity Cube in Middle<\/td>\nEquity, Red’s cube<\/td>\nEquity, Black’s cube<\/td>\n<\/tr>\n
11\/7, 10\/7<\/td>\n+1.000<\/td>\n+0.715<\/td>\n+1.000<\/td>\n<\/tr>\n
10\/6, 9\/6<\/td>\n+0.934<\/td>\n+0.788<\/td>\n+0.978<\/td>\n<\/tr>\n
Difference<\/td>\n+0.066<\/td>\n-0.073<\/td>\n+0.022<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Very similar charts for the second position:<\/p>\n\n\n\n\n<\/colgroup>\n\n\n\n\n
<\/td>\nWin<\/td>\nW g<\/td>\nW bg<\/td>\nLose<\/td>\nL g<\/td>\nL bg<\/td>\n<\/tr>\n
9\/2<\/td>\n0.824<\/td>\n0.115<\/td>\n0.004<\/td>\n0.176<\/td>\n0.005<\/td>\n0.000<\/td>\n<\/tr>\n
7\/4, 7\/3<\/td>\n0.833<\/td>\n0.145<\/td>\n0.006<\/td>\n0.167<\/td>\n0.005<\/td>\n0.000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n
<\/td>\nEquity Cube in Middle<\/td>\nEquity, Red’s cube<\/td>\nEquity, Black’s cube<\/td>\n<\/tr>\n
9\/2<\/td>\n+1.000<\/td>\n+0.728<\/td>\n+1.000<\/td>\n<\/tr>\n
7\/4, 7\/3<\/td>\n+0.925<\/td>\n+0.781<\/td>\n+0.970<\/td>\n<\/tr>\n
Difference<\/td>\n+0.075<\/td>\n-0.053<\/td>\n+0.030<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

I find it also interesting that the drop in equity for leaving an indirect shot is a lot lower when black owns the cube in both positions as well. I think either of these would make a good “quiz” question for Phil Simborg. Having them back to back like that in a game definitely made me stop and think about the value of owning the cube!<\/p>\n

-Mark<\/p>\n","protected":false},"excerpt":{"rendered":"

Not surprisingly, I was playing some backgammon against the computer today. What was surprising, to me at least, was the following position came up that got marked as “doubtful” by GnuBG: Now, I didn’t even think about this one, clearly the right move is 11\/7,10\/7\u00a0and making the 6 prime. But GnuBG said no, 10\/6, 9\/6 … Continue reading “Man versus machine”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-107","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"http:\/\/pdxbg.club\/index.php?rest_route=\/wp\/v2\/posts\/107","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/pdxbg.club\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/pdxbg.club\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/pdxbg.club\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/pdxbg.club\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=107"}],"version-history":[{"count":2,"href":"http:\/\/pdxbg.club\/index.php?rest_route=\/wp\/v2\/posts\/107\/revisions"}],"predecessor-version":[{"id":111,"href":"http:\/\/pdxbg.club\/index.php?rest_route=\/wp\/v2\/posts\/107\/revisions\/111"}],"wp:attachment":[{"href":"http:\/\/pdxbg.club\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=107"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/pdxbg.club\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=107"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/pdxbg.club\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=107"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}