Repeat of 2013 post with visible images.
A chapter in my book Backgammon Funfair (www.backgammonfunfair.com, available in Europe from me and in the USA and elsewhere from Carol Joy Cole) describes a few cube provocation plays which were analysed three decades ago by Danny Kleinman.
A cube provocation play is a correct checker play after which your opponent should double or redouble, when you have at least one wrong checker play after which your opponent should not double or redouble.
Jeroen Sikkema has made the amazing discovery that there are hundreds, perhaps thousands, of cube provocation plays in late bear off races. (So this has nothing to do with gammons.)
Here are three examples from Jeroen's list. In the first two cases, the equity difference is quite big. In the third case it is marginal.
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| XGID=---CA-A-------------c-----:1:-1:1:62:0:0:3:0:10 | |||||
| Blue to play 62 | |||||
| 1. | XG Roller++ | 6/Off 3/1 | eq: -0.354 | |||
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| 2. | XG Roller++ | 6/Off 4/2 | eq: -0.424 (-0.070) | |||
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eXtreme Gammon Version: 2.19.208.pre-release
Correct play is 6/off, 3/1 after which White should redouble. Wrong play is 6/off, 4/2 after which White should not redouble.
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| XGID=--B--AA-------------a-ab--:1:-1:1:31:0:0:3:0:10 | |||||
| Blue to play 31 | |||||
| 1. | XG Roller++ | 6/3 2/1 | eq: -0.417 | |||
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| 2. | XG Roller++ | 6/3 5/4 | eq: -0.480 (-0.064) | |||
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eXtreme Gammon Version: 2.19.208.pre-release
Correct play is 6/3, 2/1 after which White should redouble. Wrong play is 6/3, 5/4 after which White should not redouble.
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| XGID=-----BB------------aaaa---:1:-1:1:43:0:0:3:0:10 | |||||
| Blue to play 43 | |||||
| 1. | XG Roller++ | 6/3 5/1 | eq: -0.448 | |||
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| 2. | XG Roller++ | 6/3 6/2 | eq: -0.453 (-0.005) | |||
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eXtreme Gammon Version: 2.19.208.pre-release
Correct play is 6/3, 5/1 after which White should redouble. Wrong play is 6/3, 6/2 after which White should not redouble.
Here is my limited understanding which I am sure can be improved.
When Blue has made the correct play, White should redouble because there is a low probability (i) that White could have a later more efficient redouble and/or (ii) that Blue, if redoubled now, could have a later efficient redouble to 8.
When Blue has made the wrong play, White should not redouble because there is then a sufficiently high probability (i) that White could have a later more efficient redouble and/or (ii) that Blue, if redoubled now, could have a later efficient redouble to 8.
Congratulations to Jeroen for creating a program to search for these plays.
Tom Keith has identified over 70,000 cube provocation positions (arrangement of checkers of each player, cube location, dice roll) for up to ten checkers for each player.