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BGonline.org Forums
Is TG/T possible at an even match score?
Posted By: Sean Garber In Response To: Is TG/T possible at an even match score? (Bob Koca)
Date: Thursday, 4 May 2017, at 6:46 p.m.
This is my main reason for calling this a paradox. Normally when TG/T is the correct cube action, the player on roll is ahead in the match and cube turn would drastically decrease his own gammon value while the opponents gammon value might increase. For example let us look at 2-away, 4-away with a centered cube. This match score seems to me to generate more TG/T situations than any other match score. The leader has a .9 gammon value with the cube on 1 and a zero gammon value with the cube on 2. The trailer has a .3 gammon value with the cube on 1 and a 1.0 gammon value with the cube on 2. With a tied match score gammon values are always the same for both players. The condition that has generated just about every TG/T situation ever does not exist at a tied match score.
Secondly, when I read JOH's post a few days ago with the 11-away, 11-away position, it was not obvious to me at all that a TG/T situation was possible at a tied match score. Later, I did a little math that was enough to prove to me that it was at least theoretically possible at the score. From the original post in this thread, it seems that it was not obvious to Timothy Chow either.
Rarity. This is just my opinion with absolutely no studies to back it up, so take this as you will. If someone plays a couple decades worth of backgammon, that person will probably see at least one Kauder Paradox, a Jacoby Paradox, and a Latto Paradox (not very often, but those do happen). In a lifetime's worth of backgammon, someone may never see a TG/T situation at an equal match score.
For me at least, this is a legitimate paradox.
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