by Gerry Tansey
I don’t worry too much about the plays I agonize about over the board. If I care enough to take a picture of the position, I know I’ll get further feedback on my decision, first from other players, and then, most definitively, from a bot. Sometimes I’m right or wrong by a lot; sometimes the plays I’m considering are so close that I shouldn’t have cared that much. But no matter what, I’ll know that there was a backgammon problem that I wasn’t sure how to solve, and I’ll get an answer.
No, what I worry about are the positions I just fly through, thinking there is no thinking required. My live matches are rarely recorded, so if such a situation arises then, I’ll never know about it. Fortunately, most of my matches are either played against a bot or online, and when I’m done, XG will let me know about every play it thinks I butchered, whether I was aware of it at the time or not.
The following position came up in an online match. The score is 6-5 to 7, and we have passed the Crawford game, so the trailer was allowed to use the cube. Therefore, we are at Double Match Point (DMP). Whoever wins this game wins the match. Gammons and future cube actions matter not a whit. Both players should make plays that maximize their chances to win this game.
In the game, White wasted little time with this play. He might have uttered a silent curse to himself, but he quickly played 13/2. Black failed to hit, White rolled 65, and soon the players were shaking hands (virtually, of course). Nothing to see here, right?
XG took a look at this position and did its best impression of Frank Costanza’s Airing of Grievances: “I got a lot of problems with you people!”XG prefers clearing the midpoint, a play that leaves two blots and twenty shots, to 13/2, which leaves just one blot. It is not a close decision. The right play wins the game (and thus the match) over two percent more than the second best play. What is going on here?
Well, first note that 13/2 is not immediately as safe as one might think. Let’s count the shots: Any roll containing a 3 (eleven numbers), 21 and 11 (three more numbers), and 62, 44, and 22 (four more numbers). That’s eighteen hitters, only two fewer than the 2-blot play. But still, it is two fewer. What else is happening?
If White gets away with 13/8 13/7, the match is basically over. All of White’s rolls play safely, and most of them leave at most one point to clear in front of Black’s 20-point blot. White’s worst roll is 31, which leaves two points to clear (played 8/7, 5/1).
Now, if White gets away with 13/2, there is more work to do. Let’s assume that Black has not rolled 55, 66, or 65, and is thus able to keep roughly the same defensive position (potentially with a made 2-point). White leaves another shot on the rolls 51, 41, 31, 21, 62, 42, 32, 53, 33, 22, and 11, a total of 19 numbers. White is an underdog to roll a safe number! Let’s do some rough arithmetic. After 13/2, Black will hit initially with 18 numbers. On the 18 misses, White will leave another shot about half the time, which Black will hit about a third of the time. 18 times (1/2) times (1/3) is 3 more hits, bringing the total number of hits to about 21. All of a sudden, the 1-blot play looks less safe than the 2-blot play.
There are some shortcuts we are taking, such as ignoring Black’s big numbers that compromise his defensive position, and using one-third for the proportion of Black’s hits in all cases when he gets a second shot. But over the board, this type of analysis is quite manageable, if one will only recognize that it is necessary and then take the time to do it.
In the online match, it was my opponent who made this mistake, but I’m counting it as my own error, as I am 100% certain I would have done the same thing if faced with the same decision. I would have thought, “One blot good, two blots bad,” and just made the “safe” play. Normally it is right to worry much more about the immediate shots you leave rather than what might happen on your next turn. However, when the shot count for two plays is close, the ease of cleaning up after survival can become the deciding factor.