Black has been playing a 1-5 back game (probably the weakest of all back game formations) and now faces a roll that messes up his plans even further. With a 4-4 to play, he has to sacrifice something. He can move off the 24-point, move off the 20-point with one or both men, or try to keep both back game points and play entirely on his side of the board. Nothing is really appetizing, but he needs to make the best of a bad situation.
In all variations, his chances of winning are small. His chances of being gammoned are also small. He needs to balance these two chances, keeping in mind that every extra win balances two extra gammon losses. (In other words, keeping winning chances alive is twice as important as saving gammons.) In many such positions, the best play is not the play that wins the most games, or the play that loses the fewest gammons, but some sort of middling play that achieves the best result between the two. Having said all that, let’s look at the reasonable choices.
Play (A): 6/2(2) 8/4 7/3 (or any other play which doesn’t move any back checkers). This is hopeless and can be dismissed quickly. Keeping both back game points is useless if the home board is gone. This play reduces winning chances while increasing gammon chances, the very opposite of what we’re trying to do.
Play (B): 20/4. Running only one checker from the 20-point is the best play to win the game, and it would be correct in a tournament match at double match point. The checker that stays behind on the 20-point will garner Black a few extra hits, which is good. The play, however, has some liabilities. The obvious downside is that White has some pick-and-pass numbers which will cost Black a few extra gammons. A less obvious downside is that the extra shots that Black gets from 20/4 come quickly, while Black’s home board may still be weak. Rollouts show this play winning 20.5%, while losing 19.5% gammons. Let’s keep those numbers in mind as we look at the alternatives.
Play (C): 24/16(2). Running off the 24-point is the play to minimize gammon losses, but it sacrifices a huge portion of winning chances in the process. Without the ace-point to generate long-term shots, Black is pretty much staking his winning chances on getting a shot immediately. He gets 8 shot numbers on the first turn (1-1, 3-3, 2-1, 3-1, and 4-3) and hits those between 30% and 50% of the time, depending on just where White leaves the shot. (White’s worst rolls are then 3-3, 1-1, or 2-1, which give Black 18 shots when White stays on his 12-point.) Black also gets some shots when White gets safe this turn but still has to clear the 6-point or 7-point. Note also that with Black’s home board, immediate shots are not necessarily winners.
Rollouts show Black winning a bit less than 10% of the time after 24/16(2), with gammon losses dropping to about 10% as well. (Many of his gammon losses now come when he hits an immediate shot but gets hit back.) Compared to Play (B), Black is trading wins for lost gammons at a 1:1 rate, an unfavorable trade when wins are worth twice as much.
- Play (D): 20/12(2). With this play Black simply abandons the 20-point, electing to play an adequately timed ace-point game instead of a poorly timed 1-5 back game. At first glance this play looks like a surrender, but it’s not. The ace-five is the weakest of all back games. It gives you some extra shots as White tries to clear his 7-point and 6-point, but that’s it. As soon as White clears those points, the position reverts to a straight ace-point game anyway.
Clearing the point now has a couple of additional bonuses: Black now has plenty of time to build a winning board, and his ace-point game is a little stronger than usual because of the open 5-point he leaves behind. White will have only a couple of rolls each turn to fill the point, and in all likelihood it will remain open until he finally clears his 6-point. Compared to 20/4, rollouts show Black gives up a few winning chances but saves a lot of gammons. His wins drop by a couple of percent, from 20.5% to 19.0%, but his gammon losses drop more than 6%, from 19.5% to 13.4%. That’s a huge saving in gammons lost, and moves this play to the top of the list.
Note that running from the 20-point isn’t the best play to win the game (that’s 20/4), or the best play to save the gammon (that’s 24/16(2)). Instead it’s a well-balanced play, preserving plenty of winning chances while saving lots of gammons.
Note also that this play will be correct in many other back game situations. That is, if you’re in a marginally-timed back game and you roll a big double, running off the front back game point will most often be the right play. It will leave you with a good anchor game (with a gap in your opponent’s board), preserve what timing you now have left, and save a lot of gammons in the process.