What is a Back Game?
In a back game, you keep two or more anchors in your opponent’s home board, hoping to wait until he has weakened his position, and then hit a blot near the end.
The best combination of anchors are the opponents two-and-three, one-and-three, or two-and-four points. In general, a back game with widely separated anchors, such as 1-4, 1-5, or 2-5, is weak, for scattered points hinder the opponent’s bearin only minimally. Such a back game offers little more winning chance than a holding game with a kicker, but carries a greater gammon risk.
A 1-2 back game hinders the opponent’s bearin greatly, but all too often lacks the extra timing (extra pips that can be played contructively) needed to preserve the strong board that makes a late hit effective.
To retain adequate timing in a back game, you must arrange to have checkers not only sent back, but also recirculated. Your opponent will often own his bar point as well as his eight point, and if your most advanced anchor is on his two point, you will have to play your 6’s destructively on your own side of the board instead of constructively to run extra checkers to your opponent’s outer court.
Paul Magriel (in his Backgammon) compares the holding game and the back game. In each you maintain an anchor or anchors to impede the opponent’s bearin or bearoff while waiting for a shot. They differ, however, in when you aim to hit that shot.
In a holding game, you should hit as soon as you can. But in a back game, an early hit may prove futile. You must usually wait until your opponent has started to crash so that you can easily bring your back men around to join the struggle to restrain the blot you have hit.
Magriel warns against piling men on your own one and two points when playing a back game. Checkers on those deep points are out of play, reducing your building material for the blockade you need to restrain the blot you hope to hit.
Once you’ve made your higher points, you can reasonably make your two point, but your one point is highly undesirable, for it wrecks your chances of picking up the second blot, which can be so useful if your hit comes late in your opponent’s bearoff.
Your best strategy is to avoid back games. They are often fragile, suffering irremediable cracks when large doublets ruin their delicate timing, and they incur large gammon risks.
Nonetheless, you must be prepared to play back games because they are your fallback position when the aggressive yet worthwhile move you make early in the game backfires. A player who fears back games excessively won’t battle fiercely enough for the key five and four points in the opening.
||Black to play 6-2|
Black should not play 22/16*, 7/5. After this hit black will still be at a terrible disadvantage. White will still have four inside points to black’s two, only one man back against black’s three, and a 5-prime against black’s sieve.
Instead, black should simply play 13/5, strengthening his board and blockade on his own side of the board, move by move, while white’s position slowly crumbles. White is likely to leave blots later, when black’s hit will be effective.
||Black to play 6-1|
Even though it’s early, black should hit, 22/16*, 8/7 (a slightly better ace than 16/15 or 10/9). By hitting, black retains both anchors and keeps white from making the 6-prime he has slotted. If white hits back. black gains extra timing, and the 16 point is still open to him as a path for recirculation.
Note that black does not hit intending to trap white’s checker permanently, but as a tactic to keep traffic flowing. The game winning shot, if any, will come later.
Should black take?
Black has too little timing and should pass. White has killed 6’s and will eventually kill 5’s.
This happens often when playing against a 1-2 back game. The prospect that his opponent will kill 6’s and 5’s increases the timing problems of the 1-2 back-game player even further.
Meanwhile, black must plays 6’s and 5’s to his one and two points. It will be bad enough if black is forced to make his one point, but worse still if he must bury a third or fourth checker there.
Should black take?
Having borne off three checkers already, white threatens to improve his position further by clearing his six point safely. He’ll succeed on 15 rolls — all 16 combinations of 1’s, 2’s, 4’s, and 6’s, except the blot-leaving 6-6.
Black faces a severe gammon threat — unless he hits a shot, he must advance 78 pips to bring all his checkers home, plus three more to bear a checker off. These 81 pips represent about 10 average rolls and are more than black can expect to move before white finishes bearing off.
Against this, black has adequate timing, with his best four inside points already built and other checkers poised to extend his prime. If black hits a shot early enough, he will be able to win with the cube. The shots white leaves will be double shots, hittable 20 ways, and 11 of white’s rolls blot immediately: 1-3, 1-5, 3-5, 3-6, 5-6, and 6-6. More shots and double shots loom later if white avoids getting hit this turn.
Despite the gammon threat, therefore, black appears to have enough shot equity to take. To verify this, I rolled out the position 180 times, in five series of 36 games untilizing the 36 different initial rolls for white. Rolling out games in such series of 36 ensures that favorable and unfavorable initial rolls will be represented in proportion to their probabilities.
To take Black’s ownership of a 2-cube into account properly, I adopted a procedure suggested by Kit Woolsey (“Rollouts,” Inside Backgammon, Volume 1, Number 5, September-October 1991). When black has a possible redouble but white has a clear take, I continue for at least one turn more with black keeping the cube. When white’s take was only marginal, I ended the game and scored it as a win for black.
In these rollouts:
- White won a plain game 22 times (12%).
- White won a gammon 51 times (28%).
- White won a backgammon 14 times (8%).
- Black won a plain game 93 times (52%).
Thus by taking, black obtains an equity of
|93 × 2 − 22 × 2 − 51 × 4 − 14 × 6|
which is better for him than the one-point loss he suffers by passing.
Hypothesis confirmed: Black should take.