Levels of Complexity in Backgammon

Take this backgammon position:

levels-of-complexity-1

No one ever said that backgammon was an easy game. If it was then people would have lost interest in it long ago and moved on to other things. Luckily its complexity keeps us coming back for more and although it can be infuriating it is that very complexity which makes backgammon the game that it is.

Occasionally apparently simple positions such as the one illustrated above can contain hidden depths of complexity.

This position is taken from a high-stake chouette that I got wrong over the board. How should black play his 43? There are four possible options:

(a) 8/4*, 7/4
(b) 16/13, 8/4*
(c) 13/6
(d) 16/9

Before we take a look at the moves we have to consider what the salient factors in the position are. They are as follows:

• Black has three of white’s checkers trapped behind a four-point prime.
• Black has escaped all his checkers from white’s home board but cannot play this roll safely – he will be leaving a blot (or blots) whatever he plays.
• Black has a two-point home board whilst white has a four-point home board.
• The doubling cube is in the centre and therefore available to both players.

Given these factors what is black’s plan? Of course nothing is ever certain but it does look as if these should be the elements of the plan:

1. Given the strength of white’s home board black should only leave one blot.
2. Minimise shots if feasible.
3. When your opponent has two or more checkers back then priming them is an excellent game plan (with one checker back you should attack).
4. Look to give white a difficult doubling decision

Point 1 eliminates play (a). Play (b) leaves 15 shots, (c) leaves 15 shots and (d) leaves 13 shots. This indicates that play (d) is slightly the better play as far as shots are concerned. With regard to priming play (d) is also best as it slots the back of the prime. Play (b) does knock white away from the edge of the prime so that should also be a contender.

Analysing this and then proceeding to make a judgement over the board is very difficult and human nature tends to be aggressive and lead us to hit whenever possible. A lot of players would choose (a) or (b) on this principle but in fact the non-hitting plays are both better and the quiet 16/9 minimising shots is actually the best play by quite some distance as we can see from the rollout data.

Over the board I was seduced by the fact that after 8/4*, 7/4, and no return hit by white, I would have a powerful double. Sadly 15 hits (16, 26, 36, 25, 34, 14, 24, 22) is too high of a price to pay. My opponents threw 36 (bar/22, 24/18*) and after I fanned they correctly doubled. I accepted (also correctly) and was lucky not to lose a gammon.

levels-of-complexity-2

The key lesson here is to always have a plan and then find the best move to play that fits the plan. Just moving checkers without a plan is a one way trip to poverty !

Chris Bray