Backgammon

Mrs Hudson had cleared away the final remnants of our most excellent Christmas dinner and Holmes and I were relaxing in front of a roaring fire. At times such as these Holmes is wont to reach for his violin. To distract him and thus preserve the peace and calm of the evening I decided to ask him a question on his favourite game.

"Holmes, when contemplating doubling your opponent you have often talked of market losing sequences. I am still having difficulty with the concept. Perhaps you could explain it to me?"

"Certainly Watson, nothing would give me greater pleasure. Whenever you are considering doubling your opponent you must have a threat which, if carried out, would cause him to drop your double next turn. The important point to remember is that before that next turn both you and your opponent will have rolled the dice and made your moves. Thus in considering how the position may look next turn you have to consider a sequence, your own roll and your opponent's. A market losing sequence is one which changes a position from a take one turn, to a drop on the subsequent turn."

"Now I understand," I replied. "Do you have a rule of thumb for how many market losing sequences justify a double?"

"Ah, Watson, you touch on a subject close to my heart and one on which I may shortly produce a short monograph. Firstly, remember that evaluation of backgammon positions is dependent on the skill of the person performing the evaluation, so that what may be a take to one player is a drop to another. That should always be an influencing factor in your doubling decisions.

"However, let us assume that you are playing someone who you think will make rational doubling decisions. In that case my analysis leads me to believe that you should double if at least 25 per cent of sequences would lead to you losing your market. This equates quite simply to 50 per cent of your rolls followed by 50 per cent of your opponent's. I have more work to do to refine this further but I think you will find that a useful guide for the time being."

"Succinct as ever, Holmes. Now, how about a glass of post-prandial port?"

"Provided it's not too sedimentary, my dear Watson."