Simulating Positions
Dan Heisman, 1984

From Backgammon Times, Volume 4, Number 1, Spring 1984.

Except for races, the best way for establishing the equity of a given position is to play it out by hand. Usually the question involved is: "Which of two moves is better?", "Is this a double?", or "Is this a take?". The proper procedure for each is:

  1. Which is the best move? Play out each position. The result with the higher equity is the best move.

  2. Is this a double? Usually (but not always) this indicates a take. (Unless we are talking about too good to double, in which case it is a drop.) Therefore, play out the position with the original cube position and then with a take; whichever yields the higher equity is the proper cube action. Note the difference is the availability of the cube. Also remember that many positions that are not a double now may well be a double and even a drop next turn.

  3. Is this a take? Assume a take. If playing out the position yields the taker a better equity than dropping would have, then it is a take.

All this is easy to understand. Playing out the position as a proposition wherein each player is betting on his side would then work in accordance to the above rules. For example, suppose one player says a cube turn to 2 in a certain position is a drop and his opponent says it is a take. Then the dropper is claiming the equity of the position is less than the previous value of the cube, or 1. So, to be fair, the person who claims it is a take should be given the value of the cube if dropped (in this case 1 unit) for each playout of the proposition.

This method is nice for propositions, where unequal strength opposition is to be assumed. However, suppose a serious student wants to know the best way to go about it. In this case the student should play out the position many times with equal play for both sides. This playout is called "simulating" the position.

Simulation Tips

When simulating the position, the student wants the results to be as fair as possible. Therefore, certain rules (or tips) can be followed to ensure that the results are useable.

  1. If playing out the position with others, do not play it as if it were a proposition because of unequal strength of the players. Make sure all players involved make equal suggestions for both sides. This rule actually extends to one player who sometimes "roots" for one side. This is of no use, as the results tend to become biased toward that side. It is essential to get the best and most equal play in terms of quality from both sides. For this reason, no money should be involved.

  2. It is easier to make doubling decisions with more than one simulator, and since doubling decisions are often critical for calculating equity, more than one person performing the simulation is preferable for this reason.

  3. A good method suggested by Jeff Ward and others is to start with all 36 dice combinations in sequence and to repeat this sequence, playing the games out in multiples of 36. This takes some of the luck out of the simulation.

  4. The more games in the simulation, the better. Most close questions would call for a minimum of three sets of 36 games (see tip 3 above). Note that some questions to be decided are not as close as they first seem and that even one set of 36 would make this obvious. On the other hand, close or complicated positions may call for more games than normal.

  5. It is very important that correct strategy be employed for both sides. If you begin to feel your initial strategy (like playing for a backgame) was incorrect, it is required that you change your strategy for either player. This spot in the simulation should be marked for later referral. If further results show that the new strategy is inferior for that side, throw out all the results since the change in strategy and then continue with the old strategy. On the other hand, if the new strategy is indeed showing superior results to the old strategy, throw out all the results before the change in strategy and continue with the new strategy. Of course, both sides may change strategy and the only results that are worthwhile are when it seems both sides are using the proper strategy against what the opponent is doing. Following this rule may result in throwing out many hours of work, but you will have better results and, just as importantly, you will have learned a lot more about how to play that position.

  6. In view of the above tips, it should be obvious that if there is only one simulator and he is better at playing one side's type of position than the others, the results will be biased. Try to keep an open mind about your deficiencies and apply rule 5 with strategy changes for both the superior and inferior sides.

  7. When in doubt, be conservative with the cube. Give and take doubles with caution. The reason is that if you use the cube loosely, then there will be big swings and single games which will have a large effect on the outcome, which may tend to lead to misleading results. By being conservative, fewer games will be needed for the correct result to become apparent because every game will have meaning. On the other hand, do not overdo this; any position which calls for a double should be doubled and any position which is just as obviously a take should be taken.

Dan Heisman, a longtime backgammon player and chess master, was a chess columnist for the Bucks County Courier Times (Penn.) and has won three national awards for his weekly chess columns.

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