Game

We think analyzing backgammon under the following headings is important becuse it reveals more understanding and achieves solid improvement:

GAME PLAN

A plan is usually used for making a goal explicit by defining ways of reaching that goal. Plans are not in any way fixed, they must be updated or redone accordingly. A plan starts a navigation to a desired end by carving windows to the current situation. In backgammon, game plans can be used in a similar perspective. Candidate checker moves and cube actions are formed according to a plan tailored to reach the goal of that game or match. Then a decisions is reached among the most suitable candidates. Goal, plan, candidates and decision form a staged thinking process to reduce the complexity of playing and drifting randomly. The power of human beings compared to bots is this capability of efficient complexity reduction. Bots try harder and use brute force methods to reach the same end but they are not efficient in any sense. As plans do change in life, game plans in backgammon also change frequently. Feasibility, sustainability, risks that can be taken and returns that can be obtained are some of the important inputs to planning.

As an example let us take frequently arising and therefore well studied position. Let us form a game plan for the side who is going to play first (opening position) in a 1-point match (it can also be called Double Match Point – DMP): Since backgammon is essentially a race then it will be wise to run with big numbers. To support racing the player also need points in his home board so that if the opponent can be kept on the bar then race advantage will grow. The game can be long therefore it is better to keep checkers in play and not make deep points. Fundamental weakness of the opening position are the heavy points of 13 and 6. Therefore it is wise to make the game more flexible as early as possible by even slotting to make the 5-point. Since gammon wins/losses have the same value as single point wins/losses making an advanced anchor (especially for reducing gammon losses) has lower priority compared to flexibility and obtaining a good structure to establish a powerful game. For the same reason, it may not be wise to bring two checkers down from 13 just to increase gammon chances alone instead defense and offense balanced flexible checker play can be more effective.

As with other plans, game plans must be continually checked to see that they are still working. Stratejies and tactics; indicators of structural health such as timing, flexibility, connectivity, non-commitment, and robustness can be used to question the validity of game plans.

REFERENCE POSITIONS

Positions like Double Match Point (DMP) opening roll are reference positions because they have been studied extensively. Since reference positions happen to arise frequently studying them can bring better understanding of the game, less errors in this kind of positions and also playing fluency. We can use books or our match records to collect and study reference positions. Before bot revolution experimenting with reference positions were done using propositions, i.e., playing these positions many times to get an understanding and evaluation of the position. Nowadays bots can effectively do the same with rollouts rollouts in a much faster way than human beings. However, rollouts do not ususally give an understanding of the position but only an evaluation of winning and losing probabilities. Another disadvantage of rollouts is that they play both sides as bots playing considerably better than most players. Therefore to be able to have personal reference positions players must use both methods to get a feeling of what happens against which player.

As examples of reference positions, opening rolls and their replies, end-game cube positions, race cube positions, positions where making 5-point is more valuable than other points and customized positions where a player will compile from his/her correct and incorrect decisions can be listed.

MONITORING and MEASURING

Backgammon presents us some measurable criteria to evaluate how the game is progressing. In a game where instant changes happen frequently, it is very important to keep track of a relevant criteria set and decide whether to change the game plan or not. Taking strong and weak aspects of each position into consideration, we try to determine whether to build or repair our game.

Examples of measurable criteria may include pip count as a race indicator, number of checkers in the zone, number of checkers on the bar, number of blots, distribution of blots, number and distribution of points in home boards, number of spares on the mid-point and number of spares on 6-point. In addition to these instant performance indicators, criteria related to game plan can be used. For cube decisions, volatility and equity can be taken into consideration. For games involving double primes anf backgame, timing is an important measure. Near the end of bear off, number of crossevers can be used when gammons are probable.

RISK/RETURN ANALYSIS

Decision making mechanism in backgammon is built on risks and returns. In every position cube and checker decisions involve some probabilities of occurence. A backgammon position has a numerical value called equity which can be approximated by computer analysis software. If the game ends without playing a position, equity difference shows how much the player owes to the other or vice versa. Human players with analysis software experience, a large collection of reference positions knowledge and vast over the board and online playing experience can have good estimates of the value of most positions. They use these estimates to increase their equity by moving checkers and making cube decisions accordingly. For example, if their equity rises when the cube is turned they turn the cube. Or in checker play, if the move they consider will bring more long and short term gains compared to future and immediate risks, they will decide on that move after evaluating the resulting position in their knowledge base and performing a dice combination test to what happens shortly.

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