BlackGammon

Probabilities and chances of backgammon

Backgammon is, above all, a logical game. There is no logic without mathematics, so, no matter how you spin it, the backgammon strategy is subject to mathematics in its entirety. Success in the game also depends on probability and correctly calculated chances. It is described in more detail in this article.

The real world gives a huge number of unexpected events, which may be pleasant and not very surprising. This pattern is clearly visible through the need to cast lots in many games. Perhaps that is why many games are so enticing gamblers to play with fate. After all, they allow you to plunge into a special reality, where you need to quickly make the right decisions.

One of these games are backgammon. Luck, attention and resourcefulness – the main qualities for players. After all, every move dictated by Mistress Fate, and it is luck here decides their staging.

But to properly use any chance, you must know the basic rules. The very purpose of backgammon – getting rid of all the chips on the board. White pieces are allowed to move clockwise relative to field 25, and Black must move counterclockwise towards field 0. There is nothing more hindering the movement of the chips: they go to any field if there are not several enemy pieces. All single pieces of the second player are captured and the opponent starts the movement from the beginning.

I will give a simple example to make it clearer. The draw prophesies 6-5 points to white pieces, so there are 4 possible moves: 5-10 and 5-11, 5-11 and 19-24, 5-10 and 10-16, and 5-11 and 11-16. But only one should be chosen.

It would seem that White has an advantage, but they do not know the points brought by the will of the opponent’s team, and therefore simply do not have the opportunity to determine the options for the movement of black. Thus, despite the seeming ease, in backgammon it is impossible to apply any standard algorithms, such as in crosses or chess. The algorithm of actions and moves must include maximum and minimum, as well as draw nodes. Conditionally, the nodes of the draw are usually indicated by circles. Lines or arrows from each of these nodes determine the desired results for the roll of dice. Above each such line, data is drawn indicating the points and the probability of achieving them.

In total, there are 36 possible options for points. However, there are only 21, as the combinations of points, e.g. 5:6 and 6:5 are identical. And with such combinations, the following probability is highlighted: with takes from 1:1 to 6:6, it is 1 to 36. Each of the subsequent combinations corresponds to a 1 to 18 probability.

Our next task is to understand which solution should be considered the only correct one. It is important to find the most advantageous move or its combination. To do this, we need to calculate the possible values that the throw can produce. This will lead to a generalization of the value to the expected one.

In this case, all nodes, both nodes of maximum and minimum values, as well as terminal ones, are used as before. The colt nodes are determined by the average value of all possible drops. The general principle can be calculated mathematically:

The node of the draw N supplements the state N with each possible value of the falling out points to form the next successor S, and P(s) – the value of the probability, which is determined at each falling out of certain numbers on the cubes.

The results of these calculations may be applicable to all game resolutions. This is a kind of algorithm, substituting values into which one can feel a quite material result. Go ahead and you’ll do it!