Neural network engine reviews 170,000 long nardy moves and finds where humans go wrong

The author of an analysis on Habr ran about 170,000 moves by real long nardy players through a neural-network engine to see where humans lose the most. The losses cluster in two places: the start of the game and the size of the defeat, that is, mars and kox. The material includes four problems from real games that readers can try to solve themselves before checking the engine's answer.

Why long nardy is hard even for a move generator

The rules of long nardy look simple, but they are not easy for an engine. Before a neural network can evaluate a position, the program has to list every legal move, and here that is a separate task. The head rule allows only one checker to be taken from the starting position per roll, with exceptions for doubles at the very start of the game. The ban on a full block forbids building six occupied points in a row if the opponent has no checkers ahead of them. On top of that come the obligation to play both dice when possible and the priority of the larger die when only one can be played.

An error in any of these rules produces illegal moves or drops legal ones. The evaluation itself stays correct, but the engine ends up choosing from the wrong set of options. That is why the analysis treats the move generator as a separate component of the engine, not as a technical add-on to the neural network.

Neural-network evaluators in backgammon-type games have existed for a long time. Gerald Tesauro's TD-Gammon showed in the early 1990s that a network can learn to evaluate positions in a dice game by playing against itself. The principle has not changed. The network outputs a position score, and the engine enumerates the legal moves and picks the one that leads to the better score.

What turned up in 170,000 moves

The engine compared human choices with its own. The author lists three main observations:

• Sample: about 170,000 moves by real players.
• Where the most is lost: at the start of the game, when the structure has not yet formed and every roll sets the plan for the next ones.
• Which losses are the heaviest: in the size of the defeat, that is, mars and kox, where a loss costs more than usual.

The first finding is expected. The long nardy opening has many forks, and the head rule tightly limits tempo, so it is hard for a human to calculate the consequences. The second finding is more interesting. It shows that players lose less on win probability than on risk management. When a game is slipping away, a person often keeps playing to save it. The engine, presumably, evaluates not only the chance of winning but also the cost of losing, and therefore picks moves that are less likely to risk a heavy defeat.

One limitation should be stated up front. The announcement gives no data on which network was used, what level the human players were, or how large the engine's average advantage is. Those details appear only in the full article, and without them the scale of the errors cannot be judged.

How to use the analysis

The material is most useful for people who play seriously and want to improve their results. A few practical steps:

• Solve the four problems before reading the answers. A disagreement with the engine is itself a sign of a weak spot.
• Study the opening separately. According to the author's data, this is where the most is lost, and the head rule makes the choice of the first moves more important than it seems.
• If you are losing, assess the risk of mars or kox, not just the chance of coming back.
• Run several of your own games through the engine. Typical mistakes repeat, and the 170,000 moves confirm this.

The material also has value for developers of game AI. It is a reminder that in games with non-standard rules, the reliability of the move generator matters as much as the quality of the neural network.