Long Nardy Through AI's Eyes: 170,000 Moves and Human Mistakes

The creators of an online nardy platform conducted a large-scale analysis: they broke down 170,000 real moves from 6,383 games played by 938 players. Using this data, they trained a neural network engine and figured out how it chooses moves — and where humans make critical mistakes. The rules of long nardy turned out to be far more intricate for an algorithm than they are for a human.

How the engine evaluates positions

The approach traces back to Gerald Tesauro's famous TD-Gammon (1990s), which proved that neural network position evaluation works in backgammon. Today this method is the standard for every program in the genre, from GNU Backgammon to eXtreme Gammon. The engine doesn't compare moves themselves — it evaluates the positions those moves lead to.

The algorithm works in three steps. First: for the current position and the dice rolled, enumerate all legal moves. Second: build the resulting position after each move. Third: evaluate each position with the neural network and pick the most favorable one. Critically, one arrangement can often be reached via different paths. For example, with a roll of 4-1, you could play 24→20→19 or 24→23→19 — the outcome is identical. That's why the generator first enumerates all step sequences, then collapses them by final position. This matters especially with doubles, where four steps of the same number create many permutations with the same result.

Why long nardy's rules are hard for an algorithm

Unlike backgammon (short nardy), which has hitting and a bar, long nardy — under the rules of the Russian Nardy Federation (Ministry of Sport order No. 347 of April 30, 2025) — works differently:

A single checker blocks a point — you can't land on a point occupied by the opponent's checker. Blocking is the main weapon; tempo is the key resource.

The head point — all 15 checkers start stacked on a single point, and only one can leave it per turn. The generator tracks a counter for departures from the head point within a single move.

An exception for the opening roll — on doubles 3-3, 4-4, or 6-6, the second player to move bears off... rather, moves two checkers. This exception exists precisely because, with these doubles, the first checker runs into the opponent's head stack on point 12 and can't advance further. The second checker plays out the remaining pips.

The ban on a closed prime — a block of six consecutive points is forbidden if it traps all 15 of the opponent's checkers (provided the opponent hasn't moved at least one checker past it already). This check is performed at every intermediate step of a move, not just on the final position.

The obligation to play the maximum — if both dice can be played, both must be played. If only one can be played, it must be the larger one. On doubles, as many numbers as possible must be played.

Bearing off only from home — bearing off can only begin once all 15 checkers are in the home area.

Three types of wins: oin, mars, koks

Long nardy has three possible outcomes, each worth a different number of points:

Oin (1 point) — the losing player managed to bear off at least one checker.

Mars (2 points) — the losing player bore off no checkers at all; all of their checkers are either past the opponent's home or inside their own home, but none have been borne off.

Koks (3 points) — the losing player bore off no checkers, and at least one of their checkers remained in the starting quarter (points 7–12 for red, 19–24 for white, using red's numbering).

The engine returns six probabilities — three outcomes for each side. The expected result (equity) is calculated using the formula: E = (P_wn − P_ln) + 2·(P_wm − P_lm) + 3·(P_wk − P_lk), where w/l stands for win or loss, and n/m/k stand for oin, mars, and koks. Equity ranges from −3 to +3: zero means an even position, +1 means a guaranteed win, +3 means a guaranteed koks.

Measuring quality of play

Move quality is measured simply: error = E(best move) − E(move played) ≥ 0. Forced moves and essentially equivalent options aren't counted, so as not to dilute the average. The average error per game is multiplied by 500 and called the Performance Rating (PR): a PR of 10 means losing 0.02 points per move on average.

To verify its evaluations, the engine uses rollouts: a position is played out to completion many times, with the program moving for both sides and fresh dice rolls each time. The average result serves as a benchmark. Rollouts are computationally expensive and aren't used during live play — they're a way to check contentious positions and catch errors in the neural network.