Articles about backgammon

Dice in backgammon: odds and fair rolls

Updated: October 16, 2026

"Another double for him!" — every player knows the feeling. Let's look at how often the rolls you need really come up, and why on NardPlay you can check the dice yourself.

A little maths

• Two dice have 36 equally likely outcomes.
• Any double comes up in 6 of 36 — on average once every six rolls (about 17%).
• A specific double such as 6-6 is 1 in 36 (under 3%).
• A specific pair of different numbers such as 6-5 (shesh-besh) is 2 in 36 (about 6%).
• At least one six on two dice is 11 in 36 (about 31%).
• On average a roll is worth about 8.17 pips of movement, counting doubles as four moves.

Why other people seem luckier

Streaks happen. Three doubles in a row is a 1 in 216 chance for three particular rolls, but a player gets 25–30 rolls per game, so such a streak shows up in roughly one game in ten. Almost everyone sees it in an evening of play. We also remember other people's luck better than our own. Over the long run it evens out, and the winner is the one who plays the rolls better.

Who rolls the dice on NardPlay

The server rolls the dice, not the player's browser, so they cannot be changed on your side. The bot does not choose the dice either: it receives them just like you do and only chooses its move.

Verifiable dice

Every game has its own secret key. From the first roll players can see its hash (SHA-256), and the server reveals the key itself when the game ends. Every die in the game is computed from the key and its number, so the server cannot pick rolls during the game: any change would not match the hash shown at the start.

1. After the game, press "Verify the dice" in the result window.
2. Your browser checks that the key matches the hash and recomputes every die of the game from it.
3. If everything matches, you will see "Fair" and the number of dice checked.

For those who want to check by hand: die number n of the game is the first byte below 252 in HMAC-SHA256(key, "n:0"), "n:1" and so on, taken modulo 6 plus 1. That way each number from 1 to 6 is equally likely.

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