Roll

1. 01

   Roll does not use your seed pair: one result is shared by all players. When a round opens the server draws a 64-character seed for it and shows its SHA-256 before any bet is taken.

2. 02

   mac = HMAC-SHA256(key = the seed as text, message = the round id). Read mac as eight big-endian 32-bit words.

3. 03

   tile = the first word below 4,294,967,280, modulo 29. (4,294,967,280 is the largest multiple of 29 below 2³², so every tile is exactly as likely as any other.)

4. 04

   Tile 0 is gold. Odd tiles are cyan, even tiles are violet. Tiles 1, 2, 27 and 28 are the flank.

5. 05

   If the tile is gold: mac₂ = HMAC-SHA256(key = the seed, message = the round id followed by ":light"). light = its first word below 4,294,967,200, modulo 100. The star lights when light is below 29.

6. 06

   If the star lights: mac₃ = HMAC-SHA256(key = the seed, message = the round id followed by ":star"). stop = its first word below 4,294,967,280, modulo 29. Gold is paid the star at that place on the reel.

7. 07

   The star reel, place 0 first: 100, 60, 40, 85, 12, 75, 100, 65, 30, 90, 16, 80, 100, 70, 25, 45, 95, 100, 55, 60, 8, 35, 85, 100, 50, 80, 20, 75, 50. They add up to 1,806.

8. 08

   When the round ends the seed is published: check its SHA-256 against the hash shown before betting, then run the lines above.

float(k) and the rest of the notation are defined in the byte stream.

Every player is in the same round. Bets are open for 15 seconds, then the strip rolls and stops on one of 29 tiles: 14 cyan, 14 violet and 1 gold.

Cyan and violet pay 2×. Flank pays 7× when the strip stops on one of the two tiles on either side of gold; those four are two cyan and two violet, so a colour bet on them wins as well.

Gold pays 14×. But 29 times in every 100 that the strip stops on gold (1 round in 100), the tile lights as the star: a second reel of 29 stars turns, and gold bets are paid what it stops on instead, from 8× to 100×. Every star is as likely as the next, and what each pays is listed below.

Each bet is priced one tile short of fair, so all four return 96.55%: 14 of 29 at 2×, 4 of 29 at 7×, and gold, 1 of 29, at 28× on average (71 landings in 100 at 14×, 29 on the star reel, whose stars average 62.28×).

The star pays 8× less often than it pays 100×: of its 29 stars, five pay 100×, fifteen pay 50× to 95×, six pay 20× to 45×, and three pay 8×, 12× and 16×. Two of them pay less than gold does without the star.

One bet per choice per round, on as many choices as you like. A bet cannot be changed or taken back once it is placed.

A round is settled by the rules it opened under. Rounds played before the star paid gold a flat 28× and the flank 14× on the two tiles beside gold; the verifier checks every round by its own rules.