Roulette Verifier (European)

How digital roulette wheels work

In a physical casino, a croupier launches a ball in the opposite direction of a spinning wheel. In a provably fair online casino, this physical process is replaced by a cryptographic hashing function. The game merges the server’s committed seed, your client-provided seed, and the round’s nonce to generate a random floating-point decimal.

This decimal is then mapped directly onto a single-zero European wheel layout (containing 37 numbers, from 0 to 36). Because the server seed hash is displayed before you place your bets, the casino is mathematically blocked from moving the ball to a losing sector after seeing your chips on the layout.

The math: Mapping seeds to wheel pockets

Here is the exact mathematical pipeline used to calculate the winning pocket:

1. Converting the hash to a float

The verifier runs your server seed, client seed, and nonce through HMAC-SHA256. The first 4 bytes of this hash are converted to a decimal fraction U between 0 and 1:

U = Hex_To_Decimal(First_8_Chars) / 4294967296

2. Mapping to the wheel

To find the winning number, we multiply the fraction U by 37 (the total pockets on a European wheel) and floor the result:

Winning_Number = Floor(U * 37)

This creates an even, unbiased distribution where every number between 0 and 36 has an identical 1/37 chance of winning.

3. Deriving color, parity, and layout attributes

Once the winning number is found, the verifier maps it to its standard wheel attributes:

• Zero: Green, neither even nor odd.
• Red/Black Map: Numbers [1-10] and [19-28] are odd-red, even-black. Numbers [11-18] and [29-36] are odd-black, even-red.
• Dozen: 1st Dozen (1-12), 2nd Dozen (13-24), or 3rd Dozen (25-36).

Data Sandwich: Auditing a Red 32 spin

Let’s audit an actual spin. You bet $50 on Red. The digital wheel stops on Red 32, paying out a win. You rotate your seeds and paste the details into the verifier:

• Server Seed: 3e42ab...
• Client Seed: roulette_spin_seed
• Nonce: 8

The verifier runs the HMAC-SHA256 hash. The first 4 bytes yield a decimal fraction of U = 0.874291.

Applying the mapping formula:

Winning_Number = Floor(0.874291 * 37) = Floor(32.348) = 32

Checking the pocket attributes, 32 maps to **Red**, **Even**, and the **3rd Dozen**. The mathematical outcome matches your game history exactly. The spin is validated as fair.

Frequently asked questions