There's only 65536 different nonces a user can apply. You give the users secrets which when all those different nonces are applied, has a higher average, or more losses depending on the game they're playing. This will inherently change the odds advertised.
The secret is given out before the player chooses a number to play on, so is your concern that we could only chose secrets which were more likely end up with a high number when being nonced with every number in the range 1-65536? This is certainly possible, but computationally impractical.
In our tests performing dsha256(secret + nonce), where nonce is in the range 1-65536 gave quite an evenly random distribution. If necessary we can increase the size of the nonce field, maybe 32-bits would provide a more even distribution.
Edit: Valid point. I'll increase the size of the nonce.
Edit again: Nonce fields are now 32 bits, this is working in the api, but the html and javascript are cached and will clear in the browser after an hour.
