Dice, Explained — Roll Ranges, Win Chance and the Exact Payout Math

Where the roll comes from

Every roll is a number from 0.00 to 99.99 — ten thousand equally likely outcomes. It is derived from the provably fair hash (see how the hash is built ): take the first 13 hex characters — 52 bits of the HMAC-SHA256 output — read them as an integer, and map into the range:

roll = ( int(hash[0..13]) mod 10000 ) / 100

52 bits is deliberate: it is the largest slice that stays exact in standard floating point, and it makes the modulo bias against 10,000 outcomes negligible (about 0.0000002%). The roll exists before the animation — the slider and tumbling dice are presentation, not physics.

Over, Under, and your win chance

You pick a target and a direction. Roll Over wins when the roll is strictly greater than the target; Roll Under wins when it is strictly less. Because there are 10,000 possible rolls, the win chance follows directly:

            chance(Over t) = 99.99 − t   (in %)
chance(Under t) = t
          

Note the asymmetry: Over 50 wins on 49.99% of rolls — the roll exactly 50.00 loses — while Under 50 wins on a clean 50.00%. The equality case always belongs to the house side of the line, which is one of the two places the numbers stop being “intuitive” (the other is the edge, next).

The payout formula

A fair payout would be 100 / chance — a 50% shot paying exactly 2×. Dice applies a 2% house edge to that fair price:

payout = ( 100 / chance ) × ( 1 − 0.02 )

So the expected return is 98% at every setting — chance × payout always comes back to 0.98:

Every setting costs the same

Look down the table: multiply any row’s chance by its payout and you get 0.98. Sliding toward a 49× long shot or a near-certain break-even grind changes how it feels — the swings, the streaks, how long a bankroll lasts — but never what it costs. There is no target that “beats” another, and no streak logic (“due” numbers, hot ranges) that changes a fresh 10,000-way draw. That trade-off between swings and cost is volatility vs edge — covered in House Edge vs RTP .

Check a roll yourself

After rotating your seed, paste the revealed server seed, your client seed and the bet’s nonce into the verifier (choose Dice). It recomputes the HMAC and the exact formula above in your browser — the roll you got is the only roll that hash could ever produce.