Two laws shape every game
The expectation law: win rate and multiplier are one dial. For a win-or-nothing game,win rate = (1 − edge) / multiplier. At a 3.5 % edge:
A high win rate costs nothing in capital.
The capital law: only the top prize costs money. The pool reserves the worst case,
stake × top multiplier − pool credit, and the per-wager cap bounds it. Nothing else in the paytable enters the cap. A game that pays out 90 % of the time can be trivial for the pool to carry; a 1 000× jackpot needs a large pool.
Worked paytables
All at a 3.5 % declared edge, soΣ p·m = 0.965.
Loot box: every box pays something
Loot box: every box pays something
The common tier must return less than the stake. If every outcome paid 1× or more, the expected return would exceed 1 and
open_wager would refuse the paytable.Slot with a jackpot: frequent hits and a rare 100×
Slot with a jackpot: frequent hits and a rare 100×
Half the expected-value budget goes to the jackpot; the rest buys a 47 % hit rate.
Jackpot demo: five outcomes
Jackpot demo: five outcomes
The devnet demo’s paytable, as the program stores it:
Mines, decided up front
Mines, decided up front
A 25-cell grid with 3 mines and a player who commits to 5 safe cells: the chance that 5 cells miss all 3 mines is 26 334 / 53 130, about 49.57 %, so a two-bucket paytable at a 3.5 % edge pays up to 1.9469× (
m = 19 469 bps) on that outcome. The interface can still reveal cells one by one, but it animates an outcome already drawn. Crash with a cash-out set before the round is the same construction.One wager for a whole round
A wager has one draw, but nothing says it belongs to one player. A studio running rounds (a multiplayer crash, a wheel, a roulette table) can fold every bet of the round into one paytable and open one wager for the total, with itself as beneficiary, then pay its players from the result. Everyone sees the same draw, and one oracle call serves the table. Example, crash at a 1.5 % edge, Alice stakes 10 at a 2× cash-out and Bob 20 at 5×:
Limits: at most 32 distinct payouts per round, and players trust the studio to pay them from the result. The studio can make that checkable by publishing the bets behind each round’s on-chain paytable.