What your odds cost
One draw serves every partner in the round, whatever size of game each runs inside it. Two numbers you control and two the round supplies price your entry exactly — your chance, your prize, and what asking for a prize beyond the pot costs. One identity covers the whole scheme:
Pr(i) = (Aᵢ ÷ Jᵢ) × (1 − Hᵢ)chance = your stake ÷ the prize it plays for, discounted by the draw edgeFour numbers set every term.
Everything the draw computes for your entry is derived from these. Amber values are yours to move, purple values belong to the round, and green terms are derived from both — the same coloring the calculator uses.
AᵢYou set itAggregate contributionEvery ticket you sell adds its contribution to your round total. The sealed manifest commits the final figure at close, along with a hash of your exact receipt list.
TᵢYou set itDesired prizeThe prize you want your entry to play for. Change it while sales are open; the value at lock becomes immutable and is committed with the draw terms.
ΣAⱼThe round supplies itEveryone else's contributionsAll other partners' tickets in the same round. Together with
Aᵢit forms the ticket-funded potP— every contribution, yours included, grows the shared prize.QThe round supplies itPrize bankrollThe funds Luckotto provides to underwrite prizes above the pot. Fixed when the previous round settles, committed in the manifest, and never part of the pot itself.
A prize above the pot costs probability.
The pot P = Aᵢ + ΣAⱼ is what ticket money alone can pay. Where your desired prize sits against it decides which of two cases prices your entry when the round locks.
The pool pays for itself
A desired prize the pot already covers is a plain pool. Your chance is your share of the pot and the draw withholds nothing — a pot-backed entry pays no edge, only the fixed per-ticket fee at creation. A round in which every partner is pot-backed always pays someone.
- Prize
Jᵢ = P- Draw edge
Hᵢ = 0- Chance
Pr(i) = Aᵢ ÷ P- Expected value
Aᵢ
1 BTC staked of a 10 BTC pot: chance 10.00%, prize 10 BTC, expected value 1 BTC.
The bankroll carries the shortfall
A desired prize above the pot makes the bankroll commit the shortfall Eᵢ, and carrying that risk is charged in probability: the fair stake-per-prize chance is scaled by (1 − Hᵢ). A desired prize is capped at P + ⌊Q ÷ 2⌋ — one winner never takes more than half the bankroll.
- Shortfall
Eᵢ = min(Tᵢ − P, ⌊Q ÷ 2⌋)- Prize
Jᵢ = P + Eᵢ- Draw edge
Hᵢ = Eᵢ ÷ Q- Chance
Pr(i) = (Aᵢ ÷ Jᵢ) × (1 − Hᵢ)- Expected value
Aᵢ × (1 − Hᵢ)
The same 1 BTC stake asking for 20 BTC from a 200 BTC bankroll: shortfall 10 BTC, draw edge 5.00%, chance 4.75%, expected value 0.95 BTC.
Same stake, double the prize: the fair chance halves to 5% and the edge takes another 5% of that. Neither number is final while sales run — every later ticket raises P, shrinks a live shortfall, and pulls the edge back toward zero.
Every term, live.
The sliders run the exact LUCKOTTO-1 arithmetic, integer floor division included, and the derived-terms panel fills every formula with the current numbers. The defaults reproduce a production-scale round; drag any input and watch what it moves.
Core payout if your partner wins
20 BTCJᵢ = P + EᵢThe ticket-funded pot plus the shortfall supplied by the prize bankroll. The partner applies its own game rules to customer prizes.
Pr(i) = vᵢ ÷ (2³² × P)Hᵢ = Eᵢ ÷ QThe final prize shortfall as a share of the prize bankroll, applied directly to draw probability.
- Ticket-funded pot
- 10.0001 BTC
- Prize shortfall
- 9.9999 BTC
- Draw allocation
- 20,401,309,404,472
- Projected prize
- 20 BTC
- Draw edge
- 5.00%
- Win probability
- 1 in 210,526
P = Aᵢ + ΣAⱼ = 0.0001 BTC + 10 BTCThe base prize funded by every ticket in the round.Eᵢ = min(max(Tᵢ − P, 0), floor(Q ÷ 2))Extra value supplied by the prize bankroll if this ticket is selected.vᵢ = floor(2³² × P × Aᵢ × (Q − Eᵢ) ÷ (Q × (P + Eᵢ)))The partner's exact final allocation, derived from its aggregate contribution, desired prize, P, and Q.Jᵢ = P + EᵢThe total Core payout the partner receives if selected.Hᵢ = Eᵢ ÷ QThe bankroll-backed shortfall rate used directly in the draw-allocation equation.Pr(i) = vᵢ ÷ (2³² × P)0.0005% · The partner's final draw allocation divided by the complete draw range.Where the discount goes.
Each bankroll-backed partner's discount — its plain-pool chance Aᵢ ÷ P minus its actual Pr(i) — is probability handed to nobody. Those discounts sum to exactly the round's no-winner chance: when the draw lands there, the pot accrues to the prize bankroll, which collects a pot precisely as often as the probability it was paid to carry.
None of this is taken on trust. Before the randomness exists, the sealed manifest commits every partner's aggregate contribution, locked desired prize, and receipt-list hash alongside Q — and the draw replays deterministically from public data.