Catch the Ace is a progressive raffle in which a ticket draw selects a participant who then receives an envelope reveal, with the designated ace awarding the progressive jackpot. Winning the ticket draw and winning the jackpot are separate events.
Ticket probability and conditional ace probability
Let N be the number of valid tickets in one weekly draw. If every ticket is equally likely to be selected, one ticket has a 1/N chance of winning that draw.
Let m be the number of unopened envelopes, with one ace remaining. If those envelopes are exchangeable from the participant’s information and the selection is valid, the probability of revealing the ace after winning the ticket draw is 1/m.
The complete jackpot probability multiplies the first probability by the second conditional probability:
Jackpot probability per ticket = 1/N × 1/m = 1/(N × m).
Take 1,000 valid tickets and 10 unopened envelopes. One ticket has a 1 in 1,000 chance of reaching the envelope reveal and a 1 in 10 chance of finding the ace conditional on reaching it. Its jackpot probability is 1 in 10,000.
A smaller envelope pool and a larger ticket pool
Removing a non-ace envelope increases the conditional ace probability for a later draw. It does not determine the later draw’s ticket count.
Take a later draw with five unopened envelopes and 3,000 valid tickets. The conditional ace probability has doubled from 1/10 to 1/5. The jackpot probability for one ticket is now 1/(3,000 × 5), or 1 in 15,000. The larger ticket pool more than offsets the smaller envelope pool.
That comparison concerns jackpot probability. Cash value also depends on the prizes and ticket price. Increased sales can change the weekly award and the progressive contribution, so a probability comparison alone does not establish which ticket has the higher expected cash return.
Weekly awards and progressive awards
The Fergus-Elora Round 4 rules, commencing December 11, 2022, allocated 20% of each week’s sales to the weekly winner and added 30% to the progressive jackpot. Each ticket expired after its own weekly draw. The progressive balance carried forward under the event rules; an unsuccessful ticket did not become a continuing claim on that balance.
For a draw that pays a weekly award W whether or not the ace appears, and an additional progressive award J when it does, one ticket’s expected gross payout is W/N + J/(N × m). J is the amount payable at that draw, including any current-week contribution. Counting that contribution again would overstate the award.
Take 1,000 tickets costing $2 each, a weekly award equal to 20% of the $2,000 sales, a $10,000 progressive award and 10 unopened envelopes. The expected weekly award per ticket is $400/1,000 = $0.40. The expected progressive award is $10,000/10,000 = $1. Expected gross payout is $1.40; expected net cash return after the $2 ticket cost is −$0.60.
Event rules define the calculation
The two-stage model requires one ordinary ticket draw followed by one envelope reveal. A forced final draw or a procedure that continues revealing envelopes until the ace appears changes the outcome distribution. Ticket bundles require the actual number of eligible chances and the bundle’s price.
The historical Fergus-Elora percentages describe that event’s rules. Another raffle’s allocation, ticket validity and final-draw procedure must be represented by its own inputs. Under the stated two-stage model, the break-even ticket cost is W/N + J/(N × m). The number of envelopes alone cannot supply that price.