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Play & Draw Rules

Odds & Probabilities

QanVault operates with absolute statistical transparency. Because every ticket purchase is recorded on an immutable ledger, players can calculate their exact winning probabilities in real time before placing any transaction.

Single-Draw Probability Model#

In any single draw tier with N total participating tickets, holding k tickets provides an exact winning probability of:

P(\text{Win Single Tier}) = \frac{k}{N}

Because each 100 QANX ticket is entered with equal weight, the draw represents a uniform discrete probability distribution.

Multi-Slot Sampling Without Replacement

When a draw awards multiple distinct winning positions (for example, Tier 1, Tier 2, and Tier 3 prizes) and each winning ticket must be unique, the probability of winning at least one prize follows the hypergeometric distribution:

P(X \ge 1) = 1 - \frac{\binom{N - k}{m}}{\binom{N}{m}}

Where:

  • N = Total tickets entered in the draw
  • k = Number of tickets held by the player
  • m = Number of winning slots drawn without replacement

4-in-1 Cumulative Probability#

Because every ticket participates in four sequential and concurrent draws (Daily D, Daily D+1, Weekly W, and Monthly M), the player's cumulative probability of winning at least one prize across all four events is:

P(\text{At Least 1 Win Across 4 Draws}) = 1 - \prod_{i \in \{D, D+1, W, M\}} \Big(1 - P(\text{Win Tier}_i)\Big)

Worked Scenario

Assume the following ticket totals:

  • Daily Draw D: 10,000 tickets
  • Daily Draw D+1: 12,000 tickets
  • Weekly Jackpot W: 70,000 tickets
  • Monthly Jackpot M: 300,000 tickets

If you hold 100 tickets (k = 100):

  • P(\text{Win Daily } D) = \frac{100}{10{,}000} = 1.00\%
  • P(\text{Win Daily } D+1) = \frac{100}{12{,}000} \approx 0.833\%
  • P(\text{Win Weekly } W) = \frac{100}{70{,}000} \approx 0.143\%
  • P(\text{Win Monthly } M) = \frac{100}{300{,}000} \approx 0.033\%

Combined 4-Draw Chance:

P(\text{At Least 1 Win}) = 1 - (1 - 0.01)(1 - 0.00833)(1 - 0.00143)(1 - 0.00033) \approx 1.99\%

Holding 100 tickets yields nearly a 2% cumulative chance of winning at least one prize across the four draw cycles.

Expected Value (EV) Analysis#

Expected value measures the mathematical return of a ticket relative to its cost:

\text{EV} = \sum_{i=1}^{n} \Big(P(\text{Win}_i) \times \text{Prize}_i\Big) - \text{Ticket Cost}
  • Rollover Boost: When a preceding draw rolls over unclaimed funds, the effective pot size increases without increasing the ticket cost, creating positive Expected Value (+EV) conditions for subsequent players.
  • Protocol Overhead: 92.5% of all funds flow directly back to players across the four prize pools, while 7.5% covers keeper infrastructure, VRF oracle gas, and platform operations.

Interactive Odds Calculator#

You can simulate customized scenarios and model your exact chances using the built-in Prize & Odds Calculator. The tool connects to live contract data to display current ticket volumes, accumulated pot sizes, and hypergeometric win projections.

Next Steps#

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