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Lecture 15. Designing a lottery. What do we need to consider? Random structure Prices Risk Making it attractive for consumers. Making it attractive. People prefer huge sums of money Rollover in jackpot increases excitement

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designing a lottery
Designing a lottery
  • What do we need to consider?
    • Random structure
    • Prices
    • Risk
    • Making it attractive for consumers
making it attractive
Making it attractive
  • People prefer huge sums of money
    • Rollover in jackpot increases excitement
      • Rollover requires to have the jackpot split by winners (pari-mutual: a fixed amount is split)
      • Smaller prices are not usually split –each winner gets the same amount (this creates extra risk for the lottery)
  • The top price must be won often enough
    • This depends on number of players (target audience)
  • Usually there is some “good cause” for which the proceeds are targeted
formats of games
Formats of games
  • Genoese type
    • Draw m balls out of M; players also select m numbers
      • UK National lottery 6/49
      • NC Cash 5: 5/39 (most prices are pari-mutuel)
      • Powerball 5/59&1/35 (most prices with fixed, jackpot pari-mutuel)
  • Keno type
    • Draw m balls out of M with players select k numbers
  • Number type
    • m digits (0,1,…,9) drawn with replacement – players try to match numbers in order or out of order
      • NC pick 3, NC pick 4
our game
Our game
  • Genoese Type
    • Select m/M
  • How many people will play?
  • Select the payouts
    • What is the proportion we target to pay out in prices (usually 50-60%)?
    • How much to roll over for jackpot?
      • Small prices – more predictable; people win more often
      • Large prices – less predictable; people get more excited about them
nc cash 5 5 39
NC cash 5 - 5/39

Match Prize % of Prize Pool Odds 1 in

  • 5 of 5 Pari-mutuel54.71% 575,757.0
  • 4 of 5 Pari-mutuel 14.76% 3,387.0
  • 3 of 5 Pari-mutuel 9.74% 103.0
  • 2 of 5 $1.00 20.79% 9.6
  • The distribution of prices is skewed towards higher prizes. Because prices are pari-mutuel there is almost no risk to the lottery.
slide7
Risk
  • With large fixed prizes – we have higher risk
    • Larger variance means that we need to keep money on hand to cover unusual occurances
    • Will use R to investigate
how many ways to select balls
How many ways to select balls?
  • How many ways one can select m balls out of M?
    • When ordered:
        • M(M-1)(M-2)…(M-m+1)
    • Drop the order
        • M(M-1)(M-2)…(M-m+1)/{m(m-1)…2 1}
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