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Lecture 15

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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Lecture 15

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  1. Lecture 15

  2. Designing a lottery • What do we need to consider? • Random structure • Prices • Risk • Making it attractive for consumers

  3. 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

  4. 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

  5. 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

  6. 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.

  7. 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

  8. 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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