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Lecture 15

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# Lecture 15 - PowerPoint PPT Presentation

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

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
• 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
• 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
• 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

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.
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 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}