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## PowerPoint Slideshow about ' Lecture 15' - terena

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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)

- Rollover in jackpot increases excitement
- 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)

- Draw m balls out of M; players also select m numbers
- 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

- m digits (0,1,…,9) drawn with replacement – players try to match numbers in order or out of order

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)

- When ordered:
- Drop the order
- M(M-1)(M-2)…(M-m+1)/{m(m-1)…2 1}

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