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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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Lecture 15

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Lecture 15

Lecture 15


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

MatchPrize % of Prize PoolOdds 1 in

  • 5 of 5Pari-mutuel54.71%575,757.0

  • 4 of 5Pari-mutuel14.76%3,387.0

  • 3 of 5Pari-mutuel9.74%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.


Lecture 15

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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