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1. Which one of the following correctly places common forms of gambling in decreasing order in terms of their average returns, or payout, per dollar gambled? |
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| a) Slot Machines, Black Jack, State Lotteries, Roulette, Craps
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| b) Black Jack, Craps, Slot Machines, Roulette, State Lotteries
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| c) Slot Machines, Black Jack, Craps, Roulette, State Lotteries
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| d) Black Jack, Craps, Roulette, State Lotteries, Slot Machines
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2. State Lotteries are often touted as an easy way to raise revenue for public projects. Many lottary opponents, however, complain that they are an inefficient tax. On average, what percent of lottery revenue, the money spent on tickets, is returned to the state for public use? |
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| a) 31%
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| b) 51%
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| c) 75%
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| d) 83%
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3. It is often observed that, according to standard Expected Utility Theory (von Neumann Morgenstern), it would be irrational to purchase both insurance and chances in a lottery. This statement assumes that the expected payout for both is negative (i.e. that they are actuarially unfair.) In reality, a large potion of lottery players also purchase some sort of insurance. Assuming lotteries and insurance are always actuarially unfair gambles, which of the following modifications to the standard story would explain this paradox? |
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a) Contrary to the standard assumption of diminishing returns, many lottery players find that each additional unit of wealth increases their utility more than the previous unit did.
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b) Lottery players may be risk adverse for small or medium gambles, but risk-seeking with respect to gambles with extremely large payoffs.
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c) Many lottery players overweight – give undue consideration – to extremely low probability events.
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| d) b and c only
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| e) All of the above
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4. The winner of the Massachusetts Big Game Mega Millions jackpot must match five numbers out of a pool of 52 options (order is irrelevant) and also match an additional number out a separate pool of the same size. Assuming all numbers are selected at random, what are odds that a given ticket wins the jackpot? (Hint: 5! (ie., five factorial) = 5 x 4 x 3 x 2 x 1.) |
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| a) 47! / (52 x 52!) or about 1 in 16 billion |
| b) (5! x 47!) / (52 x 52!) or about 1 in 135 million |
| c) (5! x 47!) / 52! or about one in 2.6 million |
| d) (6! x 46!) / 52! or about one in 20 million |
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5. Most lottery jackpots are pari-mutuel – that is, lotteries allocate a percentage of ticket sales to the jackpot for that round. If no winning ticket is sold in one round, the jackpot typically rolls over and is added to the jackpot from the next round. Occasionally, lottery payoffs are a fair or even more than fair bet. In some cases, organizations have attempted to capitalize on this by purchasing every possible number combination, guaranteeing a jackpot. This is known as buying the Trump Ticket. Authors disagree about the effect of purchasing a Trump Ticket on the average expected returns for the holder. Assuming the purchase can be executed without influencing other players’ choices, which statement is true. |
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a) Purchasing a Trump Ticket decreases returns, because it increases the number of tickets purchased and therefore the odds that there will be multiple winners and a shared jackpot.
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b) Purchasing a Trump Ticket increases returns, because the purchase of the Trump Ticket increases the size of the jackpot.
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c) Purchasing a Trump Ticket has an indeterminate effect on returns, because it increases the jackpot and increases the odds of having to share that jackpot.
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d) Purchasing the Trump Ticket has no effect on expected payoff. Rather, the Trump Ticket serves to covert the expected payoff to a certain payoff.
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