{P = 0:n} The Game is Rigged
In response to State-sponsored lotteries coming under fire for selling scratch-off tickets after the grand prize has been awarded, Tony opines:
Reflexively I side with the state’s position in this case as long as the practice is disclosed…
Or I could be totally wrong and the state’s engaging in shady practice. I seem to be in the minority in thinking the state shouldn’t be in the gaming business, to say nothing of imposing a monopoly. Maybe I’m also being a silly here in thinking the contract is the contract.
[ Insert Libertarian rant contra State Lotteries, here. ]
To the extent that the State is involved in the gaming business, it should not have a monopoly on the practice. Honestly, isn’t a monopoly on violence enough for anyone, anymore?
Although I concur that the State shouldn’t be in the gaming business, I think the rest of Tony’s analysis is wrong.
I’m going to simplify for the sake of argument, and assume that there are no lesser prizes to be awarded. I think a game like this, aside from being an oppressive instrument of the State, is at best a pseudo-contract for a couple of reasons: Because one winning ticket is known to exist ex ante, there’s no lawful consideration given by the State to the vast majority of participants whose true “odds” of winning were 0:n from the get-go. This problem is compounded by the fact that such an instrument is necessarily a deceptively ambiguous adhesion contract.
Each individual ticket does not have an equal probability of winning. It could be argued that each individual purchaser has equal probability of buying the winning ticket; but these things aren’t quite the same, since this condition only holds when late-comers are unaware of the changing odds. In a free market, the odds are the same for everyone, regardless of when they enter the game.
In a normal draw lottery, where a winner is chosen at random from a pool of participants, the amount of the prize is determined by the number of tickets sold, and the odds of winning that prize are determined primarily by the number of participants. This game, on the other hand, can only generate profit when all tickets are sold, which can only be done when participants are kept in the dark. Imagine going to a high-school football game, or church social, or Elk’s Lodge meeting, and being asked to participate in the 50/50 raffle, only to find out that Jim from Accounting had already been declared the winner.
A simple question could be posed:
Would you play the lottery if you knew that your odds of winning were 0?
Of course, you would not. All else being equal, knowledge of the winning ticket having already been sold, the odds are (no pun intended) that nobody would buy the remaining tickets, the game would be constantly under-funded and go bankrupt as a result. Once the winning ticket is sold, the proprietor has an obligation that can only be met by selling more tickets, but there should be no willing buyers.
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Mmmmhmmm. Even so, I still maintain that lotteries are a tax on people who are bad at math.
Thanks for considering the issue. I’d hoped to generate even a little bit of discussion because I thought the story interesting. Instead, I’ve seen what amounts to outrage just because the state is involved. Yeah, conceded. But why is it outrageous? You’ve done a bang-up job of going after that question. I’ll blog a response later today.
You neglected to factor in the non-pecuniary benefit of gambling. Many people are simply entertained by the thrill. Those people, ignorant of their zero probability, still receive the entertainment value that they expected.
State Lotteries, Round 2…
In response to my entry on state lotteries continuing scratch-off games after the top prize is awarded, this response from David Z. at no third solution.Although I concur that the State shouldn’t be in the gaming business, I think the……