I was thinking about lottery odds, and how so much of the pitch is, essentially, you miss 100 percent of the shots you don’t take, with the thought that you should at least enter because your odds go up so much with just one ticket. The odds were non existent before, and now they exist even if they’re vanishingly small.
Is the difference between 1 in a million and 0 in a million actually somehow more than the difference between 1 in a million and 2 in a million, or between 492,368 in a million vs 492,369 in a million? Or are all three of these functionally the same?
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You’re absolutely right. Buying the first ticket and buying the second ticket are identical bets (in a game where there are millions of tickets). Slogans like “you have to be in it to win it” are technically true in a trivial sense, but the first ticket is no more likely to make you a winner than the second ticket.
>Is the difference between 1 in a million and 0 in a million actually somehow more than the difference between 1 in a million and 2 in a million
In terms of calculating your expected winnings, no. With one ticket, you’ve spent, say, $1 for a one in a million chance of winning $500,000, so your expected winnings are 50c, and your expected return after the ticket cost is -50c. With two tickets, you’ve spent $2 for a two in a million chance of winning $500,000, so your expected winnings are $1 and your expected return is -$1. It’s the same bet every time, you’re just putting more money onto it.
Again, it is trivially true that if you don’t buy any tickets, you can’t win. But that doesn’t make the maths of buying one or ten or a hundred tickets any better.
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