From jewishfeminist02’s husband: depending on the lottery, the odds of winning are more like one in several billion. There is only one winning ticket, and the number of possible tickets is the product of the number of choices for each ball. For example, in Powerball, there are 59 choices for each regular ball (5 of them) and 35 choices for the bonus ball. That makes 59 x 59 x 59 x 59 x 59 x 35 – 1 losing tickets (subtract the one winning ticket), a total of over 25 billion (25,022,350,464 to be exact). A 1 in 25 billion chance of winning say $200 million is worth a little less than a penny.
The most reasonable situation in which I can imagine someone offering $2 million (if they know the numbers on your lottery ticket, you probably have other privacy and safety issues to worry about) is if the person knows that the winning ticket was purchased at the same store as you bought it, but the person doesn’t know if you have the winning ticket or not. Strictly speaking, if 25 people bought tickets at that store, a 1 in 25 chance at $50 million is worth $2 million (and I suspect most stores sell at least 25 tickets, making this a potentially good deal).
This means that if the seller betting $2 million on a regular basis (the odds become more precise the more times you bid), the seller would on average come out even – losing $50x million from 25x bets and winning x bets worth $50x million. Technically, it’s a good deal for the seller if your odds are any worse than 1 in 25 (i.e. the store sold less than 25 tickets, such that you would have to gamble more than $50x million to recover $50x million), but it’s only a reliable predictor over many, many trials, and I assume that the seller isn’t going around offering $2 million to tons of people. This means it’s a bad deal for the seller, and you should grab it.
Here’s a more concrete example of how you need many, many bets for odds to be reliable. Imagine you bet $1 that you will roll a 4 on a regular die, with a payoff of $6 if you win. As many of us know from board games, it’s fairly easy to end up with a bunch of non-4’s for many turns, but then to get several 4’s in a row. If you can only bet once, there is an 83 1/3% chance you will lose, and a 16 2/3% chance you will win. The more you roll, the more things even out. After 100 rolls, odds are you will win around 15-20 times (I can’t remember the exact odds of ending up in that range, but I’m pretty sure it’s at least 60%). After betting $100, 15 wins would be a loss of $10 and 20 wins would be a profit of $20 (as opposed to an 80% chance of losing everything). At this point, it’s a lot less risky.
Here’s a cooler example. There’s a great exhibit in a museum in Boston that shows how a bell curve works. (For those who don’t know what a bell curve is, there are many websites that give at least something of an explanation). There is a machine that drops balls randomly from a particular point and allows them to spread out as they fall, and the balls end up stacking into the shape of a bell curve. Let’s say you bet that a ball will land at a particular spot (odds are best at the middle). Each individual ball could end up anywhere in any order. There could be a particular spot that’s only supposed to get 4 balls (and only will get 4 balls after everything falls), but the first 4 balls end up in that spot. That spot ends up with a significant profit (since the odds were slim), and everywhere else ends up with a greater loss than expected. But after those 4 balls, that spot won’t get anything else, and the balls will have to fall on the other spots.
I’m sorry if this didn’t explain things clearly. I’m kind of a probability nerd, and am trying my best to not include the greek letters, exponents, and calculus necessary to explain what’s actually going on. If anyone’s interested in a more formal and rigorous explanation, PM my lovely wife.
L’maaseh, $2 million is a good deal, and probably an amazing deal (if the seller doesn’t know anything about the ticket and it’s worth less than a penny). The only good reason not to accept the deal is if you’re planning to play the lottery millions of times and the seller is willing to buy every single ticket.
Of course, one must ask how the yid acquired the ticket to begin with, as we know that lottery tickets are an asmachta and asmachta lo kanya (Sanhedrin 24a), not to mention that a habit of gambling makes one pasul eidus (Ibid).