Monday, June 2, 2014

The canard about the lottery, liars for Jesus

In many discussions with apologists for Christianity, the overwhelmingly poignant fact that a bunch of people believing something like the Resurrection story or other miracle claims is far more believable than the notion that any miracles actually happened. Granting that resurrections or miracles are even possible, which we have no right to believe, they're certainly very rare.

This frequently leads to the canard about the lottery. It goes something like this, which is something like how it showed up in a comment on this very blog the other day.
Winning the lottery is a very rare event, but you have no trouble believing that it is more likely that someone won the lottery than that it's a story (implied: that isn't true).
Sigh. If I had a dollar for every time I ran into this kind of thing, I wouldn't need to win the lottery to fund my dream of driving a Tesla that I power entirely by solar panels. We don't even have to get into the "rare occurrences occur all the time" stuff for this one.

The objection is superficially convincing, particularly to people who want to be convinced, and without a little experience with these kinds of things, the error in thinking is a bit difficult to spot. The fact is, though, that it's equivocation. Either the person who is making this argument is confused or prevaricating.

Here's how it works:

That my friend Cal wins the lottery, meaning the jackpot, is, indeed, a very rare event. If he buys a ticket, Cal's odds are just one in 175,223,510 for winning the jackpot of the American Powerball lottery. If Cal comes to me and says, "hey man, I won the Powerball jackpot!" my initial reaction is skepticism.

For me to believe Cal, he's going to have to produce evidence, even though he's my friend. It's simply easier to believe that Cal is putting me on than that he won a contest that he is 99.9999994% likely to lose. Even producing a winning ticket might not be good enough because producing an elaborate forgery for a joke is still more likely than winning. The lottery commission saying he won, though, would be different.

On the other hand, and here we see the slight of mind, someone winning the lottery jackpot is not a rare event. It happens all the time, several times per year.

How can this be? Volume and equivocation.
Volume: Lots of lottery tickets are sold every week.
Equivocation: Someone winning the lottery means at least one of those lots of tickets came up a winner. Cal winning the lottery means his comparatively very few tickets, or maybe just one ticket, came up a winner. The first of these is not rare. The second of these is very rare. By changing the focus from "someone" to "Cal," it's easy to dupe someone.

Let's do some numbers to show what I mean, as if someone winning the lottery several times a year isn't good enough to convince us. To calculate the odds that at least one ticket wins, we calculate the probabilistic complement that all of the tickets lose. If the probability that one ticket wins is w, the probability that that ticket loses is 1-w. The probability that n tickets all lose is (1-w)^n. The probabilistic complement that tells us the probability that at least one ticket wins is thus 1-((1-w)^n) when considering n tickets.

Here are some various chances of winning:
Cal buys one lottery ticket: 0.00000057%
Cal buys two lottery tickets: 0.0000014%
Cal buys five lottery tickets: 0.0000029%
Cal buys ten lottery tickets: 0.0000057%
Cal buys one hundred lottery tickets: 0.000057%
This isn't looking good for Cal. Winning the lottery is a rare event for any individual.

America buys 500,000 lottery tickets: 0.285% chance that someone wins
America buys 1,000,000 lottery tickets: 0.569% chance that someone wins
America buys 10,000,000 lottery tickets: 5.55% chance that someone wins
America buys 100,000,000 lottery tickets: 43.5% chance that someone wins
Every American buys one lottery ticket: 83.3% chance that someone wins
Every American buys two lottery tickets: 97.2% chance that someone wins

The chance that someone wins the lottery isn't small at all. It's not a rare event for someone to win the lottery. It would be rare if it was a specific person predicted in advance.

This line of argument that is supposed to increase confidence that the Jesus Resurrection story, or miracle claims, might be legitimate is a canard that should embarrass the person making it, and now you know why.


  1. It's funny how for the religious, that argument works for miracles, but not, say, for abiogenesis or beneficial mutations...