Nov 07 2008

If I Had a Nickel….

….for every time I stood in line behind some #^$%@ buying a lottery ticket….  Thank God for pay-at-the-pump.

Recently I wrote that lotteries are a tax on the innumerate (clueless at math), which may have insulted some people, so I thought I’d explain.  While many lottery players are spending money they really can’t afford, I know others who are well-off, who say, “Hey, I can afford a few bucks a week, so why is it any worse than buying a movie ticket or a magazine, if I have fun?”

But is it really that much fun?  Wouldn’t gambling on almost anything else—football games, poker, the weather—be more entertaining?  Watch the Kentucky Derby; now those people look like they’re having fun.

The usual response to that is, “Yeah, but with those things I can’t win big.  I know my odds of winning the lottery are a lot lower (massive understatement), but if I do win, it’ll change my life.  I can’t win millions betting on football games.”

And that’s where the innumeracy comes in, because your chances of becoming a millionaire are actually better with betting on football games, or almost anything else.  The numbers are just so big that people can’t get a handle on them to compare.

The Powerball, which I guess is the biggest lottery around here, is currently at a cash value of $12.5M, and the odds of winning are 1 in 146,107,962.  Now, let’s look at football games.  To keep this simple, we’ll assume you’re betting the point spread, nothing fancy, so you have a 50% chance on each game.  If you win, you double your money; if you lose, you’re out.  Start with one dollar and keep re-betting your winnings on the next game.  How long would it take to pass 12 millon dollars?

Well, one game gives you $2, two wins gives you $4, three gives you $8, and so on.  Keep doubling, and you’ll find that after 24 wins, you’ll have $16,777,216.  Bet one game on Sunday and one on Monday, and you’ll be a millionaire 2/3 of the way through the season—if you’re lucky.

At this point, most people will say, “Yeah, but there’s no way you could pick 24 games right in a row!  That’s not just improbable like the lottery; it’s impossible!”  Oh really?  Well, the odds of winning twenty-four 50-50 bets in a row are 1 in 16,777,216.  So you’re 8.7 times more likely to be able to win 24 football bets in a row than you are to win the lottery.  Looked at from the other direction, the odds of winning the Powerball are just a bit worse than the odds of winning 27 football bets in a row.

The problem is that we can’t really feel numbers that big, so we focus on the ones we can handle: one lottery ticket is easier to win than 24 straight football bets, right?  Well, no, it’s a lot harder to win with that one ticket, but it’s hard for us to accept that.  The numbers don’t lie, though.

So, the next time you feel like gambling a dollar, bet on something that’s actually fun and holds a better chance of winning, and stop holding up people behind you who just want to pay for their gas and get moving.

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