In Which We Are Smarter than the Minnesota Lottery

This one was sent in by Mike, a faithful reader. Yes, I have at least one faithful reader!

MAPLEWOOD, Minn. (AP) – An airline pilot from Maplewood won a $25,000 lottery jackpot – two days in a row.

Raymond Snouffer Jr. matched the winning numbers 11-14-23-26-31 to win Saturday’s Northstar Cash drawing with odds of about 170,000 to 1, Minnesota Lottery officials said.

On Sunday, Snouffer stuck with 11 and switched to 3-7-19-28 – and won again.

Lottery officials said such a sequence was so farfetched that the odds against it were “virtually incalculable.”

Virtually incalculable? “You keep using that word. I do not think it means what you think it means.”

Just square the probabilities!!! The “virtually incalculable” odds are about 1 in 28.9 billion.

(Working backwards, it appears that the structure is 31 numbers, of which you choose 5, which gives odds of 169,911 to 1. Assuming that’s true, the precise odds of winning twice in a row are 28,869,747,921 to 1.

Those are the odds of a particular person winning any two particular drawings in a row. Their odds of ever winning twice in a row ever are greater, since you has many chances to win twice in a row. Another way to look at it is that there is always a winner from last drawing. Assuming they play again, their odds are 170,000 to 1. That is the odds that there will be a repeat winner for a particular drawing.)

Welcome any Wikipedia readers. Note the parenthetical above, the probability of “this” happening depends on what you think “this” is.

4 thoughts on “In Which We Are Smarter than the Minnesota Lottery

  1. The bad news is that the guy took a 1 in 28 billion event of good luck and only parlayed it into a measley $50K. $25K payout for a 1 in 170K probability of winning — sounds like a negative expected value to me, unless his lottery ticket cost him a dime or so.

    Reminds me of an excellent email Muttrox sent me pre-Muttroxia, about when you should technically play the Powerball (i.e. when your expected value is positive).

  2. Ed, your aliases are getting more subtle. I didn’t catch on this was you at first. Met any nice undergrads lately?

    I might have to go back on that positive expectation bit. The logic was that if the odds are 1 in 300 million, and the jackpot is 400 million, than your expected payoff is $1.33 for a $1.00 bet. Even a bit better, since there are other prizes offered.

    However, I now think that may be incorrect. Because there are too many people playing. If you win, you’re not guaranteed of the entire jackpot. Say there’s a 60% chance you’ll split it with someone else. Then your expected payoff goes below $1.00 again.

    I don’t know what the stats are on how many people play the lottery when the jackpot gets higher. That would be an interesting correlation, match up size of jackpot with how many tickets were bought, or maybe how many winners there were.

  3. Glad you caught the reference. If I wanted to be really subtle, I could have used William A., but I figured I’d give you a chance. Speaking of William A., he’s dead now, I think.

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