Wednesday, April 20, 2005
Lottery tickets and mathematical puzzlers.
Since I'm not sure who I want to slap upside the head next, I'll leave that alone for the time being and toss out another math teaser. Most folks are familiar with the "6-49" style of lotteries where, in this case, you buy a ticket for the chance to pick six different numbers of your choice out of the possibilities of one through 49.
Come draw time, six numbers are selected (allegedly randomly) and, if you have all six winning numbers, you get a fistful of cash. If it turns out that more than one person selected exactly the same six winning numbers, all winners share the pot equally. (Some variations have smaller prizes if you get at least some of the numbers right, but that just complicates life so let's ignore it for the time being.)
Naturally, lots of folks have "systems" that they think increase their chances of winning, and lots of other folks just pick numbers that have some kind of personal significance or sentimental value. But, as we all know, in the end, if the winning numbers are really drawn randomly, then any set of six values is no better and no worse than any other set of six values.
Or is it?
In fact, if you're clever, you can get a sneaky advantage over others playing the same game. Based on just the rules you've read above, how can you maximize your expected return from playing this game? No tricks, it's all above board. Think about it. And if you're stumped, go back and read the challenge carefully. The first correct answer will, of course, win absolutely nothing. I don't get paid enough to give out actual prizes.