When I told my friend Craig about the golf story I wrote about yesterday, he didn’t seem terribly impressed. I was surprised at his reaction. I know that some things can appear to the mathematically unsophisticated to much more improbable than they really are. A case in point was when a psychology professor long ago in a classroom far away told us that the odds of two people in our modest sized class sharing the same birthday were a lot higher than we might think. In fact, he said, it was almost certain that at least two of us had the same birthday. We were skeptical. So, he proposed that we put his assertion to the test by having people call out their birthdays until someone else had the same birthday. The first person to call out her birthday was a young woman in the first seat in the front row. She said, “March 24,” and I said, “Bingo” and raised my hand, and everybody laughed.
I don’t know what the probability was of that happening, but it was surely many orders of magnitude higher than that of the three holes-in-one that some mathematician calculated to have a probability of one in 27 trillion. But my friend wondered how easy it would be for three consecutive bowlers to score a perfect 300 game. I opined that I thought it would be much easier than the three consecutive holes-in-one, but Craig didn’t think so. He thought the three 300’s would be at least as difficult and probably more so, and I thought that if he was right, three holes in one wouldn’t be that difficult after all, for I could easily imagine three consecutive bowlers bowling 300. Why my friend Tim and I began a game last week with our first seven strikes in a row. I got tapped with a ten-pin on the next ball and ended up with eleven out of twelve strikes for a 279 game; he got eleven strikes in a row before leaving a ten pin on his final ball and shooting 299. All that separated us from back-to-back 300’s were two measly strikes. If there had been a third bowler with us throwing the ball as well as we were on that lane, it’s quite conceivable that we could have had three consecutive perfect games.
But would that have really been equivalent to back-to-back-to-back holes-in one on the same hole? Craig argued that in order to bowl a 300 game, you have to strike twelve times in a row as opposed to having to make only one good shot to get a hole-in-one. But it seems to me that this is a little like saying that it’s it’s harder for a good high jumper to clear a six foot bar twelve times in a row than it is to clear a seven-and-a-half foot bar once. I don’t know the statistics on this, but I suspect that holes-in-one are far less prevalent than 300 games, because I suspect that they’re much harder to get. And the odds against getting back-to-back-to-back holes-in-one must be, well, somewhere around 27 trillion to one.
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