Sunday, April 01, 2007

Magical Weekend (April 1st)

It all started with numbers. A couple years back, I started buying lottery tickets, using numerical patterns that would make sense only to me. Of course, I realized the odds of ever winning were lower than getting struck by lightning, comparable with coming home to find one of the women I've loved but lost waiting for me in my bed.

Yet, almost out of some superstitious belief, I kept buying and playing, never coming even close to the winning sequence. Then, about six months ago, I started noticing something quite interesting.

The winning numbers tended to recur in clusters for a while, and then disappear. A new bunch of numbers (in groups of 36) would then supplant the previous group. Given that there are six winning numbers, if my observation proved correct, the odds of picking at least one of them was far better than one in ten million; it was more like one in six.

But how could this be?

Even if true, this would hardly guarantee I could ever win, because of course I would have to cover all of the various combinations of the precise six of those 36 before the sequence evolved on to its next grouping. Upon closer examination, I realized the sequences changed before all options had been exhausted, in fact, roughly (as far as I could observe) around halfway through the natural cycle.

I needed a calculator to compute the 6/36 to the sixth power, spread evenly over the number of weeks needed to exhaust the sequence, then divided by two. The first five months, I foundered hopelessly.

Then, this past week, I had an epiphany. The computers programming each week's lottery numbers must only be able to handle a pool of 36 numbers, randomly distributed. Although this is almost incalculable, I then noticed something else.

It was that old doubling pattern that appeared to me as a child: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, etc. (Some of these numbers will be familiar to all computer user.)

Suddenly, it all became clear. There would be a way to predict the next sequence of winning numbers if I could reconcile the sixes with the twos, i.e., 6, 36, 216, 1296, 7776, 46,656.

It took me days to solve this puzzle, but eventually it became obvious.

After a series of simple calculations, I started listing the possible winning calculations and compared them with the winning numbers the past six weeks. Yes! We were near the end of this group's turn, so there were fewer possible sequences left than at any other point in the cycle.

This would be my best chance. I ran the numbers and had six possible options. After that, it was easy. I took out two dice and rolled them. This would yield precisely a one-sixth sequence that would have as good a chance as any other.

If you've followed this, you realize I was playing odds along a .167 probability curve. In order to maximize my chances, I bought (of course) six tickets. And rolled the dice five more times. Of course I was only covering one thirty-sixth of the total range of possible sequences at this point, but I didn't feel it was wise to spend $216 dollars last night, just in case I was wrong.

Six bucks felt like the right amount to risk to find out if my theory was true.

Glory is to God! I won. Last night, as I watched TV at 7 p.m., when the winning numbers are announced, I had picked three of the six!

Thus, today I am $10,000 richer!

p.s.

April Fools. :-)

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