Wednesday, March 16, 2005

Oh man, yesterday, I could've won the lottery!

Now before I explain how all of that came about, I need to make a necessary mathematical digression, and I apologize, but bear with me for a minute....

For those of you who haven't heard me state this before, this is the Pasquali Law of Conservation of Luck:

"The amount of luck in a closed system remains constant."

with the Probabilistic Quantum Corollary #1:

"The probability of hitting a particularly bad stroke of luck increases exponentially with time over the closed system time period after hitting a particularly good stroke of luck."

and Quantum Corollary #2:

"The probability of the subsequent stroke of luck being of greater than or equal to but opposite in magnitude to the one preceding it is proportional to the magnitude of the original lucky (or unlucky) event."

And is best illustrated by example:

Suppose your closed system is your life during a 2 week period. If you have a stroke of particularly good luck on the 2nd day of your 2 week period, the probability of your having a bad stroke of luck is much greater on the 6th day of the two week period than it would be on the 3rd day, but with the result that at the end of the two week period, the amount of bad luck that you obtained after your particularly fortunate 2nd day adds up to balance out the total amount of good luck in the system such that you end up with about the same amount of total luck you started with. This is true regardless of how long the time period is (years, days, minutes), and what is also true is that in this example (2-week time period), due to corollary #2, if you had really good luck on your second day (for instance), and the bad luck was on the last day, the last day's bad luck needs to make up for all the fractions of good luck you had throughout the 2 week period, thus making it even more terrifying and devastating than it would've been had it occurred in small increments spread throughout the full 14 days, but due to corollary #1, the probability of the bad luck being spread about in small increments is much smaller relative to the probability that it would all come in a fell swoop at the latest, most inopportune moment.

Anyway, the proof involves a lot of logarithms and imaginary numbers and 7-dimensional tensors and Bessel functions and stuff like that, so I won't burden you with it here, I'll just go ahead and continue with the story....

So yesterday I went and got some Skittles, as is my custom on workday afternoons, from my workplace's vending machine. Imagine my surprise when upon opening the packet and shaking some Skittles out, I discovered 5 Skittles resting on the palm of my hand, all of them purple.

I love occurences like these (I have a very boring life otherwise), so I quickly calculated the probability of this happening: given 5 colors of Skittles, assuming all colors of Skittles are equally likely, the probability of picking 5 purple Skittles in a row is 1 in 5

^{5}= 3125 ! Imagine that! In the California Lotto, such odds pay out approximately 112 dollars. Now, if every Skittles package costs 65 cents (yeah we have expensive vending machines), then that makes....172 packages of Skittles! Enough to last me half a year!!! That is a very lucky occurrence....So given the Pasquali Law of Conservation of Luck, yesterday's occurences show that that day, instead of going to the vending machine to get my Skittles as usual, I should've invested my money on the lottery ticket instead, which would've produced, by way of winnings, 172 packages of free Skittles, because the chances of me getting such a large stroke of luck again anytime soon are pretty much zero.

On the other hand, the Pasquali Law of Conservation of Luck also implies that, had I actually bought the lotto ticket, in order to balance out my original lotto-winning stroke of luck, events: 1)that my 172 x 65 cents of winnings get eaten by the vending machine or 2)my Skittles packages get stuck in the glass if I were to use my lotto winnings to purchase them or 3) my co-workers steal all my winnings-purchased Skittles or even worse event 4) that all Skittles in all 172 packages purchased with the winnings turn out to be the dreadfully inedible red-colored flavor, are pretty much guaranteed.

Blech. Physics laws can be vindictive.

Comments:

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Oy, QC1 needs a minor amendment!Probabilities do not increase exponentially (by axiom 0<=P(A)<=1). Perhaps on the margin they approach the asymptote exponentially, however. ;)

Fascinating. Although I believe there is at least one closed system where bad luck is normally more prevalent than good luck . . . players in casinos. Of course, since the laws of physics are clearly skewed there (different Calabi-Yau spaces and all), then that may not apply to the universe of closed systems you've described. :)

There is a flaw in your maths there. You claim that by purchasing an lott0 ticket you would have gained 172 free packets of skittles.

But you would have had to spend $1 on the ticket so your net gain is only 170.46 packets.

Plus your initial investment in a lotto ticket would have been greater and so scaling the winnings the correct amount you would have only gained 110.8 packets of skittles.

But you would have had to spend $1 on the ticket so your net gain is only 170.46 packets.

Plus your initial investment in a lotto ticket would have been greater and so scaling the winnings the correct amount you would have only gained 110.8 packets of skittles.

I think you are assuming that the bag of Skittles is infinite - otherwise after removal of first skittle the statistics on the remainder will be different. Of course you could replace the removed Skittle each time, but that would be non-hygenic.

Heh, you're right, I should've said: "assuming all colors equally likely, and each draw independent", thus effectively accomplishing the "infinite bag of Skittles/replace each time" part.

On second thought, with an infinite bag of Skittles, can you imagine how wonderful that would be? I wouldn't even have to buy a lotto ticket, after all! :D

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On second thought, with an infinite bag of Skittles, can you imagine how wonderful that would be? I wouldn't even have to buy a lotto ticket, after all! :D

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