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Posts Tagged ‘probability’

You may not have noticed, but the PowerballTM Jackpot is up to $600 Million ($376.9 Million cash value.)

The odds of winning the jackpot are 1 in 175,223,510.00.

They've got BALLS!

They’ve got BALLS!

For the sake of argument, let’s assume everyone bought the standard $2 ticket.  That’s 300,000,000 million tickets sold.  The odds of winning are slightly less than half that.  Therefore, the odds of someone (or some ones) matching tonight’s drawing are actually pretty good.

I think most people buy a ticket, and then PRAY that those numbers come up.

Like any gambler, I’m always in search of an edge over the house.  Some of us are really poor at math, and refuse to be constrained by silly laws of probability that apply to the rest of the human race.  I hoped to find a way to PREDICT which numbers were going to come up, rather than sitting back and waiting and praying for them to match.  I wanted to be PROACTIVE!

So I downloaded all the winning numbers since 11/1/1997.  The numbers are actually listed in the order in which they are drawn.  I decided to look and see what was the average number drawn for each ball, fully ignoring understanding that the chance of any given ball being drawn at any given time is always the same.

I discovered something interesting–or not so interesting if you consider the Law of Averages.  A truly random sample over a large number of attempts will eventually reflect the underlying probability.  There are white balls numbered from 1-59, of which five are drawn.  There is a set of red balls numbered 1 through 35 which represent the powerball; one of these is drawn.  One must match all six to win the big prize.  So with an event that has an equal chance of drawing a number between 1 and 59, the average should fall between those two–roughly 30.

But when I did the calculations, the average number of the first ball drawn was . . . 27.

At first, this was a head scratcher.   If the odds are that the first ball will be less than the expected average, I may be on to something here.  Perhaps there is some variable which we cannot see or understand which keeps some of the higher balls from falling first.  Maybe the amount of ink on the ball–single digits have less.  I don’t know!  I am starting to tingle!

The lottery states that the odds of matching one red ball (the power ball) is 1 in 55.41 rather than 1 in 35.  It’s not because they are cheating, but rather that is the odds of matching ONLY the red ball, and none of the white balls.  The odds of matching a red ball are still 1 in 35, but some of those people will also match white balls, which makes the odds of getting only the power ball slightly higher or less likely.  But I digress.

After a little research, I discovered that the power ball drawing used to pick five balls from a pool of 55, rather than 59, and the power ball used to be drawn from a selection of balls numbered 1 through 42, rather than 35.

Twenty-seven is roughly the average of a sample between 1 and 55.  The tingling, it turns out, was from my butt going to sleep spending so much time doing these calculations.

So then I checked the other numbers.  The average number drawn for the second number was . . . 27.  The third . . . 27.  The fourth–and fifth . . . you guessed it, 27.  Damn you, statistics!

I can’t play a ticket with nothing but 27’s?

So then I reordered the picks into numerical order.  If the actual draw was 6, 23, 19, 43, 13 then the new array was 6, 13, 19, 23, 43.

So guess what the average lowest ball to be drawn each time is?

Nine.

The second lowest ball to be drawn?

Eighteen.

The third lowest ball to be drawn?

Twenty-seven–same as the overall average for the picks in order.  Do you see a pattern emerging here?

The fourth lowest (or second highest) ball to be drawn averages 36.

The highest ball drawn for over more than a decade of draws is 45.

A ticket with 9, 18, 27, 36, 45?  Try again.  That combination NEVER came up since 1997.

The stats seem to affect the Powerball a little more.  The average Powerball drawn is 20, which is higher than what you would expect for 35 balls (17 or 18 depending on how you round it off) but lower than when they used 42 (which would be an average of 21.)  That number will supposedly start to creep down towards 18 as more draws are done with only 35 numbers.

In the end, I bought a quick pick (letting the computer randomly pick my numbers since I haven’t the faintest idea what numbers to pick) and will spend tonight praying and promising God a percentage of my winnings if only He would let me win.

Six numbers for $600 Million?  That can’t be too much trouble for the Almighty?

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