# Let's Play The Lottery

Discussion in 'General Discussion' started by g5000, Mar 29, 2012.

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### g5000Diamond Member

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The Mega Millions jackpot is now over half a billion dollars!

As of one minute ago, it was reported at \$540,000,000.

Ever wonder how to calculate the odds of winning? Well, pay attention and I will show you.

Since the order the numbers come out of the cage don't matter, this is a combination calculation rather than a permutation. In a permutation, the order matters. For instance, 9-6-3 won't open a lock which opens with 3-6-9. Which is why combation locks should really be called permutation locks.

But I digress.

The secret formula for calculating your odds of winning a lottery is...

n! / r!(n-r)!

Where n is the number of balls in the cage, and r is the number of balls drawn out.

The exclamation point means it is a factorial. You multiply the number times every number below it, down to 1.

For example, 5! = 5 x 4 x 3 x 2 x 1

Powerball and Mega Millions toss in an extra sixth ball which is drawn from a separate set of balls. So after you calculate the odds for the first set of balls, you then need to multiply your result by the number of balls in the second set.

So...Powerball draws 5 balls from a cage of 59 balls, and then 1 ball from a cage of 35 balls.

59! / 5!(59-5)!

This equals:

59 x 58 x 57 x 56 x 55 x 54! / 5! x 54!

Cancel out the common factors of 54! and you have:

59 x 58 x 57 x 56 x 55 / 5!

This gives you 5,006,386. So your odds of drawing the right combination of 5 balls from a cage of 59 balls is 5,006,386 to 1.

But you are drawing a sixth ball from a cage of 35 balls, so you multiply 5,006,386 x 35 to get:

175,223,510

Those are your odds of winning Powerball.

That is almost exactly 75% of the US adult population. 3 out of every 4 adult Americans would have to buy a unique combination of numbers for someone to win in a single draw.

Since not that many Americans actually buy tickets every drawing, and some people have the same combination as others, we rarely have a winner every draw. And that is why the jackpot climbs and climbs and climbs.

Notice that for every ball you add or subtract from the powerball cage, you increase or decrease the odds of winning by 5,006,386.

In 2011, there were 39 balls in the second cage, instead of 35. Which means your odds of winning decreased by almost another 20 million. The exact figure is:

195,249,054

So your odds in Powerball are actually better this year than last year.

But...it now costs \$2.00 to play instead of the \$1.00 it cost every year since its inception.

Speaking of Powerball's inception, that was 1996. And back then there were 5 balls drawn from 50, and one ball drawn from 25.

That means in 1996, your odds were 52,969,000. When you compare that to the 175,223,510
of today, there is clearly a whole lot of scamming by the government going on.

That is also why jackpots that exceeded \$100 million were very rare from 1996 to 2000.

Last edited: Mar 29, 2012
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### g5000Diamond Member

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To continue, Powerball draws 5 balls from 59, and one ball from 35. This gives you:

175,223,510

Mega Millions, on the other hand, draws 5 balls from 56, and one ball from 46. This means your odds of drawing the first 5 balls is much better. Close to 3.8 million instead of Powerball's 5 million to one odds.

However, when you multiply Mega Millions' 5 ball odds times the 46 balls in the second cage, you get:

175,711,536

Amazing! Almost identical odds!

But Mega Millions still costs \$1.00 to play.

Now think about that. There are only 175,711,536 possible combinations, each costing \$1.00 to play.

And the jackpot is \$540,000,000.

If you bought every possible combination, you are guaranteed a profit of \$364,288,464!!!

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### laughinReaperSenior Member

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All that math made my head hurt. I do have my ticket. Don't know what i'd do with that much cash other then pay off my bills.

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### California GirlBANNED

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We should have a USMB syndicate. LMAO

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### Mr. H.Diamond Member

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Good job.
I used to do that kind of math in school, but have forgotten most of it.

I put \$5 on quick picks. Wishmeluck.

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### g5000Diamond Member

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The short version is that if you bought every possible combination of numbers for Mega Millions, it would cost you close to \$176 million.

The Jackpot is \$540 million. We're talking over half a billion dollars. So you come out ahead, even if someone else buys a winning ticket.

Myself, if I won, I would become a real life Santa Claus. I would travel from children's hospital to children's hospital, paying bills for kids whose parents can't afford their lifesaving treatments.

I would fly over neighborhoods in a helicopter, dropping teddy bears with parachutes.

Ho! Ho! Ho!

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Last edited: Mar 29, 2012
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### g5000Diamond Member

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Update bump. I started this topic when Mega Millions was at its biggest jackpot ever.

It is now at its second biggest jackpot ever.

Mega Millions grows to second-largest jackpot

Are there long lines where you live?

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Last edited: Dec 13, 2013
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### Mr. H.Diamond Member

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Nope. But I put a 5 on quick pix

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### g5000Diamond Member

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There are no long lines here, either. But every time the jackpot gets really big, the news shows lines of people in other states waiting literally for hours for a ticket.

Crazy stuff.

But then I live in a small town and have never seen more than six people in line at the Post Office during the peak of the Christmas season.

We have self serve lottery machines. I do remember one running out of the special paper once when the jackpot was really big. I let the people responsible know so there would not be a riot.

Villagers with torches.

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Last edited: Dec 13, 2013
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### g5000Diamond Member

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Every time I think of lottery madness, I think of this:

Instant rep reward for the first person to identify what it is.

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