- Nov 26, 2011
- 123,585
- 55,138
- 2,290
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.
Nowadays, they are quite common.
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.
Nowadays, they are quite common.
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