Winning the Big One.....

[poltr1]

This Friday, the multi-state Mega Millions jackpot is at $476 million. Yesterday, it was $363 million...and nobody won it.

So,what are the odds of you winning? In a nutshell, not bloody likely!


Game mechanics: There are 56 white balls (numbered 1-56) and 46 red balls (numbered 1-46). Players pick 5 white balls and one red ball.

With the 56 white balls, what is the probability of getting all 5 of your numbers drawn? Let's figure it out. Draw the first ball from the pool of 56. Then draw the second ball from the remaining pool of 55. Then draw the third ball from the remaining pool of 54. Then draw the fourth ball from the remaining pool of 53. Then draw the fifth and final ball from the remaining pool of 52.

Mathematically, that would expressed thusly: 56 x 55 x 54 x 53 x 52 = 458,377,920

Then divide this number by the number of permutations possible within those 5 numbers. If you're familiar with number theory and factorials, you know that there are 120 possibilities. (1 * 2 * 3 * 4 * 5 = 120.) Try it out: with the letters a, b, c, d, and e, how many five-letter combinations can you come up with? With one letter, there's one permutation -- a. With two letters, there are 2 permutations -- ab, ba. With 3 letters, there are 6 permutations -- abc, acb, bac, bca, cab, cba. With four letters, there are 24 permutations. And so on.

Back to the math: 458,377,920 / 120 = 3,819,816

Now, bring in the draw for the red ball. A player has a 1-in-46 chance for their number to be drawn. So let's multiply the previous result by 46.

3,819,816 * 46 = 175,711,536

There you have it. 175 million to one against. Happy playing!

The grand formula: ((w!/(w-d)!)/d!) * r!, where w is the number of white balls, d for the number of white ball draws, and r for the number of red balls.

So, for Mega Millions, the formula is ((56!/51!)/5!) * 46.

Powerball, anyone? This multi-state lottery has drawings on Wednesdays and Saturdays, and the jackpot for tonight's drawing is $50 million.

The game mechanics are slightly different: Players choose 5 out of 59 white balls/numbers and one number out of 35 red balls. Using our formula:

Using our above formula: we get ((59!/54!)/5!) * 35. That is....

59 * 58 * 57 * 56 * 55 = 600,766,320

600,766,320 / 120 = 5,006,386

5,006,386 * 35 = 175,223,510

Also 175 million to one against.

And play responsibly!

"You'll laugh, you'll cry, you'll kiss three bucks goodbye!"

Comments

[billroper]

Oh, the odds are always lousy.

On the other hand, the utility of $251 million after taxes compared to the utility of this spare dollar that I've got lying around looks pretty good, even when I adjust for the probability of winning vs. the probability of actually having that $1 in hand.

But as you say, play responsibly. The utility of $1000 in hand is a good bit higher than the utility of $1 in hand. And there's the entertainment value...

[zorya-thinks.livejournal.com]

Just FYI, MegaMillions and Powerball (at least in Tennessee) are $2 a play.

Occasionally I'll risk a buck (or two, now) when the pot is really big. It's fun to play "what if" even though I know how long the odds are for winning. And buying a ticket every 6 months to a year isn't the same to me as spending $30 or $40 dollars a month on the lottery.

I'm thinking of buying a ticket for this drawing and playing a bit of "what if." I need something to lift my mood this week.

[tigertoy.livejournal.com]

Mathematically, the problem with "playing the odds" when the jackpot gets to this size is that it's fairly likely that even if you do win, you won't be the only person to play those numbers. When you consider splitting the winnings, the expected value goes down a lot.

Practically, the problem with "playing the odds" is that the reality is that you will not win when the odds are millions to one against. So, it's only worth buying the ticket if having the excuse to think about what you would do with that money is actually worth the dollar.