Lottery--odds of winning

Factual Questions
1

OK, down here in GA we have a projected $300 + million dollar lottery drawing on Tuesday. I was in a bar looking at one of the slips you fill out, and this just doesn’t jibe with me. I’m hoping someone can clear it up.

Here are the rules, yoinked from http://www.georgialottery.com/lottery/biggame.html –

Now, unless I’m wrong, there are two ways they could do the drawing.

1.) They could pull the 5 balls from 5 different lots, each with balls #'ed 1-50, then the BIG MONEY BALL (heh–all caps added for extra excitement) This would be from a lot of balls #'ed 1-36.

This would make the odds 1 in (50^5 * 36), or 1:11,250,000,000

2.) The 5 balls are pulled from the same lot of balls #'ed 1-50, Then the BIG MONEY BALL (oohh…goosebumps) from a separate lot of 36, so the odds would be 1 in (5049484746*36) , or 1:9,153,043,200.

Everyone with me so far? If I have messed up, please let me know.
Now, from the same URL listed above, here are the odds of winning.

Now, am I wrong, or are they? I assume I would have to be somewhere, because I doubt they could have gone this long without someone pointed it out to them. So, If I’m wring, where is it?

BTW, If I’m not wrong, I’m going to sue them for misrepresenting the odds and thusly forcing me to spend money on their crooked system. :wink:

2

I have no idea but if your right good luck!!

3

Order doesn’t matter. At first there are 50 balls. You have five chances out of 50 to pick one of the 5 good numbers. Assuming you draw one of the good balls, the number of good balls remaining is now 4, and the total number of balls remaining is 49. Continue until 5 balls have been drawn. The chance of picking 5 balls correctly is
P1 = 54321 / 5049484746 = 5! * 45! / 50!

Then from a separate batch of 36 “big money” balls, one ball is drawn, reducing your chances by a factor of 36

P2 = 5! * 45! / 50! * 36 = 1 / 76,275,360

4

Taking the first part first: The 5 out of 50:

You were getting close with your second formula. What you did was find out the number of permutations of 5 things taken from a pool of 50. This is denoted [sub]50[/sub]P[sub]5[/sub]. Mathematically, this is:


         50!
  P  = -------
50 5   (50-5)!

or what you derived: 5049484746 = 254,251,200

(The “!” after the number is “factoral”. It means the product of all the numbers from 1 to the given number.)

But you must divide that by the number of ways any 5 balls can be picked. That is, you can draw 5, 15, 10, 30, 20, but this would be the same as drawing 30, 20, 15, 10, 5 or 5, 10, 15, 20, 30. This number is 5!. Dividing the permutations by this gives the combinations:


          50!
  C  = --------- = 2,118,760
50 5   5!(50-5)!

Finally, you multiply this number by 36 (no fancy formulas needed for this, as the Big Money ball is independent of the others drawn), and you get 76,275,360.

5

We have this same lottery here in Virginia (it’s interstate) . Here’s a little help visualizing the odds:

Tickets are printed with up to 5 sets of numbers, with the resultant ticket being about 3 inches long. If all 76,275,360 combinations were printed up on tickets in this way, they’d line up, end-to-end, 722.3 miles.

6

Thanks AWB.

Believe it or not, I did take a statistics class in college a while back. So I do know about combinations vs. permutations, and factorials, and all that jazz. Getting it out of the archives in my brain is no easy task, as I haven’t ever used it since I took the final. I was not considering that you have the 5 picks to start with.

Thanks for the info. You too, biblio.

7

(Drumroll) From:http://www.georgialottery.com/lottery/biggame.html#Odds

Odds of winning: 1:76,275,360

8

Um, yeah, Handy, that was in my OP.

9

Ah, statistics…

Here are a few things with better odds:

Death by Eating Peanut Butter (average lifetime consumption) - 1 in 3,300.
Death by Diet Sodas (200 sodas a year) - 1 in 3,000.
Death by Lightning in the U.S.- 1 in 17,400.
A fatal elevator ride - 1 in 77,000.
Being Killed by a Falling Aircraft - 1 in 320,000.
Being Killed by your own dog - 1 in 260,000.
Being Killed by Someone’s Dog - 1 in 700,000.
Death by Flesh Eating Disease - 1 in 1,000,000.

I never knew peanut butter was more dangerous than lightning…

10

Ah, you guys aren’t much fun. Here is a book that makes it all much more fun (amazon.com):
How to Lie With Statistics
by Darrell Huff, Irving Geis (Illustrator)
List Price: $8.95
Our Price: $7.16
You Save: $1.79 (20%)

                 Paperback Reissue edition (November 1993)
                 W W Norton & Co; ISBN: 0393310728 ; Dimensions (in inches): 0.35 x 8.21 x 5.51
                 Amazon.com Sales Rank: 3,823
                 Popular in: St. Olaf College (#5) , Pleasanton, CA (#19)
11

Though I’m sure this has been said here before, it probably bears repeating. IF you are going to risk a few bucks for a huge payoff, it’s best to try to pick random numbers. For instance, if you pick 1,2,3,4,5, and 6–well, that possibility has just as much chance to come up as any other. But, as you can imagine, several people will have picked such a combination each time a drawing occurs. Hence you have to split the jackpot with them.

In the VA pick 6 lotto (not the BIG GAME) I believe the odds are something like 1 in 7,100,000. The odds are, therefore, that if you and your family play every week then sometime in the Jetsonian future one of your down-the-road offspring will win. Best to reap back as much as possible.

Therefore:
1.Pick no numbers in order.
2. Avoid picking the ages of everyone in your family–(many people do this, and your family makeup will likely be similar to many others.
3. When trying to come up with numbers off the top of your head at the convenient store, remember others will likely pick 7 and 11 too.
4. etc. etc. If there’s a logic to the numbers you use, it may have relevance to someone else. Go random.

In short:

A. use the EZ pick feature which will give you a truly random number and

B. Kiss the cash goodbye.

12

‘use the EZ pick feature which will give you a truly random number’

I don’t have the ball frequency numbers around, but Im sure there is not an even distribution of numbers. Some numbers come up more than others. odd, eh? They have to rewrite the probability theory.

13

Cecil Adams on “Systems” for picking lottery numbers.

14

The floating ping-pong balls are where it’s at if you want to score big. They have to have the numbers painted or decaled on them. Some numbers will require more paint or decal than others, and the color of the pigment used will alter the flight characteristics of the balls. I think it is unlikely that lottery officials weigh the balls to the significant figure required do demonstrate which balls weigh more, or measure how the pitch and yaw is affected. Some possible factors in choosing a randomly floating ball follow:

  • Weight. A lighter ball might stay near the top and be more often selected. A heavier ball may stay near the central axis of the receiving tube and have a better chance of being in the right place at the right time.

  • Height of number surface by comparison to non-numbered surface.

  • Heat absorption of the balls under those hot television studio lights.

  • The surface area of the numbers themselves. If they are even slightly raised, the decals might raise at the corners due to contact with other balls and alter their floating characteristics. Similarly, if painted, the raised corners might ablate. A number “38” on a ball may act differently in a vortex than a number “1.”

Then of course you have to do some turbulence and chaos theory equasions to establish what situation is ideal when taking into account the above variables and a host of others, provided of course you can get exacting performance specifications of the machines used to select the number. I believe that with a lot of thought and many, many hours of very expensive computing time one could increase the chances of winning from slightly more than none to… slightly more than none.

Good luck.

15

Of note:

“Odds” and “Probability”