The Lottery

This is a combination problem where:

nCr = n!/(r!(n-r)!) : Number of combinations of n objects taken six at a time where order does not matter.

nCr (n=49, r=6) = 49!/(6!(49-6)!) = 13,983,816

Just to add some perspective - I recently read that the odds of being born with two penises is 1 in 5 million. So, about three times less likely than that.

The odds of having the first number drawn are simply 6 in 49 (6/49).

* Since we have already picked one of our six numbers and there is one less number in the pool that can be picked, then there are only five of a possible 48 numbers left in the pool that can be drawn. Therefore the odds of having the second number drawn is 5 in 48 (5/48).

* Since we now have four of our six picks left and there are now only 47 numbers left in the pool to be drawn, the chances of getting the third is 4 in 47 (4/47).

* We now have three of our six picks left and only 46 numbers left in the pool to be drawn. Therefore the chances of getting the forth number is 3 in 46 (3/46).

* With two of our six picks left and only 45 numbers left in the pool. The chances of getting the fifth number are 2 in 45 (2/45).

* With only one of our six picks left and only 44 numbers left in the pool, the chances of getting the last number is 1 in 44 (1/44).

To calculate the odds of picking all six numbers we multiply the individual odds together to get the overall odds: 6/49 × 5/48 × 4/47 × 3/46 × 2/45 × 1/44 = 720/10068347520 which = 13983816......So your odds would be 1 in 13983816 of picking all 6 numbers...

SolarEagle

The odds to be bitten to death by your icon donkey is better.

The odds of winning can be calculated as such

for the first ball to be drawn you have got 6 numbers in contention

The odds of having this right is therefore 49/6 = 8.16666.

For the second ball the odds are 48/5 = 9.6 == 2 right = 78.39

for 3rd ball the odds are 47/4 = 11.75 == 3 right = 921.19

For 4 th ball the odds are 46/3 = 15.333

for the 5th ball the odds are 45/2 = 22.5

for the last ball the odds are 44/1 = 44

Total± 1:14 000 000

Put another way, if one played once a week for 80 years it would be >3300 lifetimes before the correct combination to win came up.

There must be better things to do...

Yes 100% true.

i could have saved myself some trouble by reading the other post first.

Just a question

If you take 3300 tickets a time you should win it once in a lifetime.

What will be the deficit when you do win?

Of course the hook is that, although the odds are as stated above, the next draw could be the one.

The Lottery is just a tax on Hope or stupidity thats all, dont do it, use your brain to Invent something and then pay tax on keeping it yours with Patents, then you die, then someone else with a big Lawyer gets rich on your efforts.

Mr Cynical

Hmmmm... I think that the best route is to "be" that someone else and get a big lawyer.

Thats OK with me as long as I can have 5% licence fee, I'm not greedy just hungry, and to be that someone else you need finance at your fingertips as well as liking big lawyer types.

Docrobgar: If you are getting any royalties, you can put them in your will and assign a person to be the beneficiary after you pass away (please don't rush!). This way you can block any robbery.

I fully agree with you but this kind of business cannot be stopped. A lottery company is sizing the game by the population of a country or state compared with the odds of winning. It's a very cynical calculation but random temptation up to gambling addiction are coming from everyone's hope to get a better life. Unfortunately, here is the catch: all studies on jackpot winners show that their life became a living hell. Instant "love and affection" of all friends, in-laws, etc. took their breath. They began to think "what the heck - I have only one life to live" and divorced, ate and drank too much - finally ruined themselves.

Another problem is that the lottery company doesn't care about the winners' safety by not publishing their name, address and photo - exposing them even to kidnappers taking their loved ones for ransom.

How many reach people (not necessary gamblers) you know to do something good with their money? How many are investing in green technologies to prevent the environmental collapse or to fund real scientific and technological bio-medical research? Or commercially-free charity? Or cover poor students tuition etc.

Whoever is thinking about all these before buying a lottery ticket will not buy it anymore or will forget everything after winning the jackpot!

Another Mr. Cynical...

I look at it like this... $1 for one chance, once a week = $52 a year. I've blown much more than that on seemingly similar wastes of time with no apparent returns so what the heck?

Heck, you can't win if you don't play, right?

But I do have to question these people that spend $20 or more on tickets. I've even read stories about people taking second mortgages out on their house and buying 10's of thousands of tickets for drawings that get especially large. Now that's nuts.

But a dollar a week? So, ok, I get one less soda out of the vending machine a week, no biggie.

Thanks for the calcs on the odds though, I forgot how to set it up when order is irrelevant. But then again having taken my probability and statistics course over 20 years and not really having to use much of it since then, there is quite a bit I've forgotten; which is why I absolutely love CR4

There's an odds calculator at: www.lottogenie.com/html/odds.html

I once tried to analyze the california state lottery (the old lottery) with a few spreadsheets. I ordered the complete history of all drawings. It showed the numbers of each drawing in the order they were drawn in. On one sheet I recorded the number of times each number appeared in a particular draw. On another sheet I recorded the number of times each number had been drawn at all. Certain sequences of numbers were more likely then others. For example, 1, 2, 3, 4, 5 and 43, 44, 45, 46, 47 were highly unlikely so, I eliminated those and all consecutive sequences in general. I also restricted my numbers to between 10 and 37 because those numbers were drawn 80% of the time. I increased my odds a bit but still never won more than $100.

We now know what the chances are of (not) winning.

Do anyone know what thew chances are of a lotto to close down?

In South Africa the lotto has been suspended for a month as from 1st April.