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design219 · Mar 16, 2009, 12:20 PM

A discussion about lotteries came up at the office last week and I threw out the idea that if you are going to pick your own numbers, you should just pick 0, 1, 2, 3, 4, 5. Some people thought I was crazy as the odds of this sequence coming up would be astronomical. I responded that any sequence of six numbers has the same odds and any other.

One person was convinced a clustering of numbers in a sequence would be less likely and being weighted to one end of the number string would be even less so. I see it as just a random number.

I still think I'm correct, but any thoughts from the mathematicians in the audience?

nonhuman · Mar 16, 2009, 12:25 PM

You're correct. All sequences have an equal probability, assuming a truly random number generator.

Chuckit · Mar 16, 2009, 12:38 PM

Most people don't understand what randomness is. They think that it means "chaotic," so recognizable patterns are unlikely to appear. In fact, if a recognizable sequence were less likely to appear than any other, the information wouldn't be random.

residentEvil · Mar 16, 2009, 12:41 PM

i don't think you want to start with 0; as that is not an option in multiball lotteries (like MegaMillions).

Laminar · Mar 16, 2009, 12:42 PM

As soon as you pick a "random" sequence of numbers, it becomes just as recognizable as a standard sequence.

design219 · Mar 16, 2009, 12:47 PM

Originally Posted by Laminar

As soon as you pick a "random" sequence of numbers, it becomes just as recognizable as a standard sequence.

I don't understand.

Laminar · 01:42 PM

We recognize 1-2-3-4-5-6 because it's sequential. design's coworkers are saying that picking something like 4-2-6-3-1-9 is more likely to win because we don't recognize it, but statistically it has the same probability of appearing.

Dakar V · Mar 16, 2009, 01:30 PM

Originally Posted by Laminar

Starman's coworkers

Who?

Laminar · Mar 16, 2009, 01:42 PM

Oops.

GSixZero · Mar 16, 2009, 03:37 PM

Doesn't matter what numbers you pick as long as you pick them randomly. People who have meanings to their numbers are less likely to win since a lot of people use dates (like birthdays), which are mostly lower than the numbers of the balls. ie, dates only go up to 31, most lotteries go up to 45 or so.

nonhuman · Mar 16, 2009, 04:01 PM

Hmm, I wonder how the payoff rate would change if the numbers only went up to 31.

Laminar · Mar 16, 2009, 04:05 PM

Originally Posted by GSixZero

Doesn't matter what numbers you pick as long as you pick them randomly. People who have meanings to their numbers are less likely to win since a lot of people use dates (like birthdays), which are mostly lower than the numbers of the balls. ie, dates only go up to 31, most lotteries go up to 45 or so.

I'm not sure I agree - a combination of 5-14-8-6 is statistically as probable as 44-42-40-38.

Spheric Harlot · Mar 16, 2009, 04:10 PM

Originally Posted by GSixZero

Doesn't matter what numbers you pick as long as you pick them randomly. People who have meanings to their numbers are less likely to win since a lot of people use dates (like birthdays), which are mostly lower than the numbers of the balls. ie, dates only go up to 31, most lotteries go up to 45 or so.

That's completely incorrect.

Probability states that you are EXACTLY as likely to win, REGARDLESS of what numbers you choose - whether they are birthdates or not, whether they correspond to the years you had sex in, whatever.

Choosing birthdates does NOT decrease your chances of winning. It just increases your chances of having to SHARE with somebody else, should you win.

sek929 · Mar 16, 2009, 05:28 PM

It's still a 50/50 chance, either you win or you lose.

WINK

Chuckit · Mar 16, 2009, 05:41 PM

Originally Posted by GSixZero

Doesn't matter what numbers you pick as long as you pick them randomly. People who have meanings to their numbers are less likely to win since a lot of people use dates (like birthdays), which are mostly lower than the numbers of the balls. ie, dates only go up to 31, most lotteries go up to 45 or so.

It is impossible to influence your chances of winning one way or the other except through the number of tickets you buy (each ticket gives a slightly increased chance of winning). Although it's certain that the chosen numbers will sometimes go above your highest pick if you max out at 31, that doesn't actually decrease your chances of winning — as you make your number higher, you just increase the chance that the chosen number will be lower than yours. The chance that it will be right doesn't change at all!

d4nth3m4n · Mar 16, 2009, 07:11 PM

you guys know they split jackpots right?

i think he's saying that you have a better chance of winning the whole jackpot if you pick numbers higher than 31.

Laminar · Mar 16, 2009, 07:22 PM

Originally Posted by d4nth3m4n

you guys know they split jackpots right?

i think he's saying that you have a better chance of winning the whole jackpot if you pick numbers higher than 31.

I was going off of this part:

Originally Posted by GSixZero

People who have meanings to their numbers are less likely to win

Rumor · Mar 16, 2009, 07:43 PM

Though, I have never heard of a winning lottery sequence being sequential. Doesn't mean it hasn't happened, just saying I haven't heard of it happening.

Chuckit · Mar 16, 2009, 07:58 PM

Well, of course not. The odds of sequential numbers winning are really bad — they're just not worse than any other numbers. In a lottery with six numbers that go up to 40, there are about 4.1 billion combinations, and only 34 of those are sequential.

OldManMac · Mar 16, 2009, 08:03 PM

Originally Posted by Chuckit

It is impossible to influence your chances of winning one way or the other except through the number of tickets you buy (each ticket gives a slightly increased chance of winning).

Incorrect. You're playing each set of numbers against another set of numbers, it does not increase your chances. I had a statistician explain it once, and I probably can't explain it easily like he did, but buying multiple tickets doesn't increase your odds.

design219 · Mar 16, 2009, 08:13 PM

Originally Posted by OldManMac

but buying multiple tickets doesn't increase your odds.

I don't agree. There is a set possible number of sequences. Just say it was a billion... you buy one number sequence, you have on in a billion chance. You buy two sequences, you have two in a billion chances.

Chuckit · 08:26 PM

Originally Posted by OldManMac

Incorrect. You're playing each set of numbers against another set of numbers, it does not increase your chances. I had a statistician explain it once, and I probably can't explain it easily like he did, but buying multiple tickets doesn't increase your odds.

Consider the logical conclusion of that statement: If I bought a lottery ticket with every possible combination of numbers, there's still a chance I could lose. That's obviously not true.

Each ticket has a one-in-something chance of winning — usually one in several billion for a big pot. When you buy two tickets, you have a two-in-something chance of winning. Your odds do increase with more tickets, but the problem is that the cost of guaranteeing a win is more than the prize money.

EDIT: Here's a math Q&A site that agrees with me

design219 · Mar 16, 2009, 08:38 PM

Now that I think more about the birthday number limits, I'm starting to wonder if there is something there.

While I still say any number is as good as another, if you think about it as a limit of choice, it seems to make a difference. For example, if a single number was chosen randomly from 1-31 from a possible random winning number up to 45, would you not have a lesser chance of winning than if the random number option went from 1-45? Or would thinking like this only come into play if you played a lottery over and over with numbers limited 31 or under?

Laminar · Mar 16, 2009, 08:48 PM

Originally Posted by design219

Now that I think more about the birthday number limits, I'm starting to wonder if there is something there.

While I still say any number is as good as another, if you think about it as a limit of choice, it seems to make a difference. For example, if a single number was chosen randomly from 1-31 from a possible random winning number up to 45, would you not have a lesser chance of winning than if the random number option went from 1-45? Or would thinking like this only come into play if you played a lottery over and over with numbers limited 31 or under?

...

Originally Posted by Laminar

A combination of 5-14-8-6 is statistically as probable as 44-42-40-38.

Chuckit · Mar 16, 2009, 08:53 PM

Originally Posted by design219

Now that I think more about the birthday number limits, I'm starting to wonder if there is something there.

While I still say any number is as good as another, if you think about it as a limit of choice, it seems to make a difference. For example, if a single number was chosen randomly from 1-31 from a possible random winning number up to 45, would you not have a lesser chance of winning than if the random number option went from 1-45? Or would thinking like this only come into play if you played a lottery over and over with numbers limited 31 or under?

You could play the number 1 over and over again and have just as good a chance. That's because it doesn't matter whether you were over the winning number or under it — if you didn't hit it right on, you lose.

If you change the range generated numbers, that would make a difference. But the range of hypothetical numbers you choose from doesn't matter, because you still get the same count of actual numbers to play.

Spheric Harlot · Mar 17, 2009, 02:18 AM

Originally Posted by design219

Now that I think more about the birthday number limits, I'm starting to wonder if there is something there.

While I still say any number is as good as another, if you think about it as a limit of choice, it seems to make a difference. For example, if a single number was chosen randomly from 1-31 from a possible random winning number up to 45, would you not have a lesser chance of winning than if the random number option went from 1-45? Or would thinking like this only come into play if you played a lottery over and over with numbers limited 31 or under?

"Random" means random. It is completely irrelevant why you choose whatever numbers you choose, or in fact, which numbers you choose - each number is exactly as unlikely to come up as any other number.

Period.