Choosing Lottery Numbers

[Tituscrow]

Ok, help me out because I have something here that's driving me mad.

I just spent nearly 10 minutes deliberating which six numbers to pick (from 1 to 49).

As usual, I went for various key numbers that pooped into my head (kids ages, birthdays, 'lucky' numbers...the usual nonsense!) and on the way home thought next time, I'll just do 1.2.3.4.5.6., as it is just as likely to come out as my selection.

But it just seems too ordered and regular to ever appear.

Supposing you grouped ALL possible six number combinations into TWO sets... those that followed a predictable, ordered arithmetic sequence or progression, and those that didn't. Now the second set would contain significantly more possible combinations than the first set.

Then when the draw is made, it is more likely that a combination I chose falls into this second set, because there are more possibilities.

1.2.3.4.5.6 would fall into the first set and therefore be a less likely combination.

There is a 6 in 49 chance of one of those balls coming out first, then a 5 in 48 chance of another coming out second, and so on, until a 1 in 44 chance of the final ball.

So the conundrum I have is this: even though statistically, 1.2.3.4.5.6 has an equal likelihood of coming up as any of the other millions of permutations (or does it, in light of my above argument?) why do I feel so strongly that it has no chance of ever doing so?

I know there are some learned folk here on TB, and this has got me baffled.

[Jaco D]

Canadian? I think it's $40 million this Saturday, right?

[Tituscrow]

Haha no, UK. Found a spare quid in the car when I went to get petrol.

[elgecko]

I think your statistics are off. The odds of 1-2-3-4-5-6 occurring are astronomically low.

The probability of 1 being chosen first is 1/49 and another number is 48/49

The odds of 2 being chosen second is 1/48 and another number is 47/48

Now, I think you have to multiply those fractions to get the probability for the series

So the probability of 1-2 being chosen is 1/49 x 1/48 = 1/2,352 (0.00043)

The probability of any other two number combination is 48/49 x 47/48 = 2,256/2,352 (0.96)

[Jim Nazium]

Originally Posted by Tituscrow

So the conundrum I have is this: even though statistically, 1.2.3.4.5.6 has an equal likelihood of coming up as any of the other millions of permutations (or does it, in light of my above argument?)

Yes, assuming the mechanism for picking the winning number is not biased in some way, 1.2.3.4.5.6 has exactly the same probability of occurreence as any other specific sequence, say 2.7.8.13.16.21

Originally Posted by Tituscrow

why do I feel so strongly that it has no chance of ever doing so?

I think you actually described the reason very well. We mentally divide the set of possible outcomes into a very small set of "regular" or "meaningful" outcomes, and a very large set of "random" or "meaningless" outcomes. The large set is much more likely. But it's really an arbitrary distinction. The set 2.7.8.13.16.21 looks random and meaningless, right? But what if those number were meaningful to me, say they were the birthdays of all my brothers and sisters? Then is it in the "meaningful" group? Did it become less likely because I told you that? No, it's just as likely as it ever was, but I've imposed some "meaning" on it that isn't really a property of the sequence.

[Tituscrow]

But isnt that the same model for calculating likelihood for ANY number combination?

Suppose I wanted to pick 3,11,25,26,39,42

No 'neatness' or predictability to that sequence, as opposed to 1,2,3,4,5,6 yes?

Now the chance of 3 being drawn first is 1/49 and any other number 48/49. This follows through the remainder of your calculation this way, yes? Or no, please correct me if I am missing something obvious!

I think it's something to do with drawing a six number combination one number at a time, as opposed to a six digit number in one go. That, and the likelihood of drawing a number in a sequence is less because there are fewer numbers to choose from to fit the chosen sequence each time. Or something.

Just trying to get my head round the calculations!

[Tituscrow]

Edit: above reply to elgecko, not JimNazium.

Cheers.

[stratovani]

Doesn't matter what you do, the odds of winning are so astronomical that any technique is as good as any other!

[Phalex]

A bass only has 4 strings....... Throw a 4 up in that mug.

[elgecko]

Originally Posted by Tituscrow

But isnt that the same model for calculating likelihood for ANY number combination?

Suppose I wanted to pick 3,11,25,26,39,42

No 'neatness' or predictability to that sequence, as opposed to 1,2,3,4,5,6 yes?

Now the chance of 3 being drawn first is 1/49 and any other number 48/49. This follows through the remainder of your calculation this way, yes? Or no, please correct me if I am missing something obvious!

I think it's something to do with drawing a six number combination one number at a time, as opposed to a six digit number in one go. That, and the likelihood of drawing a number in a sequence is less because there are fewer numbers to choose from to fit the chosen sequence each time. Or something.

Just trying to get my head round the calculations!

It's literally been years since I took statistics but I believe you're right. The likelihood of any given sequence (e.g. 3-11-25-26-39-42) being chosen is equal in probability to 1-2-3-4-5-6...now my brain hurts.

But definitely, the odds of 1-2-3-4-5-6 being chosen is in that order is far lower than 5-2-4-6-1-3

[MatticusMania]

I have better chances of slowly building up poker winnings over time. Anyone wanna come over for a game? $10 buy in...

[fhm555]

I kept up with the lottery in FL when I participated in an an office lottery pool. I actually tracked the results for a time and what I found out was the big winners were usually machine generated quick picks.

[billhilly66]

The lottery is just a voluntary tax on people who suck at math.

[Rocker949]

Or the lottery is just something for people who win the lottery.

[Tituscrow]

Originally Posted by elgecko

It's literally been years since I took statistics but I believe you're right. The likelihood of any given sequence (e.g. 3-11-25-26-39-42) being chosen is equal in probability to 1-2-3-4-5-6...now my brain hurts.

But definitely, the odds of 1-2-3-4-5-6 being chosen is in that order is far lower than 5-2-4-6-1-3

Agreed. But a win is based on all your numbers after the final ball, not the sequence you draw them.

If someone had a family whose birthdays fell on the 1st, 2nd, 3rd, 4th, 5th and 6th of whatever month, would they be less inclined to pick those numbers than someone whose family birthdays fell on a non-arithmetical series of dates?

My brain is hurting too

[Tituscrow]

Where is Eric Albany when you need him?

[Unrepresented]

I could try and sound smart, like I came up with this on my own, but this exact question was answered last week in the San Diego Reader, one of our alternative weekly magazines:

Originally Posted by Matthew Alice

Hi Matt: I’m pretty well convinced that if I work at it long enough, I can solve all my money worries with Lotto or Power Ball. One of the things I do is play the following numbers every week. Please don’t publish these numbers because I don’t want anyone else to know them. I have a good friend, though, who says the whole thing is a waste of time and it’s especially stupid to play a sequence of numbers because of the odds against them being drawn that way. I say he’s wrong. So, who’s right? — Future Billionaire

Hahahahahahahahahahah! What a brain trust I’m dealing with here. I think you two had better hook up with Wesley, who at least knows that the bright flashing lights in front of him aren’t real. Jeez! With a state full of idiots like you, I don’t see how Lotto hasn’t paid for private-school education for every child through the year 3000. I won’t try to talk you out of your Power Ball fantasy. I would suggest you figure out how to enroll in a community college and take a Probability for Dummies class, but filling out the application might be more than you can handle and, anyway, would interfere with your ticket-buying routine. Since, for whatever reason, you seem to see me as a source of wisdom (while ignoring all your past real-life experiences, obviously), I will tell you what you’ve undoubtedly heard from others: every string of numbers has an equal chance of being chosen every week, sequenced or not. Now I’ll turn on you and reveal your “winning” sequence: 1, 2, 3, 4, 5, 6. Don’t hate me. According to Lotto experts, this is a lousy bet not because it has no chance of being chosen but because so many people play it every week that even if you do win, you’ll have to share the prize with many, many others. Good luck in life, my friend.

San Diego Reader | Seeing Stars, Voodoo Hit Man, Lottery Odds

[Bassamatic]

YES - 1 2 3 4 5 6 has EXACTLY the same odds as any other number combination as they are each random. Guaranteed.

The fact that many others may bet it is a good point. SO - just do a quick pick each time. Same thing, same odds.

[Dirk Diggler]

It seems to me that when they review the winners a lot of the time they play the same numbers over and over.
Seems the odds would be better this way than just constantly changing your numbers.

But then again I look at the lottery as a voluntary stupidity tax.
Cheers,
Dirk

[Tituscrow]

Originally Posted by Unrepresented

I could try and sound smart, like I came up with this on my own, but this exact question was answered last week in the San Diego Reader, one of our alternative weekly magazines:

Thanks, that's funny.

It's not like I'm trying to 'beat the system' and bet my life away, I just enjoy maths puzzles and the like. Was curious to see if any stats whizzkids out there could confirm (or not) what I thought.

So if 1,2,3,4,5,6 has an equal chance as any seemingly random set, why is it that it 'feels' that it will never come up?

Voluntary stupidity tax? Yeah, I can go with that