Given a combinatorial set of numbers-- like, say, a lottery-- are the odds of matching the numbers by picking a random set the same as sitting at just the same set over and over again?
That is, are you more likely to catch a random number by sitting still or “chasing” it with a random number? And does it matter if it is a combination-style problem (lottery) or “pick a number between 1 and 100?”
The odds are the same. Two seperate lottery drawings (assuming they come from the same pool of numbers) have nothing to do with one another and thus the choice of numbers in drawing A has no effect on the choice of numbers in drawing B.
Similarly, the actual numbers selected all have the same probability. 1, 2, 3, 4, 5 is just as likely to win as 5, 12, 35, 36, 41.
Given that you and the lottery use different methods to generate your random numbers, and neither method is likely to be perfect, I think you might be very slightly better off choosing different numbers for each drawing. It’d take more math than I ever had to prove that statement though.
When I try to tell most people that they look at me like I’m insane…
Ants is right, but it’s not a good idea to pick 1,2,3,4,5 for a different reason. Patterns are likely to be chosen by more than one person, so a random set of numbers, especially including one or two higher than 31 is more likely to be a unique combination. Since all combinations are equally likely to win, you might as well get the prize all to yourself by having a combination all your own.
Of course, the best reason not to pick any particular set of numbers is that the lottery has a crappy payout. You’re better off playing any casino game. Better yet, you can take the money you throw away on the lottery and put those $5 a week into savings bonds or a good mutual fund and have an extra 20 or 30 thousand dollars for retirement.
Assuming you and the lottery both pick numbers uniformly, I’m pretty sure the two methods have the same payoff. The algebra’s kind of nasty, though, so I don’t really want to do it right now.
What would a big payoff lottery administration do if the numbers picked were 1, 2, 3, 4, 5? At first blush, we might guess they’d do nothing - that’d be the winning combination announced.
But it would probably be a big upset, as so many people would doubt the picking had worked properly. Do the lottery people have any tricks in reserve to rescue themselves from what might (unjustifiably) turn into a debacle of scandal for the lottery officials? Do they pick the numbers with a 10 second delay to air, for instance?
I don’t especially think so, and certainly have no evidence. It’s just the most idle speculation. But how surprising would it be if they had worked out some way to guarantee every drawing looked “random”? If they had, very unusual number combinations would be less likely to be announced as winners.
I think this is a great hypothetical deserving of it’s own thread. As Hail Ants pointed out, most non-mathematically minded people think you are insane when you suggest that the odds of picking out a nice series (1,2,3 etc) are the same as the odds of picking numbers that have no pattern. There’d be virtually rioting in the streets in my lottery mad country (Australia) if such a series came up when the lottery operators tried to explain that it just came up at random. The recriminations would fly.
On the other hand, any attempt to prevent certain combinations from coming up, or withhold the result of draws that resulted in “non-random looking” numbers would be fraud, and dealt with accordingly. Interesting to speculate about the idea. I have no answers.
I’m sort of speculating here, but I suspect that the methods used by modern lotteries are pretty darn-near perfect. Again, I’m speculating, but I believe that the lotteries employ statisticians to study the past results to make sure that the system is working properly.
And as long as the winning numbers are chosen randomly, it doesn’t matter how you choose your own numbers - perfectly randomly or something else.
[sub]except of course that as others pointed out, you’re better off picking numbers that others are unlikely to pick. From what I hear, you should pick a couple numbers higher than 31, to avoid dates.[/sub]
Spritle walks in wearing his Master’s gown, mortar board and a smug look on his face. He dusts off his advanced degree in probability and statistics and calmly walks to the microphone. Tapping it gently, he says…
It has come to my attention that my services are needed to address this vexing problem of choosing lottery numbers. My good people, he comes the definitiv… (to gopher wispering in his ear) er, wha? Really? Well lemme read all the posts. (reading, he mumbles to nobody in particular) zumma… mazuzzi… somma… frump. (clears throat) Well, it seems that it has been answered quite satisfactorily and correctly by those above. Thank you.
(to gopher as he is led off stage)I’m still getting my speaker’s fee, right?
erislover wrote:
No, that doesn’t matter, although to be equivalent to a lottery you’d need to pick a number between 1 and somewhere around 16,000,000. The reason is that each combination of lottery numbers could be put in an ordered series, so each number in the ordered series represents exactly one combination of six 1-50 numbers.
Although I fully realize 1,2,3,4,5 is as likely as any other 5 number combination, the set of five numbers in sequence is obviously a subset of all five number combinations( and a fairly small one at that, I’ll let someone else do the math), therefore making it seem like an oddity. I think that is where the “confusion” or disbelief would come in.
The math is not that bad. Consider the following sequence of sequences:
{1,2,3,4,5},{2,3,4,5,6}…{46,47,48,49,50}
which is to say that there are only 46 such sequences to choose from in a 1 to 50 lottery (more generally, n-k+1 sequences, where n is the max number (50) and k is the length of the sequence (5) ).
Given that the odds of choosing any one 5 number combination is in the 8-digit range, the odds of choosing a sequence is 50 out of that number - fairly small, but larger than any arbitrary combination which is 1 out of that number.
But you don’t win the lottery for choosing any sequence, you win the lottery for choosing an exact match whether or not it is a sequence (or all even numbers or all prime numbers or whatever) and so we are back to one in astronomical as our odds.
Best,
Glenn
Does your Master know that you’re wearing his gown?