Originally posted by: tangent1138
Originally posted by: DrPizza
(Hopefully you realize that hypn0tik is being sarcastic.)
However, having given this a good 30 seconds worth of thought, my intuition tells me that the auto-picked numbers show a greater variety of combinations, simply because a lot of people play numbers that have meaning to them.
um... "variety of combinations" doesn't matter in randomness.
the balls are just as likely to come up as 1-2-3-4 as they are 7-13-16-31
or did I misunderstand you?
What I mean: Lets say there are 3 doors: red, blue, and puke green. And behind one of those doors, at random, is a prize. People were told to pick one of the three doors. And, a machine randomly picked one of the three doors. We can expect the machine to be almost truly random, while it's fair to believe that the people would avoid puke green in favor of the red or blue, lets say for the sake of argument, the people never pick puke green (this will make it easier to understand the math) And, we'll say there are an equal number of people choosing as the number of machine chosen numbers (again, for simplicity) Now, no matter which door someone (or the machine) picks, every door has a 1/3 chance of winning, every time.
The machine would tend to pick the puke green door and get it correct more often than the people would. But, the people would *still* win 1/3 of the time; they just wouldn't have a chance whenever the winner was puke green. That's the simple answer. But, it's wrong.
12 people, 12 machines... For the sake of simplicity, over the long run, we'll expect 1/2 the people to choose red each time, 1/2 to choose blue; machines over the long run would be 1/3, 1/3, 1/3. So, keeping things simple, we'll simply say that 6 people choose red each time and 6 choose blue. And the 12 machine chosen doors are split 4, 4, and 4.
Every time it's blue, we'll expect 6 people to win, every time it's red, 6 people, every time it's green, 0 people. Machines: 4, 4, and 4 win each time. It's a tie! Or is it? The number of people chosen winning doors is equal to the number of machine chosen winning doors. Hmmm, but isn't there a prize associated with winning?
Let's just do 3 drawings with each door winning once. $20 is won each time and divided among all the winners. Count them. There'd be 10 winners for red, 10 winners for blue, and only 4 winners for green.
When red wins, everyone gets $2 (the 6 people and the 4 machines.)
When blue wins, everyone gets $2 (the 6 people and the 4 machines.)
When green wins, there are only 4 who get any money: The 4 machines get $5 each.
Final tally:
people: $24
machines: $36
So, if there were equal numbers of people choosing based on what they like as people who use machines to choose, we can expect the frequency of winning to be about equal. However, over the long run, the people chosen numbers will tend to overlap (and have to share the prize) much more frequently than machine chosen random numbers. Anecdotal evidence: look how many people won when they all used the same number combination from a fortune cookie... Have you ever heard of more than 2 or 3 people all winning at the same time with quick picks?
edit: I should probably point out that in the case of the lottery, we would most likely see only a very small statistical deviation in the frequency of numbers chosen by people. As such, it would take a HUGE number of samples before there was statistical significance as to the machines being better than humans.
Also,
Originally posted by: Chaotic42
I think I'm going to play 1-2-3-4-5-6 and see what the people at the counter say.
That's the exact same combination I use when teaching statistics to 9th graders to get them to understand why the lottery is for entertainment purposes, not a good get rich scheme. i.e. "if you think it's stupid to play that combination then you shouldn't be playing the lottery." (Of course, I don't attempt the argument that there's probably a lot of people out there playing 123456 just for shits and giggles, or in the case of one of the other teachers at my school, just for the 1 in millions chance of being able to show up to my door the next day and laugh at me)