Let me explain. We have the multi-state lottery in my state. And if you want, the lottery machine you buy your ticket from can pick random numbers for you. The only problem is that the numbers the machine picks don’t look random to me for some reason. Alot of numbers are repeated in each row, it seems. Anyways, partly to solve this problem and partly just for my amusement, I guess, I came up with a system…
I start with two dice. The numbers must be between 1 and 52 for the first five numbers and betw. 1 and 52 for the bonus ball. For the first digit of the the first number I roll one die. Numbers 1 thru 5 on the die represent those numbers respectively for the first digit. Six represents zero. Then for the next digit I roll two dice. numbers 2 thru 9 on the dice rolls represent those numbers for the last digit. 10 and 11 represent zero and 1 respectively. 12 is discarded immediately. I follow these rules carefully–careful not to taint the results. But if I end up with a number larger than 52, I simply discard the whole number and start over again.
Now my only question is, Are these numbers truly random? I know that the lottery machines are probably carefully designed to pick numbers that are random (and I still use that feature–like I said this is partly for fun). How should my method fair against the machines: better, the same or worse? And another question I have often wondered about: What about deliberately discarding some of my results? How would that affect the randomness of my results? Like I said, I deliberately finish each number before discarding it, so as not to taint the randomness of the results. Is there anyone out there who knows something about probability that could answer these questions?
Technically, no computer can generate true random numbers, merely psuedo-random numbers. For the purposes of most people, even most statistical simulations, psuedo-random numbers are good enough, however, how random they actually are depends on the exact algorythm used. Automatic card shufflers, for example, have a bad reputation for using poor “random” sorting algorythms, however, some models are very, very close to random.
I guess it depends on the lottery machine, then… how advanced an algorythm do they use? A large statewide lottery is going to use at least a moderately advanced system… such that no real trends exist which will signifigantly add to you probability of success… however, cards and games prinited up on local machines may have poor algorythms… which like the card shufflers, could give you up to a 25% edge… assuming you bought many cards in a row.
Well… they are of course not totally random either… with very detailed physical analysis, you could calculate the postion of every ball, and seed the starting values… however, no super computer exists which could make a successful calculation. However, it is more random than rolling a six sided dice or a spin of a roulette wheel (which in fact, now have bumps on the surface to prevent computer aided cheating based on knowledge of the start position and the angular velocity…)
At any rate, they’re pretty random, but not at say, a quatum level of randomness ala the uncertainty priciple, which is from a human perspective, true randomness!
Rolling a six-sided die for the digit in the tens place seems like it would work okay, though in the very long run you could see non-random effects from irregularities in the shape of the die.
But adding the total of two six-sided dice to get the digit in the ones place is not really a sound practice, as different sums have different probabilities of occurring.
12 (thrown out): 6 + 6
11 (–> 1): 6 + 5
10 (–> 0): 5 + 5 or 6 + 4
9: 5 + 4 or 3 + 6
8: 4 + 4 or 3 + 5 or 2 + 6
7: 1 + 6 or 2 + 5 or 3 + 4
6: 1 + 5 or 2 + 4 or 3 + 3
5: 2 + 3 or 1 + 4
4: 2 + 2 or 1 +3
3: 1 + 2
2: 1 + 1
Your method is going to create proportionally too many numbers ending in 6, 7, and 8 and proportionally too few ending in 1, 2, or 3. In a truly random sample, all numbers are equally probably.
I know you said that you’re playing the lottery for fun, but you do realize that “random” numbers are no more likely to be picked than your lucky numbers, right? So keep on rolling dice, or playing the dog’s birthday, or whatever makes you happy.
Probably not. The numbers in each sequence get larger from left to right, not counting the “bonus” number. Did you sort them by size after generating them, or just get lucky ?
Your method of generating the second digit is flawed. Since you are adding two die results, you’ll get a bell curve, rather than a flat distribution. That’s because there is only one way for the dice to add up to 2 (1,1), but there are 6 ways for the dice to add up to 7 (1,6; 2,5; 3,4; 4,3; 5,2; 6,1). Of course, the other possible numbers each have their own probabilities. But you’ll get a lot more from the middle range than from either end.
You need to go to a gaming store and get yourself a 10- or 20-sided die to get even results. But the lottery machine will do as well as the dice, anyway.
This is not true. No mathematical algorithm can produce truly random numbers, since whatever process determined them can theoretically be repeated. However, it’s quite possible to generate nonpatterned and irreplicable sequences through a computer interface, by using known sources of (mathematical) entropy , especially aspects of user input patterns. Linux, for example, automatically turns user interface data into a string of random digits that’s available to any process running on your computer.
Yes, but on the other hand, some sets of numbers are more likely to be picked by other people with which you would have to share your winnings, so you should avoid those. For example, if some nationally syndicated psychic said in a column “The lucky numbers of the week are …” then there might be a bunch of people choosing those numbers, so you should avoid that particular set of numbers.
But why would you avoid those numbers? If they are the numbers that come up, you win-- if they don’t come up, you don’t win. It’s not like you can save up your luck and hit big if you don’t bother with the numbers that everyone else is picking.
You’re absolutely right–your odds of winning has nothing to do with the number of others picking the same number, but your share of the jackpot does.
In the ideal world, because one set of numbers is just as likely as another to come up, if you knew which numbers were picked by others, you should never duplicate their picks.
Think of it this way, would you want to pick the same set yourself 20 times in the same day?
Fair enough. Though I was thinking more in terms of playing personal lucky numbers vs. rolling dice as a part of some kind of personal “system.” The randomness / non-randomness of the dice algorithm is irrelevant to the likelihood of Jim’s having the winning ticket.
Indeed, your odds of winning are identical by picking the psychic’s numbers, but the payoff is much lower since the pot will be split by a higher number of winners. By picking those numbers, you are essentially going for a much smaller jackpot at the same odds. Why set yourself up to win a jackpot that will be split 100 ways, when at the same odds, you can try for a jackpot that’s split 1 or 2 ways?
I believe it’s been shown that people often select patterns on their ticket, a straight line of numbers, or a diagonal, or all 4 corners, that sort of thing.
Your chanced of winning are exactly the same whether you pick popular numbers or not. Your chances of winning more money do not increase or decrease, only your chances of winning less money is lessened.
So all you are doing is lessening your chances of winning overall.
Biggirl, let me try and explain it a little differently.
Say we have a lottery where 6 numbers are picked out of 44. It’s known that for each drawing, hundreds (maybe thousands) of tickets with the numbers 1-2-3-4-5-6 are picked. Now, certainly, this combination has as good a chance to be a winner as any other combination. However, when it’s time for me to buy my ticket, I have to make a choice:
Will I pick 1-2-3-4-5-6 and share the jackpot with hundreds/thousands of others? Or
Will I pick some other combination that will ensure that I won’t have to split with so many people?
I don’t have any control over whether I win or not, but I do have some amount of control over how much I win if I win. While no strategy can increase my chances of winning, I do have a strategy that can increase my potential winnings, and therefore I should pick a combination other than 1-2-3-4-5-6.
Out of 24 numbers, 6 end in a 7 - more than twice as many as you would expect by chance.
You don’t mention it in your method, but I guess you also discard duplicate numbers!
If you must play the lottery, your best method will be to use a truly random source of numbers and discard the duplicates. Avoiding popularly chosen numbers and sets of numbers is a worthwhile refinement.
PhloppyPhallus: the randomness of the machines is an interesting question. It is possible that they are truly random. The machine must have an initial state that can only be known to limits defined by quantum theory. Chaos will ensure that the uncertainty as to the initial state will mean uncertainty as to the outcome - it is the same problem as predicting the weather. It is just a question of how long does the machine have to run for the outcome to be completely unpredictable.
I think it would be best to avoid the low numbers since a lot of people pick numbers like their birth date, favorite “luck” number, etc…who are in the low range (there aren’t many people whose favorite number is, say, 37).
If I were playing loto, I would certainly tend to play numbers in the 30-40 rather than numbers in 1-12 range, for instance.
I understand that picking numbers that are not usually picked increase your chances of receiving more money if you win. What I’m questioning is the notion that you increase your chance of winning big.
You have the same chance to win with any combination of numbers, popular or not. You do not increase your chances of winning big by picking unpopular numbers, you only decrease your chances of having to share your winnings.
Friends of ours solved this problem by simply picking the number 6-7-8-9-10-11 They were sure nobody else would try it, since they knew most people would (erroneously) believe that six numbers in a row was less likely than a more random-looking six number combination, and if anyone else did try it they’d likely start at 1.
I’ve never met anyone else who picked six consecutive numbers like that.
Saying you decrease your chances of sharing your winnings is the same notion as saying you increase your chances of winning big, unless you are using the word “big” to describe your share of the winnings whatever the amount.
