rcj1@ihuxi.UUCP (06/14/83)
Why no talk on the mathematics of State Lotteries?? I'm not very good in probabilities and statistics but seems like a nifty subject to bring up. To start off, how about eliminating numbers in order to better your odds? Illinois recently started a Lotto,(pick six random numbers from 1 through 40). I think that means about 1,900,000 6-digit combinations. I came up with a Basic program to generate the 6 random, none duplicated numbers and the closest I've come is 4 out of 6! Ray, ihuxi!rcj1
no5db@ihuxl.UUCP (06/15/83)
State lotteries! Now theres a topic that interests me. I have been analyzing the Illinois state lottery and have come up with the following data. Every week, six numbers from 1 to 40 are drawn. To win the grand prize you must choose 6 of 40 numbers correctly, probability-wise this is a 1 in 3838380 chance, but you get two guesses for a dollar so you have about a1 in 1900000 chance of winning the grand prize for every dollar you spend. Now in addition to the grand prize, if you pick five of the six numbers you win a prize around $1100, and if you pick 4 of the 6 numbers you win about $30. In addition to the six numbers drawn, one alternate number is drawn. If no one wins the grand prize for the week an alternate grand prize is given. To win the alternate grand prize you must pick 5 of the 6 "real" numbers and your sixth number must match the alternate number. I believe this prize has generally been about $100,000. Now comes the tricky part. For a given week, if no one wins the grand prize, part of the grand prize money is allocated towards the next weeks' grand prize. This means that the grand prize continues to get larger until someone wins. The minimum grand prize is $1,000,000 and about 4 weeks ago the grand prize had grown to around $3,600,000. It would seem to me that any time the grand prize was over $1,900,000 you would theoretically make money by playing. As a matter of fact for a grand prize of $2,500,000 I estimate that the expected return on every dollar spent is about one dollar and eighty cents! (Try it yourself if you don't believe it!) All this has been puzzling me for sometime, if you played the lottery every time the grand prize was over $1,900,000 wouldn't you *have* to make money in the long run??? I think the fallacy in my thinking is as follows: To come out ahead you would have to win the grand prize at least once and unless you spent *alot* of money your chances of winning the grand prize would be too small to be significant(??) This still leaves room for the possibility of a group of people playing and splitting any prizes won. I would like to hear comments and/or calculations pertaining to this. If there is enough interest I will summarize the responses. Lance
mark@umcp-cs.UUCP (06/16/83)
Why wait for long run? When the grand prize is over 1,900,000 just bet ALL the numbers. Was this not tried somewhere (Florida?) with great success? -- Mark Weiser
woods@hao.UUCP (06/16/83)
This is in response to the Lance's analysis of the Illinois state lottery. He points out that: > It would seem to me that any time the grand prize was over $1,900,000 > you would *theoretically* make money by playing. [emphasis mine] This is quite true. However, the theory assumes that you can play the game an arbitrarily large number of times. Yes, you can compute the expected value (= sum over prizes of [amount of prize * probablility of winning that prize] -- note that the possibility of winning zero must be included in this sum, because the definition of expected value requires that the probabilities involved must sum to 1.) that you would win by playing the game once. And, if the number of plays is large enough, the average winnings per play will indeed approach this figure. Unfortunately, it is also easy to show that if the probability of winning the grand prize is p, if you play the game 1/p times, you have a 50% chance of not having won the prize yet! Therefore, you may well have to spend millions of dollars before your winnings per play begin to approach the expected value. The expected value is *exactly* what your winnings per play would be if you could play an infinite number of times. Again unfortunately, none of us can play an infinite number of times, and only a select few could play the number of times neccesary to insure approaching this apparently player-favorable expected value. GREG {ucbvax!hplabs | allegra!nbires | decvax!brl-bmd | harpo!seismo | menlo70} !hao!woods
rcj1@ihuxi.UUCP (06/16/83)
In case you did'nt know, when you play the 6 digit lottery game you fill out a scan-tron form with your selection/selections. Each form can have a minimum of 2, maximum of 8 selections. Each selection takes from 10 to 20 seconds from time of submittal to payment and receival of ticket. Some quick calculations tell us that it would take roughly 200 days to pick all the 6 digit combinations of numbers from 1 to 40! Remember you had to fill out the scan-tron forms beforehand. Thats roughly 1.9m forms! (Please correct me on this if needed). Also remember that by 6:55 PM on Saturdays its time to start over for the next lottery drawing! "Wondering if I'll ever hit it big"? Ray, ihuxi!rcj1
derek@sask.UUCP (06/17/83)
I think I should point out that even if you did buy all of the loto tickets, if someone else also picks the winning number, you have to split the prize.
johnl@ima.UUCP (06/18/83)
#R:ihuxi:-44100:ima:16700001:000:827
ima!johnl Jun 17 11:57:00 1983
WRT the Illinois lottery:
Unfortunately, it is also easy to show that if the probability of
winning the grand prize is p, if you play the game 1/p times, you
have a 50% chance of not having won the prize yet!
Not quite. That formula assumes that the chances of winning on each play
are independent. In lotto games you get to pick your own numbers, so
they are not. You could (assuming your grocery store had 1.9 million
entry forms) bet on all possible combinations and win the grand prize, as
well as all of the subsidiary prizes, too.
I suspect that this doesn't happen because people with $2 million to
invest and a phenomenally large pencil (to fill out all of those lotto
forms) are few and far between.
John Levine, decvax!yale-co!jrl, ucbvax!cbosgd!ima!johnl,
{research|allegra|floyd|amd70}!ima!johnl