August 2, 2007 9:50 AM Subscribe

Statistics/Lottery question; Please settle this argument between a friend and I about the Florida state lotto.

Which strategy has better odds (or are the odds equal) of winning the lotto if

a. you play the same 6 numbers every week?

b. you play "quick pick" where 6 random numbers are picked.

If you do pick an answer, would you please explain the reasoning behind it?

A friend of mine swears the answer is A, and compares it to "monkey writing Shakespeare", as if a monkey keeps typing on a type writer, sooner or later, what he writes will make sense?

What do you guys think?

thanks in adavance
posted by boyinmiami to Grab Bag (26 answers total) 3 users marked this as a favorite

Which strategy has better odds (or are the odds equal) of winning the lotto if

a. you play the same 6 numbers every week?

b. you play "quick pick" where 6 random numbers are picked.

If you do pick an answer, would you please explain the reasoning behind it?

A friend of mine swears the answer is A, and compares it to "monkey writing Shakespeare", as if a monkey keeps typing on a type writer, sooner or later, what he writes will make sense?

What do you guys think?

thanks in adavance

The odds are equal. The monkey-Shakespeare analogy is not appropriate here because those monkeys are writing towards a specific goal; in the lottery, the end result (winning numbers) is (a) random, and (b) independent of past results.

Technically speaking, in Monday's drawing 1-2-3-4-5 has just as good odds as a random group of numbers. Then in the next drawing, 1-2-3-4-5 AGAIN has the exact same odds as any other specific group of 5 numbers.

posted by inigo2 at 9:54 AM on August 2, 2007 [3 favorites]

Technically speaking, in Monday's drawing 1-2-3-4-5 has just as good odds as a random group of numbers. Then in the next drawing, 1-2-3-4-5 AGAIN has the exact same odds as any other specific group of 5 numbers.

posted by inigo2 at 9:54 AM on August 2, 2007 [3 favorites]

The dice have no memory. The odds are equal.

A "special" set of numbers has no greater chance of winning*any particular time* than a random set.

Ask them this: if they picked the same six numbers every week, and then one week they forgot to buy a ticket and that set won--would they keep using those numbers? Or would they consider that set somehow "used up"?

posted by Many bubbles at 9:54 AM on August 2, 2007

A "special" set of numbers has no greater chance of winning

Ask them this: if they picked the same six numbers every week, and then one week they forgot to buy a ticket and that set won--would they keep using those numbers? Or would they consider that set somehow "used up"?

posted by Many bubbles at 9:54 AM on August 2, 2007

This is about math and statistics. Your "friend" needs to read a bit. I suggest Innumeracy (because it talks about numbers in a nontechnical way.)

Seriously. Same odds. The act of having one number appear has zero consequence on another number appearing.

Think of it as dice. If you roll a 3....does that fact affect your next roll? It's just like lotto.

posted by filmgeek at 9:56 AM on August 2, 2007

Seriously. Same odds. The act of having one number appear has zero consequence on another number appearing.

Think of it as dice. If you roll a 3....does that fact affect your next roll? It's just like lotto.

posted by filmgeek at 9:56 AM on August 2, 2007

They're both the same.

It can be explained mathematically, but it sounds like your friend wouldn't get it. So, instead, explain by demonstration:

Have him pick a number between one and six. This is his number forever.

Roll a die a whole bunch of times. Before each roll, you pick a number between one and six - unlike him, you can vary your number from roll to roll.

Keep track of how many times each of you get the correct number.

Do this enough, and the result will become obvious. The only possible reasons for disagreement that he will have left will be religious in nature, and at that point, it's no use trying to enlighten him further.

I will, however, note that in the actual lottery, it is generally better to pick random numbers.*NOT* because you win more often; rather, because if you do win, your payout is likely to be higher:

A lot of people choose, for example, birthdays, and keep playing them, over and over.

Which means that if you choose your birthday, and keep playing it, and actually win, there's a greater chance that someone*else* won, too, and therefore you will have to split the prize.

posted by Flunkie at 10:01 AM on August 2, 2007

It can be explained mathematically, but it sounds like your friend wouldn't get it. So, instead, explain by demonstration:

Have him pick a number between one and six. This is his number forever.

Roll a die a whole bunch of times. Before each roll, you pick a number between one and six - unlike him, you can vary your number from roll to roll.

Keep track of how many times each of you get the correct number.

Do this enough, and the result will become obvious. The only possible reasons for disagreement that he will have left will be religious in nature, and at that point, it's no use trying to enlighten him further.

I will, however, note that in the actual lottery, it is generally better to pick random numbers.

A lot of people choose, for example, birthdays, and keep playing them, over and over.

Which means that if you choose your birthday, and keep playing it, and actually win, there's a greater chance that someone

posted by Flunkie at 10:01 AM on August 2, 2007

**at* any particular time. And I meant to add, "So it has no greater chance of winning over a longer period" to the end of that sentence.

Basically, strategy A is magical thinking.

But the strategies aren't equal: strategy B is better.

Not because it has a greater chance of winning, but because if you*do* win, it's more likely that you'll get to keep all your winnings. If you use a "special" set--especially one that's based on a date (how many people play their birthday?)--the odds are greater that someone else is playing the same set. So, if you win, they win too, and you have to split the winnings. If you use random picks, that could still happen, but you aren't tipping the odds in favor of it.

posted by Many bubbles at 10:01 AM on August 2, 2007

Basically, strategy A is magical thinking.

But the strategies aren't equal: strategy B is better.

Not because it has a greater chance of winning, but because if you

posted by Many bubbles at 10:01 AM on August 2, 2007

Damn, should have previewed.

posted by Many bubbles at 10:02 AM on August 2, 2007

posted by Many bubbles at 10:02 AM on August 2, 2007

lol, i knew that this was gonna be the answer.. justed wanted to prove it to her :) thanks guys, you just made me look a little bit smarter and her a little bit dumber!!!! whoop whoop!!!!!

posted by boyinmiami at 10:12 AM on August 2, 2007

posted by boyinmiami at 10:12 AM on August 2, 2007

Another way of thinking about it is that your friend wants to continually bet that today will be the day the monkeys churn out Shakespeare. But unless they wrote some Milton yesterday, and Keats the day before (and when that happens know that the war will have begun and our time will not be long on this world), they're just as likely as not to continue pounding out gibberish. Or, put another way, as soon as the monkeys write their Shakespeare, they'll immediately slip back into random typing (well, after they toast themselves for their achievement, probably).

posted by wemayfreeze at 10:56 AM on August 2, 2007

posted by wemayfreeze at 10:56 AM on August 2, 2007

Also, I really don't think there are any numbers to support Flunkie and Many bubbles' suggestion.

The odds of a solo win are only greater on that "special" set if it's MORE likely that someone else has chosen that exact "special" set than it is that a random number would reproduce those numbers.

In other words, is it really all that likely that some other person who is playing the same lottery as you has chosen the EXACT SAME special set and plays it every week?

Consider a six-number game, and pick a random birthday. Choose month, day, and last two digits of the year. Three are still three numbers to pick. In the florida lotto you have 53 options. That means the number of different picks left is 117,600. Making the odds that someone else with your birthday, playing it the same way, would choose the exact same numbers 1/117,600.

One might argue "Fine, but those are worse odds than 1:16 billion" except when you consider the fact that there are not going to be many people with your identical birthday who are also playing the lottery and choosing to play their birthday.

But think about it another way: picking a random number doesn't insulate you from the "birthday people" if your random numbers happen to include a birthday... well... welcome to the same situation you were just in.

That theory also ignores the people who play the same six numbers every week that were originally randomly chosen, or chosen some other way that's indistinguishable from randomness.

In other words: the odds are incredibly difficult to compute and the difference, if there is one, is negligible.

posted by toomuchpete at 11:02 AM on August 2, 2007

The odds of a solo win are only greater on that "special" set if it's MORE likely that someone else has chosen that exact "special" set than it is that a random number would reproduce those numbers.

In other words, is it really all that likely that some other person who is playing the same lottery as you has chosen the EXACT SAME special set and plays it every week?

Consider a six-number game, and pick a random birthday. Choose month, day, and last two digits of the year. Three are still three numbers to pick. In the florida lotto you have 53 options. That means the number of different picks left is 117,600. Making the odds that someone else with your birthday, playing it the same way, would choose the exact same numbers 1/117,600.

One might argue "Fine, but those are worse odds than 1:16 billion" except when you consider the fact that there are not going to be many people with your identical birthday who are also playing the lottery and choosing to play their birthday.

But think about it another way: picking a random number doesn't insulate you from the "birthday people" if your random numbers happen to include a birthday... well... welcome to the same situation you were just in.

That theory also ignores the people who play the same six numbers every week that were originally randomly chosen, or chosen some other way that's indistinguishable from randomness.

In other words: the odds are incredibly difficult to compute and the difference, if there is one, is negligible.

posted by toomuchpete at 11:02 AM on August 2, 2007

It doesn't matter if the other person picks the same numbers every week.

The point is, when a person choses numbers, they don't do a good job of choosing randomly. Certain numbers are more likely then others people are far more likely to play 1-2-3-4-5-6 then they are to play 87-52-90-84-65-48 (which I got from here). So if you pick 1-2-3-4-5-6, and win, you're more likely to have to split your winnings. As you can see, none of the random numbers I got happened to be possible birthdays, in any arrangement, since they're all higher then 31.

The point is, when individuals try to pick 'random' numbers they do a bad job. But it makes no diffrence whether you use the same random numbers again and again or not.

In fact, if a person played 87-52-90-84-65-48 every time, and another person manually picked different numbers each time, the first person would be less likely to have to split the pot.

posted by delmoi at 11:15 AM on August 2, 2007

Let's say, just for the sake of argument, that the lottery was crooked, or that its random number generator was flawed. Would that change anything?

posted by box at 11:54 AM on August 2, 2007

posted by box at 11:54 AM on August 2, 2007

Sure, but it depends on how it changed. If "5" became more likely to come up than "6", more people who pick 5 will win. But there are lots of ways to be non-random that don't give any clear advantage.

Also, it takes a lot of samples to prove non-randomness, so it would take people a while to notice. c.f. The Chi-square test.

posted by GuyZero at 12:05 PM on August 2, 2007

Crooked? No. If they're smart enough to truly fix it for the house, they're going to have to monitor the numbers purchased and skew away from them. They won't care, then, which numbers you're picking each week.

Flawed RNG? Maybe, but only if you know how the RNG is flawed, which suggests a pretty significant breach of lottery security anyway.

posted by cortex at 12:07 PM on August 2, 2007

One point that's kind of been addressed above is that, yes, people are bad at picking numbers at random. That doesn't necessarily mean that you should pick numbers at random; it means you should pick numbers that will be less likely to be picked by other people, whether they think they're picking at random or not.

For example, I read once that in a certain lotto that had you select numbers from a 7x8 grid (I think), the numbers near the edges and corners where picked less often. When the combination came up near the edges, you were more likely to be the sole winner.

If you had tons of data on drawings and winners with a specific lotto, you could analyze which numbers were best. Of course if the lotto is not fixed, every number should come up equally in the long run. But you could compare which numbers produced winners when drawn and which didn't get any winners and had to be redrawn. This way you could get an idea of which numbers people played more often. (This method relies on none to very few other people trying this strategy.)

posted by Durin's Bane at 12:18 PM on August 2, 2007

For example, I read once that in a certain lotto that had you select numbers from a 7x8 grid (I think), the numbers near the edges and corners where picked less often. When the combination came up near the edges, you were more likely to be the sole winner.

If you had tons of data on drawings and winners with a specific lotto, you could analyze which numbers were best. Of course if the lotto is not fixed, every number should come up equally in the long run. But you could compare which numbers produced winners when drawn and which didn't get any winners and had to be redrawn. This way you could get an idea of which numbers people played more often. (This method relies on none to very few other people trying this strategy.)

posted by Durin's Bane at 12:18 PM on August 2, 2007

toomuchpete, you're vastly overstating your case and using statistics incorrectly to do so. I'm not going to go into why, but a brief explanation is that the reason that the lottery exists is because it's banally common for there to be a lottery winner, despite the fact it's incredibly rare for a specific person to be a lottery winner. The same thing applies with respect to the birthdays argument.

Anyway, I give you the following example from Wikipedia's "Powerball" entry:

Anyway, I give you the following example from Wikipedia's "Powerball" entry:

posted by Flunkie at 12:23 PM on August 2, 2007The Powerball drawing of the March 30, 2005 game produced an unprecedented 110 second-place winners, all of whom picked the first five numbers correctly, but not the Powerball number. [...]

Powerball officials initially suspected fraud, but it turned out that all the winners received their numbers from fortune cookies made by Wonton Food Inc., a fortune cookie factory in Long Island City, Queens, New York. The factory had printed the five regular numbers (22, 28, 32, 33, and 39) on thousands of fortunes. The sixth number in the fortune, 40, did not match the Powerball number, 42.

Another reason not to pick the same numbers every time is that suppose you don't buy a lotto ticket the week your numbers win. You could be kicking yourself for years for not buying that ticket. If you do the quick pick, you don't have to worry about that situation.

posted by ShooBoo at 12:38 PM on August 2, 2007

posted by ShooBoo at 12:38 PM on August 2, 2007

I'll go against the crowd here and point out that the odds are not actually *exactly* the same.

If you play six quickpick numbers, there is a (vanishingly small) [1] chance that two (or more) of them will match[2]. If this happens, you now have only five (or fewer) shots at winning, so your odds go down. On the bright side, if that number also comes up as winning number, you get two shares, instead of just one, if the pot has to be split.

So, to answer the question asked, technically, your friend is right, but for the wrong reason.

[1] Although vanishingly small, the odds of two of your six quickpicks matching are greater than your chances of winning the lottery.

[2] I remember a news story in the early years of the lottery here in Texas where this actually happened. I couldn't find a source for it on the internet, though.

posted by notbuddha at 12:39 PM on August 2, 2007

If you play six quickpick numbers, there is a (vanishingly small) [1] chance that two (or more) of them will match[2]. If this happens, you now have only five (or fewer) shots at winning, so your odds go down. On the bright side, if that number also comes up as winning number, you get two shares, instead of just one, if the pot has to be split.

So, to answer the question asked, technically, your friend is right, but for the wrong reason.

[1] Although vanishingly small, the odds of two of your six quickpicks matching are greater than your chances of winning the lottery.

[2] I remember a news story in the early years of the lottery here in Texas where this actually happened. I couldn't find a source for it on the internet, though.

posted by notbuddha at 12:39 PM on August 2, 2007

I recently this about the multistate Powerball lottery: if you buy 50 tickets a week, you can expect to win once every 30,000 years.

posted by neuron at 12:43 PM on August 2, 2007

posted by neuron at 12:43 PM on August 2, 2007

If you bought those 150,000 tickets all at once you'd probably do a lot better.

posted by GuyZero at 12:56 PM on August 2, 2007

posted by GuyZero at 12:56 PM on August 2, 2007

These threads are amazing. They always turn out the same. This is an elementary school level probability question. It has been answered. The odds are the same.

- Several people chime in to say the same thing (not so bad, its confirmation)

- OP chimes in to thank everyone and goes away.

- Now bored, someone makes the question a bit more complex.

- Several people try to answer the more complex question, again repeating themselves

- Some new guy shows up and says he disagrees with the consensus to the first question and...flawed reasoning follows

- Several people show up to shut this guy down, again, all saying the same thing.

- Nitpickers show up: "Aha! But wont balls with bigger numbers have more ink on them and thus heavier and thus more likely to..." etc... until everyone gets bored again.

posted by vacapinta at 1:53 PM on August 2, 2007 [1 favorite]

- Several people chime in to say the same thing (not so bad, its confirmation)

- OP chimes in to thank everyone and goes away.

- Now bored, someone makes the question a bit more complex.

- Several people try to answer the more complex question, again repeating themselves

- Some new guy shows up and says he disagrees with the consensus to the first question and...flawed reasoning follows

- Several people show up to shut this guy down, again, all saying the same thing.

- Nitpickers show up: "Aha! But wont balls with bigger numbers have more ink on them and thus heavier and thus more likely to..." etc... until everyone gets bored again.

posted by vacapinta at 1:53 PM on August 2, 2007 [1 favorite]

Oops.

For some reason I read "same 6 numbers" as "same 6 sets of numbers". My analysis only holds if you are playing multiple sets of numbers.

If you are playing one set of numbers as stated in the question, the odds are, indeed, identical. So I was wrong. Sorry about that.

posted by notbuddha at 2:04 PM on August 2, 2007

For some reason I read "same 6 numbers" as "same 6 sets of numbers". My analysis only holds if you are playing multiple sets of numbers.

If you are playing one set of numbers as stated in the question, the odds are, indeed, identical. So I was wrong. Sorry about that.

posted by notbuddha at 2:04 PM on August 2, 2007

ok, but it's "please settle this argument between a friend and

GuyZero: 75,000,000.

posted by mdn at 2:29 PM on August 2, 2007

Damn you GuyZero! Damn you!

posted by boyinmiami at 3:19 PM on August 2, 2007

posted by boyinmiami at 3:19 PM on August 2, 2007

Here's another perspective:

They're not going to win the lottery anyway. Yeah, someone has to^{1}, but it won't be *them*. So it's not really about the money. It's about the fun of playing. So, if your friend has more *fun* playing with special numbers than they would with random ones (taking ShooBoo's comment into account, of course--although that situation is even more unlikely than winning is, I would think), that's what they should do. Just recognize that doing so isn't actually improving their odds of winning.

^{1}Not actually completely true.

posted by Many bubbles at 6:09 PM on August 2, 2007

They're not going to win the lottery anyway. Yeah, someone has to

posted by Many bubbles at 6:09 PM on August 2, 2007

This thread is closed to new comments.

The first one seems more appealing... because the winning numbers are most likely to be different every week, it seems like they're being "used up" (they're not) and that if you wait, eventually the winning numbers will work over to "your" numbers.

In reality, every draw is independent and the odds of drawing the same winning numbers every week are the same as the odds of drawing whatever actually was drawn. There is not single-ticket-sequential-purchase strategy that can be used for lotteries. There may be a strategy for buying large numbers of tickets and guaranteeing a win, but never for sequential draws.

posted by GuyZero at 9:53 AM on August 2, 2007 [1 favorite]