Explain this statistics/probability thing for me

[JLam]

I have a friend who insists that if you play the same lottery numbers every day, you have an increased chance of winning than if you had played different numbers every day.

I tried to explain that past results are not indicative of future outcomes, but that's the best I can do. I'm not a math person. I know that her argument is bogus, but I'm not smart enough to explain it to a layperson.

Can any math people here help me out...in layman's terms?

Thanks.

 

[GreedyAlgorithm]

You could try ye ole coin flip. First, see if she agrees that playing the lottery is the same as guessing the result of a coin flip, just with worse odds. Then ask if guessing heads every time will give better than 50% results.

There _is_ a way to get better than average results at the lottery, or at least those lotteries that split winnings in the case of multiple winners: just guess numbers unlikely to be guessed by others.

 

[PixyMisa]

That's what I was going to say!

Any lottery result can be reduced to a series of coin tosses. For example, if you are picking six numbers from 32, each number can be represented by five coin tosses (2⁵=32) though you will have to throw out results that produce the same number twice.

Since the lottery can be reduced to coin tosses, and a fair coin toss is always a 50/50 chance, there's no difference between choosing the same numbers or different numbers.

 

[Schneibster]

You need to understand that I know people who drank free beer all the way through college by betting people at 2:1 that they wouldn't get heads again after they'd just gotten two heads in a row.

 

[GreedyAlgorithm]

The beauty of the coin flip argument is its symmetry. If she comes up with some explanation of why guessing heads all the time is better, introduce Person #2 who guesses tails all the time, and Person #3 who picks randomly. Can you, guessing heads, do better than #3? Only if you do better than #2, which is silly, since #2 has the same strategy you have.

Or you could take Schneibster's advice and just lay wagers on coin flips. Once you have a bunch of cash, ask if she's convinced...

 

[Paul C. Anagnostopoulos]

Why does your friend think that? I'd guess it's that she thinks the longer the lottery number selecting machine goes without picking the predetermined number, the higher the chances that the number will be picked. Ask her how the lottery number machine keeps track.

~~ Paul

 

[Paul C. Anagnostopoulos]

You need to understand that I know people who drank free beer all the way through college by betting people at 2:1 that they wouldn't get heads again after they'd just gotten two heads in a row.

You're making this up. What college was this?

~~ Paul

 

[Interesting Ian]

I'm pleased that at the bottom it mentions one of my threads as being similar to this one i.e Brains, Science, and Nonordinary and Transcendent Experiences

 

[69dodge]

I have a friend who insists that if you play the same lottery numbers every day, you have an increased chance of winning than if you had played different numbers every day.

I tried to explain that past results are not indicative of future outcomes, but that's the best I can do. I'm not a math person. I know that her argument is bogus, but I'm not smart enough to explain it to a layperson.

Can any math people here help me out...in layman's terms?

Thanks.

Which same lottery numbers? They can't all be better than average.

Suppose that yesterday I played one set of numbers and you played a different set. Today, would she say that I should reuse my previous numbers and that you should reuse yours? That doesn't make sense. Is it my numbers or yours that are more likely to come up today?

 

[tkingdoll]

dupe

 

[tkingdoll]

Why does your friend think that? I'd guess it's that she thinks the longer the lottery number selecting machine goes without picking the predetermined number, the higher the chances that the number will be picked. Ask her how the lottery number machine keeps track.

~~ Paul

It sounds more like the friend is basing her 'logic' on superstition and 'gut feeling' rather than anything that can be refuted with cold, hard facts. Alas, the lottery does seem to attract such I-feel-lucky-today emotions, and as such there's probably not a lot you can say to change her mind.

 

[ZirconBlue]

You could try ye ole coin flip. First, see if she agrees that playing the lottery is the same as guessing the result of a coin flip, just with worse odds. Then ask if guessing heads every time will give better than 50% results.

Ah, but in the lottery, you only have to be right once, then you quit. If I guess heads every time, I'm eventually going to be right.

 

[Bone_Vulture]

The idea of the lottery argument is that the numbers that come up each week are completely random. As such, the aggregate probability that over the long run one of these combinations is the one you picked over and over again increases. Also, it's about fear of this probability: if you've played the same numbers for years, are you going to risk the possibility that the old numbers will come up the week after you switched?

Anyway, the odds of winning the jackpot are typically astronomically small. But hey, a couple of dollars/euros a week is nothing for the chance of returning the investment millionfold.

 

[tsg]

The idea of the lottery argument is that the numbers that come up each week are completely random. As such, the aggregate probability that over the long run one of these combinations is the one you picked over and over again increases.

Ah yes, the "Law of Averages" fallacy.

 

[ReFLeX]

You can pick 1-2-3-4-5 as your five numbers one week. Someone might tell you, "No way that's ever going to happen, all the numbers are going to come up in order? Never." But it is just as likely to happen as any other possible, more random-looking sequence.

 

[tsg]

You can pick 1-2-3-4-5 as your five numbers one week. Someone might tell you, "No way that's ever going to happen, all the numbers are going to come up in order? Never." But it is just as likely to happen as any other possible, more random-looking sequence.

I've done this on purpose just for the reactions I get from the other people in line.

"Those numbers will never win."
"Oh, and yours will?"

 

[Bone_Vulture]

Ah yes, the "Law of Averages" fallacy.

My perspective to statistical math is quite mundane. Can you explain this fallacy to me?

[EDIT]

Meh, I checked Wikipedia's take on the law of averages. Choice quote:

"I just got 5 tails in a row. My chances of getting heads must be very good now." False. It was unlikely at the beginning that you would get six tails in a row, but the probability of six tails was the same as five tails followed by a head: 1/64. Looking forward after the fifth toss, these probabilities are still equal. The only difference is that there are no other possibilities, so the probability of either outcome is 1/2. This error can be devastating for amateur gamblers. The thought that "I have to win soon now, because I've been losing and it has to even out" can encourage a gambler to continue to bet more.

An interesting argument. I am aware that the absolute probability remains at the 50/50 in this coin toss example - although I still don't understand why a person cannot trust on the cumulative probability that'll probably "even things out".

 

[alfaniner]

You can pick 1-2-3-4-5 as your five numbers one week. Someone might tell you, "No way that's ever going to happen, all the numbers are going to come up in order? Never." But it is just as likely to happen as any other possible, more random-looking sequence.

The thing is, on most lotteries, they don't have to come up "in order". If that were required, the odds of winning would be... (what's larger than "astronomical"?) The numbers drawn could be 5-3-2-4-1 and you would win.

But I see your point -- they always come out in numerical order on your ticket.

 

[Bone_Vulture]

Ok, I did some calculations: the Finnish lottery has 39 numbers, jackpot requires seven correct picks. I will assume that the absolute probability of guessing the combination correctly at one try is 39 times 38 times [...] 33, which adds up to 77,519,922,480.

77 billion?! The odds aren't really charming. Now, if the lottery draft was absolutely random, would this mean that each week, the probability of my combination appearing would shift by... one? So if I played once every week for ten years, the probability would've shifted in my favor by a whopping... less than one millionth of a per cent?

If that is the case, I guess playing the same numbers doesn't make a lot of difference. Still, people believe in unkind fate - I've never played the lotto, but if I did for say, half a year, it'd be less of an agony to fork out that euro each week than embrace the (extremely improbable) possibility that my numbers will turn up after I've quit playing. That's superstition, yes.

 

[tsg]

My perspective to statistical math is quite mundane. Can you explain this fallacy to me?

[EDIT]

Meh, I checked Wikipedia's take on the law of averages. Choice quote:



An interesting argument. I am aware that the absolute probability remains at the 50/50 in this coin toss example - although I still don't understand why a person cannot trust on the cumulative probability that'll probably "even things out".

In simplest terms, the coin doesn't know what it did previously. The law of averages just means that, in the long run, the probabilities will average out. That is, in large enough samples the occurrence of random events will be approximately equal to the probability and that the larger the sample, the closer to average the outcome is likely to be. Tossing a coin five times and not getting any tails is unlikely, but no less likely then any other particular string of tosses (for example HHTTH). That it has happened doesn't influence what will happen next. HHHHHH is just as likely as HHHHHT.

This might make it clearer. Consider a fair coin flipped three times. The possible outcomes are:

HHH
HHT
HTH
HTT
THH
THT
TTH
TTT

All are equally likely. Now, having already flipped two heads in a row (a 1 in 4 chance), the odds of flipping tails are no more likely (HHT = 1/8) than flipping heads again (HHH = 1/8), or 1/2.

On the subject of messing with people in line for the lottery, I have also bought a ticket for the numbers that won last time just to see what they say.