Settle an arguement

Tusky

Having an arguement with a friend and wonder if any of you can settle it.

My point of view :

When you roll a dice and get a number (lets say a five). I think that you have the same chance of getting a five next time you roll (1/6). No matter how many times you roll a die, the probability that a 5 will come up on a certain roll is ALWAYS 1/6. This is because every roll of the die is exactly the
same.

The rolls that came before do not change the rolls that will come in the future. Said another way, the outcome of each roll has nothing to do with the outcomes of the other rolls. In probability language, the rolls are said to be independent.

He thinks that the more times you roll, the less of a chance you have to get the same number.

Can anyone shed some light ?

scojones

In theory, you're right.

Sam Vimes

if my memory of probability serves, the probability of 5 coming up is always 1/6 but the probability of it coming up x times is (1/6)^x. sorry

but the way you say it you're right too. the chance of 5 coming up is always 1/6 but the chances of it coming up twice in a row is different

edit:
i could be wrong about the (1/6)^x. just looking it up now

edit2: heres a similar situation with coins. it says the probability of getting heads for times in a row is 1/16
http://www.arnoldkling.com/apstats/coins.html

scojones

Commander Vimes wrote:

if my memory of probability serves, the probability of 5 coming up is always 1/6 but the probability of it coming up x times is (1/6)^x. sorry

So the probability of it coming up in the next throw is 1/6 ^ 1, which is 1/6.

Tusky

The thing I cant understand is : How does a previous throw of the dice effect the probability of the next throw ? Surely every throw is completely random and therefore is 1/6 ?

Don1

ONce the first five is thrown, then the probability of throwing a five is the same as the first time. It's when you start at zero throws that the probability of throwing two fives in a row is different................

Princess Consuela Bananahammock

It doesn't.


The chances only go up if you set the number beofre you start. EG - if you roll a die and it comes up 3, the chances of you rolling a three again are 1 in 6.

Now if you set the number at 3 before you start, the probabily jumps to 1 in 36 (1 in 6*6), because you're predicting the otucome of BOTH dices, not just the second one.

EDIT: Assuming I've understood the question, which is possible...

Tusky

Don1 wrote:

ONce the first five is thrown, then the probability of throwing a five is the same as the first time. It's when you start at zero throws that the probability of throwing two fives in a row is different................

Yeah, thats what I think aswell...you said it in a much easier way to understand though.

Gordon

It's relative.

If you see the dice as being thrown in that instance then you have 1/6 chance.

If you see the rolls as a sequence ("What's the possibility of me getting 6, then 6, then 6?" for example) then the probability changes as you specify more than one throw.

Don1

Which is odd as I detest and suck at probability and (more so) statistics!!!
Glad to be of service though!

Sam Vimes

sjones wrote:

So the probability of it coming up in the next throw is 1/6 ^ 1, which is 1/6.

no, the next throw is throw number 2, so its (1/6) ^2=1/36

if considered separately, its throw number 1 again but we're talking about the probability of it coming up x times in a row

its like he's throwing 2 dice and working out the probability of the same number coming up on both. the fact that its the same die twice doesn't mean anything to the eqn

if you think its still 1/6 no matter how many times its thrown, i bet you 1 million euro that if i throw a die 100 times, the same number will not come up each time. sure you have a 1 in 6 chance

Wez

Exactly as ikky poo2 says..

Each throw of the die has no affect on the next throw, but if you pick the number before you start, then there's a 1in 6 chance, times 6 that it'll come up a second time. Basically, if you're gonna throw for the first time, it's 1 in 6, same as there is for the second time, but for them to come up in a row, that's when it's multiplied by 6 again.

Lothaar

Tusky, going purely by the way you described the situation you are correct. Each roll is independent.

However, the probability of rolling the same number coming up multiple times in a row is different.

I think this problem has more to do with phrasing than probability.

Tusky

Lothaar wrote:

Tusky, going purely by the way you described the situation you are correct. Each roll is independent.

However, the probability of rolling the same number coming up multiple times in a row is different.

I think this problem has more to do with phrasing than probability.

Yeah I agree.

Its a difference between

A) Probability of rolling a 6 three times in a row

OR

The probability of rolling a 6 if the last roll of a dice was a 6

two different things...I think.

User45701

Your right, but luck and chance are always there.
ive seen a royal flush come up on the flop,turn,river in a 6 man game odds of that are probbley less than winning the lotto

humanji

Just hit your friend in the face, clamp your hands over your ears and start shouting "La La La La La LA LA..." That's how you win an argument!

Sam Vimes

humanji wrote:

Just hit your friend in the face, clamp your hands over your ears and start shouting "La La La La La LA LA..." That's how you win an argument!

or of course say "screw you guys. i'm going home"

oRlyYaRly

Jack hasn't rolled the die yet.

He has a 1/36 chance of rolling two fives in a row. (1/6 x 1/6)

The first roll is a five.

Jack now has a 1/6 chance of rolling two fives in a row. (1/1 x 1/6 - It's 1/1 because he's already rolled the first five.)

If he can't understand that then just "admit" you're wrong.

Feral Mutant

If the die lands on the name side multiple times, it may indicate that the die's centre of gravity is off and that may mean it's more likely to land on that side again. IRL a die isn't going to be perfect.
If you're taking it that the result is random then you're right.

kevmy

oRlyYaRly wrote:

Jack hasn't rolled the die yet.

He has a 1/36 chance of rolling two fives in a row. (1/6 x 1/6)

The first roll is a five.

Jack now has a 1/6 chance of rolling two fives in a row. (1/1 x 1/6 - It's 1/1 because he's already rolled the first five.)

If he can't understand that then just "admit" you're wrong.

Clearest and from my knowledge the most correct answer yet. However I do hate probability and try not to think about unless I have to.

Consider the Lotto. There is a 1/42 chance of any particular number coming up. But for 6 balls that you want it's (1/42) * (1/41) * (1/40) ....

Capt'n Midnight

kevmy wrote:

Consider the Lotto. There is a 1/42 chance of any particular number coming up. But for 6 balls that you want it's (1/42) * (1/41) * (1/40) ....

don't forget it doesn't matter which order they come out in

42/6 x 41/5 x 40/4 ... :1

in vegas they use trasparent die so you can't hide weight in one corner, so people drilled the spots and put platnium and other heavy stuff behind them

AngryBadger

The two events are not connected. But every single additional role is one more chance that you will get a different result.

The only way you friend is correct is if he's contending that because every time you roll the dice it's another chance for a result other than 5.

However the probability of THAT SPECIFIC ROLL coming up as a five again doesn't change.

astrofool

It sounds like one of you is looking at each roll individually and the other is looking at cumulative rolling (i.e. the chance of getting 3 5's in a row having rolled none yet).

So in a way you're both right, you're friend is right in that the chance of getting the same number (1/6) is alot less than the chance of getting ANY other number (5/6).

Think about it if you threw all the dice together, what the chances of them all being 5 is.

Tbh, it just sounds like the two of you are completely crap at explaining your reasoning (and/or are very stubborn and refuse to admit defeat)

I remember having an argument with my science teacher in secondary school about the chances of having a boy or a girl, he insisting that the chance of getting two boy's was 50% (when it should have been 33%).

0utshined

Tusky wrote:

He thinks that the more times you roll, the less of a chance you have to get the same number.

Can anyone shed some light ?

He's wrong Tusky.

That's the gambler's fallacy - thinking that because you didn't get the number\card you wanted it's due to come up soon. You're right that with a fair dice each throw has no bearing on the susequent throw. You could get 12354 6s in a row. The odds of getting that before you throw the first dice are quite poor but each time you throw it the odds of a six coming up are 1 in 6.


If he doesn't get that then just do what oRlyYaRly suggested and "agree" that he's right, it's not worth the hassle.


Edit : Here's a link to the Wikipedia page : http://en.wikipedia.org/wiki/Gambler%27s_fallacy

Capt'n Midnight

if you want to change the odds from 6:1 you need other dice

http://upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Dados_4_a_20_caras.jpg/180px-Dados_4_a_20_caras.jpg

seamus

An easier way to explain it to people I find is to say that after having rolled a six once, there's a 5/6 chance of *not* rolling a six the next time. Nothing has changed, but there's still a much better chance of rolling something else.

Sam Vimes

0utshined wrote:

He's wrong Tusky.

he's not wrong, tusky's just not explaining what his mate said properly. the chances of the number 5 coming up each time is 1/6, but the chances of getting it x times in a row are not 1/6. a lot of people have said this on the thread already

0utshined

Yeah he is wrong, as Tusky phrased what his mate said in the OP. Now it could be that Tusky has misrepresented his mates position but you would presume they would have clarified what they meant before coming to a forum about it.

Tusky needs to clear up with his mate what exactly his position is but for the problem as stated his mate is wrong. I understood the probability already but thx anyway.

poobum

its to do with phrasing as earlier stated!

each independant roll does have a chance of 1 in 6 to get whatever number...but thats on a single roll!
but when calculating the odds of getting say 3 rolls being say a 4 its different
the maths becomes instead of 1/6
its now (1/6) X (1/6) X (1/6) = (1/216) ie the odds of rolling a 4(or any other number) three times in a row on a dice is 1 in 216
same with a coin or anything else like that!
each roll has a 1 in 6 chance of being that number, but ihow you calculate it changes when you take a set of rolls!

humanji

Commander Vimes wrote:

or of course say "screw you guys. i'm going home"

That goes without saying.

seamus

If you pick any random sequence of eight numbers from 1 - 6, say 54261543, there is the same chance of this appearing in eight rolls as 66666666. This is one of the first major intuitions that has to be overcome if you start studying probability. Your brain says that's not right, even though the maths says otherwise and is rock solid.
The lotto is a great example of this. There is an equal chance of 1, 2, 3, 4, 5, 6 coming up in a draw as any other grouping of numbers. Yet if we all saw this come up, it would be national headlines, and we'd be saying "Wow! What are the chances?!". Instinctively, most people don't choose sequential numbers, or scoff when their quick pick give a sequence because they think it reduces their chances. I would admit to feeling "cheated" when my quick pick gives me a sequence of three or more numbers, even though it's not rational.

Sam Vimes

the answer is obviously 42, or in this case 1/42

i71jskz5xu42pb

Somewhat related probability problem that puts people in a spin

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Have a think and then check the answer

Lothaar

PaschalNee wrote:

Somewhat related probability problem that puts people in a spin



Have a think and then check the answer

This 'problem' is a red herring. We're working with incomplete information, as we don't know anything about the presenter. Based purely on the information we have, as you phrased the problem, there is no advantage or disadvantage to switching your choice.

Back to the OP, as I said earlier it is a matter of phrasing. And I think it is entirely possible that Tusky misrepresented his mate's stance because they are talking about different things - one is the probability of rolling a 6 on the *next* throw, the other is the probability of rolling a 6 multiple times in a row.

i71jskz5xu42pb

Lothaar wrote:

This 'problem' is a red herring. We're working with incomplete information, as we don't know anything about the presenter. Based purely on the information we have, as you phrased the problem, there is no advantage or disadvantage to switching your choice.

Why do you need to know anything about the presenter? Three doors, you pick one, one of the remaining two, containing a goat, is opened. Is it to your advantage to switch your choice?

There is an answer and and it is not that "there is no advantage or disadvantage to switching your choice". So try again.

Kipperhell

THe problem is the terms being used and phrase. Probability is the incorrect term to use when you say the probability of 5 is coming up on the last time is wrong . The chance or odds remain the same on each throw but the probability of the series of throws coming up the same is a different concept and uses a different formula as stated. So it is more the statement doesn't make sense as you can't the probability of one throw.
People often missuse the word in english and think "probability" is the same as chance. So the odds of 5 coming up are still 1/6 no matter how many roles but the probaility of 5 coming up again is dependent on the number of roles.
So the statement you made is incorrect by not making sense you can't get the probability of one event as such.

Lothaar

Did you read that wikipedia entry? It contains a detailled discussion on the various incarnations of this problem and the lack of information in some incarnations, such as the one you used.

"In general, without the behavior of the host completely specified, it is not true that switching will be successful two-thirds of the time."

Tusky

Lots of replies, cheers people!

Its all been cleared up now.

The original arguement was this :

If I roll a dice and get any number (lets say 6). I still have a 1/6 chance of rolling a 6 the second time. He disagreed with this and was arguing that there was less of a chance of rolling the same number again, which of course is wrong.

I can see where the confusion was though. In his head, he was thinking about the chances of rolling 2 or 3 sixs in a row...which of course if less.

It was more a problem of phrasing it wrong...although from the very start of the arguement I said "we are both right....we're just phrasing things wrong". H on the other hand was adamant that I was just completely 100% wrong.

kevmy

Capt'n Midnight wrote:

don't forget it doesn't matter which order they come out in

42/6 x 41/5 x 40/4 ... :1

You are of course correct an oversight on my behalf.

kevmy

seamus wrote:

The lotto is a great example of this. There is an equal chance of 1, 2, 3, 4, 5, 6 coming up in a draw as any other grouping of numbers. Yet if we all saw this come up, it would be national headlines, and we'd be saying "Wow! What are the chances?!". Instinctively, most people don't choose sequential numbers, or scoff when their quick pick give a sequence because they think it reduces their chances. I would admit to feeling "cheated" when my quick pick gives me a sequence of three or more numbers, even though it's not rational.

Like the time that the Lost numbers almost came up (4, 8, 15, 16, 23, 24[a reversal of 42]) everyone thought it was weird and it is but still has the same chance as any other set of numbers

Manic Moran

As my Backgammon book put it, the dice have no memory.

NTM

rediguana

I didn't read other posts, so apologies for repitition.

Indeed, any given roll of a dice is equally likely to turn up a five (or whatever), 1/6.

Perhaps your friend is confused as the likelihood of throwing TWO CONSECUTIVE fives is less than the probability of throwing a five in a GIVEN throw.

The chance of throwing (say) ten consecutive fives is very low but, on the eleventh throw, the chance of throwing a five is still 1/6.

What a world!

InFront

I think the answer could have been made clear in one post if the op had been clearer tbh!:p
42... no, 43 posts on this question:eek: