Is it true that coin flips are always 50-50?

[matt grime]

No mathematician thinks of probability as causal in the sense you so describe.

You realize you've now implicitly said that "everything with two possible outcomes is mathematically the same"? That is a fairly meaningless comment.

I am making no unreasonable assumptions: if the 50-50 long term behaviour is false for a given coin in a given situation then it is not a good model. Nor am I attempting to explain the reasons why a coin falls head or tail, or lands on its edge and gets stuck in a crack. Probability is a useful way of modelling such things. As a simple matter, flipping a coin 2 feet in the air is sufficient to use a probablistic argument to describe its behaviour. Ever heard of Buffon's Needle and Monte Carlo methods?

Why do you have a problem with probability failing to do things it doesn't claim to do?

A person would not determine with 100% probability the outcome of each flip, by the way. He would determine with 100% accuracy. Not that we believe that to be possible in a non-linear model, or a quantum mechanical one. We do not claim that with 50% probability we can determine the outcome, which is what you are implying there.

 

[Eyesaw]

No mathematician thinks of probability as causal in the sense you so describe.

You realize you've now implicitly said that "everything with two possible outcomes is mathematically the same"? That is a fairly meaningless comment.

I am making no unreasonable assumptions: if the 50-50 long term behaviour is false for a given coin in a given situation then it is not a good model. Nor am I attempting to explain the reasons why a coin falls head or tail, or lands on its edge and gets stuck in a crack. Probability is a useful way of modelling such things. As a simple matter, flipping a coin 2 feet in the air is sufficient to use a probablistic argument to describe its behaviour. Ever heard of Buffon's Needle and Monte Carlo methods?

Why do you have a problem with probability failing to do things it doesn't claim to do?

A person would not determine with 100% probability the outcome of each flip, by the way. He would determine with 100% accuracy. Not that we believe that to be possible in a non-linear model, or a quantum mechanical one. We do not claim that with 50% probability we can determine the outcome, which is what you are implying there.

I agree with what you are saying and my previous posts weren't a direct response to your posts really though I really don't see how probability is very useful for describing a coin toss.For like a 6 sided dice that have 5 numbers the same for example it would be useful.

I was reducing the knife throw to just two possible outcomes to make an analogy with the coin toss. The 50/50 hypothesis for the coin toss is arrived at the same way after all.

 

[master_coda]

I agree with what you are saying and my previous posts weren't a direct response to your posts really though I really don't see how probability is very useful for describing a coin toss.

The funny thing about this is that most of the time I see mathematicians talking about coin tosses, they don't actually care about coin tosses. They care about a probability model where you have exactly two possible outcomes that have the same probability of occurring. Coin tosses are just used as a physical example of such a model to make things easier to understand for people who have a hard time understanding abstractions.

Seriously; who wants to waste their time modelling coin tosses?

 

[matt grime]

I was reducing the knife throw to just two possible outcomes to make an analogy with the coin toss. The 50/50 hypothesis for the coin toss is arrived at the same way after all.

The knife is thrown in a carefully rehearsed pattern by a skilled performer. The dynamics of the knife rotating are much different from the coin. The knife is caught most definitely not at random by the same skilled perfomer.

The coin is thrown in the air without any great care, the forces of the toss will usually make it spin faster than human perception allows us to differentiate between sides, and is either plucked out of the air with no great care again, or allowed to fall onto some surface.

Yeah, they're the same.

The reason we assign a probability of 1/2 to it landing heads is that, in the long run, that is what our experience tells us the proportion of heads to tosses will approach.

It is not the fact that there are two outcomes, it is the fact that there is no reasonable assumption as to why one should be preferred over the other - they are equally likely. Completely unlike the probability that a knife juggler loses a finger.

If you don't believe this to be reasonable then please do look up the Buffon Needle experiment where probability can and has been used to calculate the value of pi to a reasonable accuracy.

 

[so-crates]

A non-mathematical way of looking at it:

Does the outcome of a series of coin flips affect the probability of getting heads/tails on the next flip? If it does, how long would you have to wait before the probabilites "reset" themselves to 50%? An hour? A day? A year?

Does the outcomes of *your* coin tosses affect the outcomes of *my* coin tosses? If you believe that the outcome of previous coin tosses affect the outcome of the future coin tosses, then why not? If I get 5 heads in a row, the probabiliti of you getting heads should be a lot lower, because the probabilit that both of us will get 6 heads is a lot lower, right?

Does the number of times people flipped heads in entire human history affect *your* odds of getting heads/tails on a given flip? If you believe that the outcome of previous coin tosses affect the outcome of the future coin tosses, then why not? Let's say the running total for the entire human race is now 51% heads. Shouldn't you have a higher chance of getting tails?


I hope I not confusing you, the answer is NO, the trials are what statisticians like to call "mutually exclusive events", and the probability is always 50/50 (well some claim you get heads slightly more often, due to the aerodynamics and weight distrubution of the coin)

 

[matt grime]

A stastician would call them, probably, independent. The mutaully exclusivity is neither here nor there.

 

[Erazman]

haha this is the funniest thread I've ever read in my LIFE.
This is logic the average 8 year old would figure out.
I'm going to jump off a bridge. If my chance of living is 50/50, and i survive
then for sure next time will be death!

LOL

 

[phyti]

lets lay it to rest

Alright, I've been trying to convince my friend that the outcomes of a coin flip x times in a row affects the x+1'th time. If you flip a coin 4 times and they are all heads, the 5th time is more likely to be a tail because if the coin is even, over time there should be as many tails as there are heads. I even tried to prove it to him using math:
P(5 heads in a row) = .5^5 = 0.03125
P(4 heads in a row) = .5^4 = 0.0625

The system of coin tossing has no memory and therefore is time independent.
Any sequence of of n coins can occur but you cannot predict WHEN!

 

[sjoly]

Peng is right. I'm having to approach this is simple terms..I'm by no means an engineer. But anyway, the odds of 2 heads in a row are .5x.5. 3 heads=.5x.5x.5..et cetera. OTHERWISE, the odds of having a roulette ball hit black 10 times in a row would be the same as it hitting just one red (out of ten). Been to Vegas? Stand there and bet black all night and you'll walk away with approx. 50% of your bets. When I go to Vegas, I wait for 7 black hits in a row (or red)..and then I start betting on the other color.
Now I could go on forever..but why doesn't everyone simply bet 1,2,3,4,5,6 on the lottery. Technically, those numbers coming up have the same chance as any other combination...but there is more to it than that. I don't know what..but if I did, it would probably be easy to hit the lottery. I'm rambling. So I'll stop. But Peng is most definitely correct. Now it is true that there is a 50/50 probability each time..but only a 25% prob. on round number 2 for the same result. And so on.

 

[LukeD]

Wow, crazy zombie thread and horrible misunderstanding of probability. It took me a while before I figured out what sjoly was even trying to say because his post contains several contradictions in its own explanation.

 

[DaveC426913]

This is logic the average 8 year old would figure out.
I'm going to jump off a bridge. If my chance of living is 50/50, and i survive
then for sure next time will be death!

Alas, my 22-year-old actually thinks this way.

"I might die from smoking and I might not, just like I might step outside and get hit by a car or I might not. The chances are 50-50, so why worry?"

Couple that with a three-second attention span for critical analysis of any sort, and I mourn for our country's future.

 

[Dragonfall]

Actually flipping a coin twice, if actually done, do not produce independent events, because the movement of the first flip disturbs the air (or other factors) in such a way that it might influence the outcome of the second flip. To ensure that they are independent, assuming it takes 1 second to perform the experiment, you must place the coins 2 light-seconds apart, then from the middle send a signal to both coins to be flipped simultaneously.

Of course for all PRACTICAL purposes they are independent.

 

[Hurkyl]

This thread is old and the necromancer is spreading misinformation; I think it's time to close it.