The first paragraph should read 1:3 rather than 1/3, or 1/4 if you prefer.

Not going to explain again where you went wrong. I will let one of the other mathematicians and physicists explain where you are so fucked up on this one. Coins are two sided so the number *happen* to come out as 25% double heads, 25% double tails, 50% one heads the other tails and maintain a 50/50 shot at at least one heads toss. But that is because 2^2 is the same as 2*2 is the same as 2+2. Dice are different. Whether you toss one die many times or many die at once, the odds work the same.

"Dice are different"

That's all I needed to hear.

The nice thing about coin flips is that you have coins in your pocket. Flipping a coin 100 times doesn't take very long, and I think you'll find the results instructive in checking your claims and building intuition for how this stuff works. Let us know what the results are!

"However if I flip one coin two times, the chance of me getting a heads on the first flip is 50/50. The chance of getting heads on the second flip is 50/50. The chance of me getting heads on BOTH flips is 50/50. This is because, unlike flipping two coins, the flip of the first coin has absolutely no impact on the probability of the second flip."

This is where you screw up. You're equating P(A) with P(A|B), where A is both coins come up heads, and B is the first coin you flip comes up heads. The rest of your post just builds upon this screw-up.

Well, they are. 6 sides means 6^n combinations where N is the number of individual dice throws. Coins have 2 sides or 2^n combinations. What is so difficult to understand? You deal a single card and reshuffle it in the deck and do the same again. You do not have a 1 in 52 chance of getting the specific card twice in a row and you do not have a 1 in 52 chance of getting a specific card in general. Probability is based on powers even when done independently.

"Dice are different"

http://i.imgur.com/XUYxDbJ.gif

This is very interesting. I would definitely suggest flipping a coin perhaps around 10,000 times and letting me know details such as:
1) how many heads/tails overall
2) how many consecutive heads/ tails you flipped
3) how many times the coin defied all probability and ended up on its side, and
4) how the results varied with different coins (try coins of all values from all different countries)

I have an interesting hypothesis about this experiment if done: the skew off of the expected 50/50 split is more affected not by the evenness of the coin, but by how the flipper flips the coin, so different PEOPLE will have different average results, but not different coins.

""Dice are different"

That's all I needed to hear."

How's that? He's just telling you that you're taking a wrong example and blowing that one too :)

I'll have a go too...
first paragraph: why the hell do you think you all of the sudden have a chance of 1/3 instead of 1/2?

second paragraph: wrong again. There are 4 combinations:
1) coin 1 heads, coin 2 heads,
2) coin 1 tails, coin 2 heads,
3) coin 1 heads, coin 2 tails,
4) coin 1 tails, coin 2 tails.

so chance of getting heads on both flips is 25%, since it's one of four possibilities.
same for tails.

Third paragraph: yeah, we know.

fourth paragraph: if you throw one coin at the time, yes.

fifth paragraph: I don't believe in God but that doesn't make me an Atheist. I believe in something else, so no nothing happens after death etc, but no God either. If you want to yell something at me that has to do with my faith your best go is probably heathen. I'm just not an Atheist :)

I just ignored the Athiest quip, steephie. I'm a Lutheran anyhow and he is now either simply a blissfully ignorant fool or trolling at this point.

This is not an explanation of how it does work because Draugnar covered that part and we both did in the original thread: http://webdiplomacy.net/forum.php?viewthread=979793#979793

And now I really have to get back to my homework... So hard...

As “Dice are different” I am going to detail in full the mathematics of dice:

Let us roll a dice once. As most of us will agree the chance of landing a 6 is 1 in 6, or 16.6666667%.

If we roll two dice, the chance of us landing a 6 is as Draug detailed in his description 11/36, or 0.305555556%. This is because the likelihood of landing a 6 is increased as you increase the number of die; as each die lands there are more probabilities that involve a 6 than not; this increases exponentially to a chance of 1, where N/6 and N is infinite.

Consider that we have rolled a dice and the outcome was 6. Now the chance of us getting a 6 in any amount of rolls is 100%, as the previous result STILL STANDS. This is the difference between rolling one dice and multiple die; the previous roll affects the outcome of the overall study – which is that we will roll a 6.

However rolling the same dice twice is different. Because each roll of the dice is a standalone event the chance is 16.66666667% of rolling a 6, despite whether or not we have rolled a 6 previously.

We roll the dice once: the chance is 1/6
We roll two die: the chance is 11/36
We roll one dice twice: the chance is 1/6, followed by 1/6

Thus the chance of rolling a 6 infinitely is not N/6 but 1/6*N where N is infinite and your chance will never increase no matter how many times you roll.

The problem isn’t mathematical but a matter of physics. Before you have begun rolling any die, the chance that you will get a 6 in the future is 16.67%. After you start rolling die, your chances may only increase, which is why it APPEARS that exponentially your chances will become higher BEFORE you roll any dice.

Well actually you also forgot that the odds aren't perfectly 50:50 when flipping a coin. Generally when flipping coins over and over someone around you will get annoyed and steal the coin, the coin may land on it's side (had this happen before), a meteoroid may hit the coin melting the coin in to a little puddle of metal making it have no sides. There are some coins that have slightly more weight on one side then the other which would toss the odds off ever so slightly. Also, your math doesn't work if you are an astronaut in space since the coin will never land.

steephie22 it annoys me that you can't even follow my paragraphs. You are clearly below the age of 16 and these concepts I doubt I can explain to you.

The first paragraph of my coin explanation explains your solutions: TT, HH, HT, TH. However the second paragraph is talking about one coin, which does not have any combination outcomes. Please re-read my paragraph slowly.

The odds of rolling a 6 in N rolls is 1 - (5/6)^N. lim(x -> inf) 1 - (5/6)^x = 1, or 100%. You will eventually roll a 6. Why does physics come into this?

@SY - Either you really are ignorant of this fact or you are trolling, but I will say it again. It matters not if it is the same die rolled multiple times or multiple die rolled together. The odds are identical. There are 36 combinations of back to back die roll. The are 36 combinations of simultaneous die roll. The odds are the same. Do you have a degree in this shit? I doubt it. Did you take a class even in high school and get a perfect A? I doubt it.

Seriosly. Just like with tossing the coin repetitively, the combinations make no difference if consecutive or concurrent. The math *is* the same. Cards do vary ever so slightly depending on if each card is reshuffled into the deck (making each draw out of 52 cards) or if they are shuffled and discarded into another pile (making each draw from one fewer than the previous).

Not so much physics, but most physicists have taken some serious advanced mathematics. And clearly even simple probability mathematics eludes SY.

Y2k your formula is incorrect and Draugnar your concept is incorrect.

Y2k your formula is correct if rolling an infinite number of die, however rolling the same die infinite number of times is 1-(5/6)*N where N is 1, 1-(5/6)*1 = 16.67

The series on events required for the existance of this thread, assuming a starting point of the creation of life on Earth, are so astronomically unlikely that we can safely say this conversation is statistically impossible and ignore it.

SY is just an idiot after all. Too bad. I actually thought he might be trolling.

Rosencrantz and Guildenstern are dead for a reason.

Draugnar you are conflating discrete and continuous probability distribution in such a obscene way I cannot argue against you. Your terms of argument are fundamentally incorrect. Please read about Bernoulli distribution and come back to me.

http://en.wikipedia.org/wiki/Probability_mass_function here's your answer steephie. I'm done with this stupid argument.

Bernoulli distribution is only for binomial probabilities. Dice aren't binomial.

http://en.wikipedia.org/wiki/Dice#Probability

The fact you didn't even bother to look this up on wikipedia amazes me

And you provided a wiki to discrete calculations, but we are not talking discrete. Discrete is about each die roll being independent of the other. By the very fact that we are looking for at elast one out of a series, it becomes continuous. Discrete says that any given die could roll a six. I haven't argued that. Any one of the die has a 1 in 6 chance of being a 6. But think yahtzee. Does the fact that I roll one die at a time versus throwing all 5 of them change their odds? No! It doesn't! Therefore we are dealing with a continuous probability.

...feeding the trolls much

From your latest wiki post.

So, for n rolls of an s-sided die the probability of any result is 1/s^n (I added the carat "^" as the font doesn't handle it).

Nope you are conflating the issue - like I said we disagree on physics/philosophy not on mathematics. Rolling a series of die is a series of discrete calculations.

SY, your physics/philosophy can make you think whatever you want. My probability will beat you in any game we set up to prove who actually knows what they're talking about. I'm not in the mood to fight someone who truly thinks that rolling a die twice consecutively is at all different from rolling two identical but separate dice at the same time, in terms of the probabilities we're calculating.

stop trying to bury my awesome threads exposing how the public is being brainwashed with your gay threads about grade 10 probability problems.

I feel compelled to just have my name appear in this thread in the hopes that it will distract you from this pointless argument.

Please, if you must continue in this thread, feel free to bash away at me with tiny, feckless insults so as to not continue with this valueless discussion.

But krell's, baby, we alls just loves ya' to death!

Synapse: the probability that Krellin will post in this thread again is 100% because he already posted in it.

Minus the word "again", that's exactly what I was trying to say.

I may post in this thread again, but I deny the correlation between past and present posts, per se. I'm perfectly capable of abandoning a thread. I choose not to in this case. Choice defies probability.

...and I'm bored.

SYnape, Not only is your math wrong and your logic wrong, but your English is wrong too, at least in the United States, not sure about other English speaking countries.

"We roll the dice once: the chance is 1/6
We roll two die: the chance is 11/36
We roll one dice twice: the chance is 1/6, followed by 1/6"

Dice is plural, die is singular. So we roll the die once. We roll two dice. We roll one die twice.

You also don't indicate the chance of what happening.

We roll a die once: the chance of rolling a 6 is 1/6.

We roll two dice once: the chance of both of them being a 6 is 1/36.
We roll one die twice: the chance of both of them being a 6 is is 1/6, followed by 1/6 which is 1/36, the same as when rolling two dice at the same time.

We roll two dice once: the chance of one of them being a 6 is 11/36.
We roll one die twice: the chance of one of them being a 6 is 1/6 plus (5/6*1/6) which is 11/36, the same as when rolling two dice at the same time.

If you are trolling, that's okay because it is fun to think about, but I won't bother trying again if you appear to still not get it.

I know, I figured out that you actually weren't trolling and you were just making the P(A) = P(A|B) mistake that most people make who haven't formally studied probability.

Listen to y2k. He is da man when it comes to mathematics. I never ever doubt him.

y2k is a Harvard grad. He knows his shit.

10/10 would troll again

Vær venlig ikke at fornærme trolde ved at sammenligne os til @SY

I'm impressed you guys are even trying to engage with somebody who refuses to believe rolling two dice at the same time is the same as rolling one die twice... the rest of the maths is pointless if that's not accepted as fact...

LOL OP is an ijit.