bad great generals

[Pantastic]

The point KCBrett is arguing is that the sequence 50 heads v 1 tails is more likely to come up than 51 heads. This is correct.

No, it's wrong. Any particular sequence of 51 flips is exactly as likely as any other; you're as unlikely to get HTHTHTHTH... as to get all H. That's one of the biggest problems with that kind of argument, any specific sequence is equally unlikely.

 

[JrK]

Err... to get 50 tails and then one head is exactly as probable as getting 51 tails in a row. Only if you ignore the order I might agree with you: it is slightly more probable to get 50 tails and one head (in any order) out of 51 throws than to get 51 tails.

Ofcourse, you're absolutely right:

Situation 50 tails then head: 0.5^50 * 0.5 = 0.5^51
Situation 51 tails: 0.5^51

If the order is ignored: 0.5^50 * 0.5 * (1 over 51) = 0.5^51 *51 > 0.5^51=51 tails

I forgot the fact that the order being specified as in this case makes a difference

 

[SoxSexSax]

Yah sorry I didn't realise he was ignoring order until I re-read either. I am shamed.

 

[Jastrow]

The problem is that the math behind this everyday "intuitive" observation is far more complicated than simple probabilities. I would have to teach you quantum physics to understand it and I have no desire to do that. If you are really interested I can suggest some reading material however.

OK, if you cant explain it to them, please explain it to me! Because I agree with them that you are wrong on this, and given the above quoted statement, since I have a PhD in quantum physics, you should be able to explain it to me.

 

[DigitalBoy]

Kcbrett: If you think the odds of an individual coin flip are 50/50, why would you bet your lifesavings on it?

Point. Game. Match.

Nah. If you got 50 tails in a row you are more likely to get another tails. It would seem to me that getting 50 tails in a row implies that you have a biased coin which is more likely to land on tails then heads. Either that, or you have just witnessed a really REALLY rare event.

If I got 50 tails in a row, I'd certainly bet on tails popping up again.

I understand where you're coming from, but I think the assumption everyone is making is that the coin is "fair."

 

[El Koeno]

I just gave this thread an "excellent" rating.

 

[kcbrett5]

Kcbrett: If you think the odds of an individual coin flip are 50/50, why would you bet your lifesavings on it?

At this moment in time, my life savings are very small. It really isn't a very big risk for me. We are talking about $100.

You see, you all just assumed I was risking a large sum of money. Now you see where assumpions get you.

OK, if you cant explain it to them, please explain it to me! Because I agree with them that you are wrong on this, and given the above quoted statement, since I have a PhD in quantum physics, you should be able to explain it to me.

If this is really true, then don't you already know the answer? I would think so.

Oh, Kudos to our mathematician friend JRK. He is the only one so far who gets the situation. Finally shedding light on the masses in a way I have been unable to do so far. Hopefully this ends our silly little debate.

 

[Veritass]

Silly me.

I thought there might be something in this thread about, you know, great generals or something, not five pages of people arguing about Statistics 101.

If you supposedly have a coin that is 50/50 odds, and you get 50 heads in row, then you have to call into question whether the odds on that coin are really 50/50, or you have a two-headed coin. That is what is being called into question: whether the represented odds are correct. Maybe they are very accurate, maybe they're just an approximation. Either way, it should not affect your play.

 

[lobster]

I just attacked a barb archer with my phalanx and lost at 96.4% winning odds. I guess that just showed that first strikes really skew the real odds. Fortunately I lost a non-Warlord unit.

 

[kcbrett5]

I just attacked a barb archer with my phalanx and lost at 96.4% winning odds. I guess that just showed that first strikes really skew the real odds. Fortunately I lost a non-Warlord unit.

Actually this doesn't SHOW anything except that you were unlucky. Re-run the battle a bunch more times with randomizing the seed and then report the results. That would actually show something.

 

[lobster]

True, I could have just been unlucky. But even if the odds calculator was right, it just showed that extreme bad luck do happen.

 

[Draconian]

@kcbrett5:
Even though JRK is correct, you are not.

What are the odds of flipping 2 heads in a row? 25% right?
What are the odds of flipping 3 heads in a row? 12.5% right?
So the odds of flipping the 3rd coin are not 50/50, it is only 12.5%. The events are not independent.

The odds of getting HHH are 12.5%, true.
But the odds of getting a H after getting HH before are 50%.
HHH has the same probability like HHT.
Any specific sequence with a given length has the same probability.

If what you said where true HHT would have a probability of 25%*0,875=21,875%
Which obviously is wrong. (I hope this statement needs no explanation)

And a litte Question: has 50*H + T at the end a higher probability than 51*H?
If you answer with "yes" you didn't understand what JRK said.
If you answer with "no" you should understand that what you said before is wrong.

 

[PennHead]

At this moment in time, my life savings are very small. It really isn't a very big risk for me. We are talking about $100.

You see, you all just assumed I was risking a large sum of money. Now you see where assumpions get you.

Now you're just trying to save face. Regardless of how much money it is, you said you'd bet everything you have on a single flip of the coin, and would surely win because of past results. You spent pages arguing that the next flip is not independant of the previous ones. That's what most of the people posting on the matter have been arguing against.

Oh, Kudos to our mathematician friend JRK. He is the only one so far who gets the situation. Finally shedding light on the masses in a way I have been unable to do so far. Hopefully this ends our silly little debate.

Except that you've never been arguing what he's saying. In fact, what JRK said in post #118(with the minor correction in #122)is pretty much what everyone else has been trying to tell you for several pages now. Heck, he made that post to disagree with something you said. If you truly agree with him, then you've changed sides.

Just for reference, the experiment you asked us to do in your original argument, wherein you state that prior flips influence future ones:

Flip a coin continuously until you get 5 heads or tails in a row. Then record what the 6th flip is. Repeat this as often as you want until you have a large enough sample. Then see what all of your 6th flips were and I guarantee you they will not be 50/50. Try it. You will see.

If you agree with JRK, then you disagree with that now.

And please, for the sake of us who know some quantum physics, indulge us. I'm no PhD on the subject, but I have studied it, and have seen nothing that would back you up here. I really want to know what you're getting at, as have others who posted here.

 

[DigitalBoy]

[In retrospect, I'm just going to delete this post and hope this thread dies.]

 

[Jastrow]

Yes. You promissed us reading material... Please provide it. I am most familia with Sakurai, Shankar, Cohan-Tannoudji, Ngo, and Feynman, having those on my bookshelf, but have access to a well stocked library... Please provide the complete reference with page number of the text you offered to provide which support your position.

 

[CIVFITCH]

THis is my first post.

This thread is great. Remember arguing with you sister when your like 7 and you KNOW your right but they're too stubborn to admit it?. I feel like i'm watching 20 people arguing with a stubborn 5 year old girl.

 

[CIVFITCH]

oh i guess second post

 

[El Koeno]

oh i guess second post

And that would be your third!

It is true that this quite a silly thread. But very entertaining.

 

[Ammar]

I wouldn't try to convince him that hard. Either he's a troll or he is one of those people who use all the big words but don't understand the concepts behind them.

Really, it reminds me of the joke about the guy who takes a bomb with him whenever he boards an airplane. After all, he figures the chance of two people taking a bomb aboard are astronomically small and he won't ignite his.

 

[JrK]

since I have a PhD in quantum physics, you should be able to explain it to me.

Isn't the general consensus that if you can explain QM or even understand it, you've really NOT understood it? Cause I sure didn't. (going to follow that course again this year )