bad great generals

[The Great Apple]

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.

I would think that this is a pretty clear statement. It's also wrong. Correct me if I'm wrong, but it would seem that I, and everybody else here thinks you mean this:

- Keep flipping coins until you get 5 heads in a row.
- Flip one coin, record this last coin's result.
- Start again

The result you are recording will be 50/50 given an unbiased coin. Your guarantee is therefore false. The events which have occured to give you the sequence will not alter the 6th throw.

I'm still not seeing where quantum physics come into this either. You seem to be reluctant to explain that, even to people with quite some qualifications.

 

[PennHead]

What are the odds of getting 5 in a row? 1 in 32 right? Do we agree so far?

What are the odds of getting 6 in a row? 1 in 64 right?

How kind of you to make the point for me.

As you say, the odds of 5 in a row is 1/32. The odds of 6 is 1/64. That means, that half the time that you get 5, you will go on to get 6(1/32*1/2=1/64). Half the time, you won't. This directly contradicts your assertion that after getting 5, getting the sixth is not 50/50.

Of course betting against a six in a row is a better bet for you than five. However, that's not what's being debated. The point of contention is, once you already have five, what are the odds of the sixth?

 

[Ryuujin]

Technically, any actual sample you took would very likely not give you a 50/50 result. The results will most likely be skewed towards either Heads or Tails. However, there is no way you could predict ahead of time which way the results will be skewed, and the degree to which the sample deviated from 50/50 would tend to shrink as the sample size increased.

 

[El Koeno]

Case closed. Everyone in this thread is stupid and magically misunderstood Kcbrett's posts. Now what are the odds of that happening?

EDIT:

Please Kcbrett: Could you just please admit your first statement (quoted over and over again) was wrong? It's totally silly to bet your life savings on tails if someone has just landed 50 heads.

 

[KrikkitTwo]

Well that depends on the odds, if he is getting a 10 to 1 return if tails comes up its a Great bet. I'd also bet my life savings for a 10 to 1 return on what that 51st flip would be.

 

[Teg_Navanis]

Please Kcbrett: Could you just please admit your first statement (quoted over and over again) was wrong? It's totally silly to bet your life savings on tails if someone has just landed 50 heads.

I think his last statement got lost at the end of the last page. It was sort of anticlimatic, actually...

 

[Draconian]

Case closed. Everyone in this thread is stupid and magically misunderstood Kcbrett's posts. Now what are the odds of that happening?

Pretty easy to calculate, let's say everybody has 50% to be stupid and 51 other people posted here. That would be 0,5^50 or 0,0000000000000888% for the first 50 people, unlikely but still possible. BUT:
If you get 50 stupid people in a row I am betting my life savings on that 51st person not being stupid. True, the odds of the 51st person to be stupid are still 50/50. But the odds of hitting 51 stupid people in a row are astronomical. This is why you can win at roulette betting only black/red, high/low, and odd/even. If you dont believe me, try a simple experiment. Talk to persons continuously until you get 5 stupid or not stupid ones in a row. Then record what the 6th person is. Repeat this as often as you want until you have a large enough sample. Then see what all of your 6th persons were and I guarantee you they will not be 50/50. Try it. You will see.

qed

 

[Ammar]

Pretty easy to calculate, let's say everybody has 50% to be stupid and 51 other people posted here. That would be 0,5^50 or 0,0000000000000888% for the first 50 people, unlikely but still possible. BUT:
If you get 50 stupid people in a row I am betting my life savings on that 51st person not being stupid. True, the odds of the 51st person to be stupid are still 50/50. But the odds of hitting 51 stupid people in a row are astronomical. This is why you can win at roulette betting only black/red, high/low, and odd/even. If you dont believe me, try a simple experiment. Talk to persons continuously until you get 5 stupid or not stupid ones in a row. Then record what the 6th person is. Repeat this as often as you want until you have a large enough sample. Then see what all of your 6th persons were and I guarantee you they will not be 50/50. Try it. You will see.

qed

Since stupid people tend to hang out with each other you are right and there is a increased probability for the sixth person to be stupid too.

 

[PurpleTurtle]

Dunno if anyone has asked this, but has anyone lost fights that say 100%? I have lost a few and it has led me to believe that the % is only a general idea of the probable outcome and that first strike is not accounted for at all.

 

[Draconian]

The way the combat system works there is afaik NO WAY to get 100% to win. You may get 99,99x% but not 100%. A combat consists of several combat rounds, in each round one of the units is hit and takes damage. The chance to hit and the damage depends on the strength of the 2 units. So even a warrior with 0,1 health could kill a full health MA (or you could as well win the lottery...). If it shows 100% it's just 99,x% rounded up.
And first strike is calculated into the combat odds. But don't ask me if it's calculated right

 

[lobster]

I haven't lost any 100% fights but got seriously wounded from those a few times.

 

[Ammar]

Dunno if anyone has asked this, but has anyone lost fights that say 100%? I have lost a few and it has led me to believe that the % is only a general idea of the probable outcome and that first strike is not accounted for at all.

It's certainly not totally accurate. There is some rounding. Due to game mechanics there is never a 100% percent to win or lose. I remember there being some problem with first strikes, too. Don't know if that ever got fixed.

 

[cicobuff]

Case closed. Everyone in this thread is stupid and magically misunderstood Kcbrett's posts. Now what are the odds of that happening?

EDIT:

Please Kcbrett: Could you just please admit your first statement (quoted over and over again) was wrong? It's totally silly to bet your life savings on tails if someone has just landed 50 heads.

This thread is so interesting that I cannot resist registering myself and making my post.

Before I start I'll like to say that I agree with everyone minus Kcbrett that his understanding of statistics of wrong and the quantum mechanics reference he tried to make is so way beyond him that he cannot even make a suggestion as to how quantum mechanics can come into play.

BUT his reference did set me thinking about the following scenario:

Suppose that before the experiment, Kcbrett says that he'll bet his life's savings ($100) on the next flip being TAILS if 50 flip preceeding are HEADS.

Now what happens is that a machine flipped the coins 50 times but the results are kept secret from Kcbrett. The result is 50 consecutive (the machine flips very very fast so that we can get the 50 consecutive same side result quickly.) We then LIE to Kcbrett that the coins had landed 50 times HEAD when in fact the coins had landed 50 times TAIL.

Now, Kcbrett will bet his life savings ($100) on the next flip being HEAD.
Is he right to do that? What if a computer does the observing before it chooses to LIE to us before we can choose to LIE to Kcbrett? What is the % of the coin landing HEAD or TAIL? What is the computer had flipped 51 times and KNOWS the result before it choose to tell us the result? EDIT: The statement should read "What IF the computer had flipped 51 times and KNOWS the result before it choose to tell us the 50 consecutive results and then just announce the 51st flip result?"

Quantum physics starts behaving very weird in the micro world. QM is a very good mathematical tool for the micro world but I had always thought that it might be flawed. What if reality does not have a absolute reference frame but depended on the reality interpreted by each observing consciousness.

Recall that before Einstein, *almost* every scientist operated with the paradigm of an absolute frame of reference using Newtonian physics. I am wondering if such a paradigm is required to explain the *weird* world of QM? EDIT the statment should read "I am wondering if such a paradigm SHIFT is required to explain the *weird* world of QM?"

What if the observer somehow affect the outcome? What if the outcome had be predetermined (machine flipped 51 times but hid the result from us)? What if we are just observers in a predetermined event, e.g. the result of a HEAD is actually 100%, just like the scenario where we had 50H and as had been tried to demostrate to Kcbrett, the probability of having the 50H sequence is 100% because it had happened.

I would like to hear what some of the people who understand QM more than me (I'm just a layman who had read on QM theory) makes of this.

For all his faulty statistics and incoherent arguments, Kcbrett does make a point. We need to keep our minds open about anything and everything. =)

 

[Sparta]

"I don't like it, and I'm sorry I ever had anything to do with it."

-Erwin Schrödinger about the probability interpretation of quantum mechanics


... Only at CFC could a discussion of a game mechanic devolve into a discussion of probability theory and then further devolve into a discussion of quantum mechanics ...

I think I follow your point(s), cicobuff, but we may just be making the problem overly complex at this stage. If we're looking at it from a perspective of a simple probability problem, I think we've all done to death the explanation of the odds remaining 50% (I personally found it amusing to see how many people italicized almost the exact same "if the 50 heads have already occured" in trying to explain the problem. Like minds, I suppose.).

If we want to turn this into a mind-warping discussion of the observer effect and how far it forays into the non-quantum-level world, I think the legitimacy of a $100 bet on a coinflip may well become superfluous to the larger issue.

Personally, I think that kcbrett5 was just reaching for a deus ex machina in order to backpeddle out of a losing argument when making the QM reference (which may work in casual conversation, but apparently is a really bad idea at CFC). I found it both amusing and impressive to see the voluminous response of posters aware of and versed in the workings of QM. Speaking of which, some (or all ) of them would certainly be far more able than I to delve into your questions, since I skipped almost all of my quantum physics class sessions when I was in college (partying >> Schrödinger's cat, at that age ).

By the way, welcome to CFC!
If you are indeed interested in a more elaborate discussion of QM, or anything else not specifically civ-related for that matter, wander on over to the Off-Topic Forum and start up a thread! Have a good one!

 

[Wodan]

The quantum state of my computer aside, people who are bothered by the miniscule chance for their general to die, why not simply always attach him to a unit eligible for flanking? For example, a Horse Archer. Then, with the 20 xp, give him Tactics, Flanking I, and Flanking II.

Not only will you still have your 95-99% chance of winning, during the times when you would have lost, you get a 80% chance to retreat.

Wodan

 

[Ammar]

Now what happens is that a machine flipped the coins 50 times but the results are kept secret from Kcbrett. The result is 50 consecutive (the machine flips very very fast so that we can get the 50 consecutive same side result quickly.) We then LIE to Kcbrett that the coins had landed 50 times HEAD when in fact the coins had landed 50 times TAIL.

Now, Kcbrett will bet his life savings ($100) on the next flip being HEAD.
Is he right to do that?

He still has his 50% chance. Why shouldn't he? Is it wise to wager your life savings on a 50% chance. Not really, only the odds are very good.

EDIT: The statement should read "What IF the computer had flipped 51 times and KNOWS the result before it choose to tell us the 50 consecutive results and then just announce the 51st flip result?"

IF the computer has observed the coin the outcome is FIXED and in terms of QM the outcome is certain. However, that does not practically change anything because of the fact that KCBRETT does not know the outcome.

Until someone has a look the coin is showing neither head nor tail. Only when someone looks, the coin "decides" for one of the two states. This is not the same as you knowing the outcome. QM works in terms of real uncertainty, not limited knowledge of any particular person.

What if the observer somehow affect the outcome? What if the outcome had be predetermined (machine flipped 51 times but hid the result from us)? What if we are just observers in a predetermined event, e.g. the result of a HEAD is actually 100%, just like the scenario where we had 50H and as had been tried to demostrate to Kcbrett, the probability of having the 50H sequence is 100% because it had happened.
=)

That's sort of correct. There are two things to seperate :

1) No one has looked how the coin has landed. Therefore, there is uncertainty at a QM level.

2) Someone has looked how the coin has landed but has not told you. In terms of QM the system is fixed at let's say Head. But because YOU don't know the result it makes no practical difference for you. The situation has however no longer anything to do with QM.

 

[El Koeno]

Since stupid people tend to hang out with each other you are right and there is a increased probability for the sixth person to be stupid too.

Well, sometimes you get stupid after reafding to many weird forum-threads.

 

[cicobuff]

Apologies in advance for going off topic again.

He still has his 50% chance. Why shouldn't he? Is it wise to wager your life savings on a 50% chance. Not really, only the odds are very good.

Agreed.

IF the computer has observed the coin the outcome is FIXED and in terms of QM the outcome is certain. However, that does not practically change anything because of the fact that KCBRETT does not know the outcome.

Until someone has a look the coin is showing neither head nor tail. Only when someone looks, the coin "decides" for one of the two states. This is not the same as you knowing the outcome. QM works in terms of real uncertainty, not limited knowledge of any particular person.

Ahhh... this is where a conundrum for me comes in. The probability *apparently* only exist because we do not have the knowledge of the outcome. Now I will go out on a limb here and make a postulate: Actually the real probability is 100% because as a system, the Universe has a way of determining the result of the next roll. I.E. there is some fundamental inner working of the Universe, which is still not revealed to us, for determining the next roll.

That's sort of correct. There are two things to seperate :

1) No one has looked how the coin has landed. Therefore, there is uncertainty at a QM level.

2) Someone has looked how the coin has landed but has not told you. In terms of QM the system is fixed at let's say Head. But because YOU don't know the result it makes no practical difference for you. The situation has however no longer anything to do with QM.

My suspicion is that the Universe knows the result even though we do not. So there is no uncertainty. I had a discussion with a Physics PHD friend once on his but his conclusion was in opposition to mine. He felt that the Universe really did not know the result until the moment of measurement.

By the way, welcome to CFC!

Thanks! This is an awesome site.

 

[cicobuff]

This MAY be on topic if only via an attempted mathematical way.

Example: Take a sequence of 10 coin flips.
The sequence HTHTHTHTHT and THTHTHTHTH occurs only in 2 cases out of a possible 2^10 (1024) combinations. In majority of them, you can find sequences of HHH, TTT occuring relatively frequently. (Note that the frequency of HTH and THT are equally frequent!)

If you plot out a probability curve of the number of consecutive HEADs and TAILs. You will find a *clumping* behaviour, depending on how you plot the curve, you will get a bell curve centering around 3-4 consectives. Since one of our brain's most powerful attributes is to *instinctively*, without conscious thought or effort, recoginse patterns, the HHHHs and HHHs (same goes for T) will stand out.

The same will apply for biased systems, e.g. 80% landing on HEAD vs TAIL. You will still get *clumping*.

Now, subsititute the HEADS for WINS and TAILS for LOSES. I think we have hit on why some people feel that Civ4's probability calculator is incorrect. They may be experiencing clumping.

Coupled with our brain's tendency to incorrect sample (counting loses without counting wins) and the calculator's failure (guess) to not take into account first strikes. EDIT: Statement should read "Coupled with our brain's tendency to incorrectly sample (counting loses without counting wins) and the calculator's failure (my guess only, need verification from developers) to take into account first strikes."

I think this may explain the situation.

 

[Enkidu_Warrior]

The way the combat system works there is afaik NO WAY to get 100% to win.

Actually, I have seen a 100.1% chance to win in several combats in Warlords.

Although I suspect it's a bug, I cannot be certain - after this thread, I realise it's better not to be certain of anything

EW