bad great generals

[merlinme]

I should probably let sleeping dogs lie, but...

As someone who's played a lot of games for a lot of years, I've effectively tried this out millions of times. You can roll a dice three times and get a six each time (1/216). On the third throw, if you give me 200-1 odds against getting a six, I will make a fortune out of you, provided we play the game long enough. You can get the same suit for all five board cards in Texas Hold'em (0.000495198, if my maths is correct). The chance of that final card being the same suit is 9/48, though, and if you give me odds better than about 4-1, I'll take you to the cleaners again.

In my worst ever bad beat, someone got the one card in the pack to improve their three of a kind to a four of a kind, when I had a better three of a kind. With seven cards known, she hit the one card in the pack (1/45) to beat me. If you consider how often that particular card would come up when I also had a better three of a kind, the odds become ridiculous, but if you play enough poker it can and will happen- I've had it happen to me. And on the turn of the next card, it's still 1/45, it's not (chances of us both having three of a kind * 1/45).

kcbrett, you've asked us to 'experiment ourselves'; well any of us who've played enough games and gambled enough _have_ experimented ourselves. People win money by gambling when they know more than the people they're playing against (whether the house, through card counting, or other players, in a game like poker). They do not make money by looking for an unlikely sequence and then betting their life savings against it happening again. In fact, gamblers throughout history have lost their life savings through exactly this method.

 

[D'Artagnan59]

I had a 96.2% chance of winning once and lost.

 

[ThePope]

I had a 96.2% chance of winning once and lost.

I had 99.8% odds and lost. And plus, 96.2% means you should lose about 4 times for every 100, so losing isn't really that big of a deal, although I agree it is frustrating to lose with high odds.

 

[Masquerouge]

I have a complete understanding of probability. That isn't the issue. Of course the odds of any individual flip are 50/50. There are only 2 possible outcomes. But this isn't a question of simple probability or statistics.

You can observe that I am right by experimenting yourself. There is nothing magical about 5 flips as some of the "weaker" arguers are suggesting. I simply picked 5 because you can actually get 5 in a row in a reasonable amount of time. If I said you had to wait until you got 50 in a row before you started recording results, well lets just say I don't think I will still be reading this message board by the time I got any responses. You can check this equally with 2 in a row or 3 in a row, you will just need to have more data points to make a significant observation. To those of you suggesting there are magical rays that affect coin flips, your comments are shortsighted, condescending, and tragically uninformed.

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.

And of course roulette favors the house. There are several reasons for this. First, the zero slots mess everything up. Second, the tables have maximum bets. I don't need to have worked at a casino (much less spent 6 years studying said casino) to figure that out. All casino games favor the house, unless you are playing against humans.

Look, this isnt rocket science. You know it intuitively, but you are struggling because the basic math disagrees with the premise. Just try it. I am not suggesting anything that isnt well known already. Just do a little research if you dont feel like flipping coins.

http://en.wikipedia.org/wiki/Independent_event

You loose.

EDIT: just for the lazy in each of us,

In probability theory, to say that two events are independent intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs. For example, the event of getting a "6" when a die is rolled and the event of getting a "6" the second time are independent.

 

[DaviddesJ]

I would have to teach you quantum physics to understand it and I have no desire to do that.

Rest assured, I know a lot more quantum physics than you, too.

 

[Gogf]

From my experience with great generals I have consistently found that just about all of the great general units die in combat so quickly. I remember one time one of my weak fodder units attacked on a 27% victory chance and won, next my warlord unit attacked with a 96% chance of victory and LOST. This happens to me all the time. Does anyone else have this problem?

You will lose about 1/20 times you attack with 96% odds. If your general is so precious that you can't risk it (perhaps it's a Medic III unit), then don't attack with it. That's the only way to guarantee it doesn't die.

 

[ombak]

http://en.wikipedia.org/wiki/Independent_event

You loose.

EDIT: just for the lazy in each of us,

I doubt that will help because kcbrett has already said that he thinks the flips are not independent (although he hasn't explained why they're not):

Of course the odds of each flip are 50/50. But the flips are not independent. And of course you can lose the 51st straight flip, its just that the odds of it happening (in a straight game) are astronomical.

I think kcbrett doesn't realize that the people he is arguing with are not talking about the odds of an entire sequence - or the odds of a sequence before you make any flip, but the odds of each flip regardless of where in the sequence it falls.

Each flip is independent btw, regardless of where it falls in a sequence, unless you are stupid enough to think that previous flips have some affect on the next ones.

Everyone here knows that the odds of one particular sequence get smaller as you add flips, but kcbrett seems to be unable to separate that from the fact that any individual flip is 50/50. To try and clear it up:

Say you flip a coin 50 times in 10 minutes while playing a game with your friends. When you flip the coin again the odds of getting heads or tails are 50/50 whether you flip it immediately after the first 50 or whether you call it a day, go to bed and wake up the next morning and flip it on your own or with another group of people present.

 

[DaviddesJ]

I think kcbrett doesn't realize that the people he is arguing with are not talking about the odds of an entire sequence

Seriously, he's just trolling. If you try to reason with him you're just playing his game. You're never going to convince him of anything. He's probably some bored 14-year-old.

 

[oneeye]

I just turn the general into that building thing.

The good old days where you could attach a general to 3 units in civ 3..... now those were useful armies.

 

[NKVD]

I played several games of civ...once i've lost 2 fight in a row...I lost the first that I was supposed to be at 99.9% of winning and the second at 98% !!! I couldnt believe it...it just happened once though so i'm ok with it...not like in civ 2

 

[jkp1187]

There is a 100% chance that I am in. Before. The. Lock.

 

[El Koeno]

Hihi, Kcbrett makes me laugh....

On-topic: It wouldn't really be fun if Great Generals were really invincible, would it? There needs to be some element of riks, and in my experience the game handles this risk correctly. However, since this forum is read by a lot of people, there is a decent chance that some people reading it experience consistent bad luck.

My only advise would be: Don't roll the dice, if you can't pay the price.

 

[kcbrett5]

http://en.wikipedia.org/wiki/Independent_event

You loose.

EDIT: just for the lazy in each of us,

I am loose now? Loose how? Honestly, am I supposed to take you seriously when you are quoting an internet encyclopedia made up of information entirely supplied by its readers and you can't figure out the difference between loose and lose?

On the bright side, I am laughing my ass off now. So keep it coming.

And just use your Great Generals for building and instructors. That way you don't place all of your eggs in one basket. You will have a lot less frustration then watching them die (which inevitably they will).

 

[kcbrett5]

Everyone here knows that the odds of one particular sequence get smaller as you add flips, but kcbrett seems to be unable to separate that from the fact that any individual flip is 50/50. To try and clear it up:

And ombak seems to be unable to read and comprehend sentences. Now I have to quote myself. How sad.

Of course the odds of any individual flip are 50/50. There are only 2 possible outcomes.

I would also say that not everyone here understands that the odds of a particular sequence get smaller as you add flips. In fact, there are many people who are arguing that the sequence is irrelevant. You may understand it, but don't assume they do.

 

[FuRRie]

Then again, the odds displayed aren't the real odds in Civ IV.
Just as a reference, I've lost several battles with 99.9% odds, just as i won a lot of battles with 0.5-1.0% odds

 

[El Koeno]

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

 

[Masquerouge]

I am loose now? Loose how? Honestly, am I supposed to take you seriously when you are quoting an internet encyclopedia made up of information entirely supplied by its readers and you can't figure out the difference between loose and lose?

Allright, English is not my first language. But if you truly believe that the 50 first flips of that coin are going to affect the 51st, then obviously the language of mathematics is not one you're familiar with either.

I do not quite see either how a spelling/grammar mistake invalidates my point. But of course, maybe in your mathematics, it does.

Note that you have yet to come up with an explanation on how, or why, the 50 first flips will affect the 51st flip in such a way that you would "risk you life savings" on predicting its outcome.

And finally, I would be delighted if, instead of saying my sources can not be trusted, you would post just one link supporting your position that after 50 flips ending on tail, the probability of the 51st landing on tail is different than 50%. Just one.

On the bright side, I am laughing my ass off now. So keep it coming.

I'm glad I made you laugh. I was trying to return the favor: after all, you're making everybody else in this thread laugh.

And just use your Great Generals for building and instructors. That way you don't place all of your eggs in one basket. You will have a lot less frustration then watching them die (which inevitably they will).

See? You can make some sense.

 

[JrK]

I would also say that not everyone here understands that the odds of a particular sequence get smaller as you add flips.

*mathematician drops in*

No no and no! There are two seperate things here that must be hold apart!

-The situation in which you're about to embark on the sequence, with the expectation that after 50 flips your chance to get the first 50 tail and the next one head.
-The situation in which you've just thrown 50 coins and they all got tails, and you're about to throw the next one.

In the first situation, you would be absolutely right that the chance to throw the 51st tail would be bigger than 50%. However, if previous coins have been thrown, you've already embarked on that path of likelyhoods. If you've thrown 50 times heads, you're already ON a probability of 0.5 ^50, so the next throw will be 50% tail or head. You can only speak of chances smaller than 50% in this case if you're talking about a sequence that has not been started yet.

EDIT: somehow the idea that previous throws have effect on the next one if you're about to throw it is just too Aristotelian.

 

[Teg_Navanis]

(...)

-The situation in which you're about to embark on the sequence, with the expectation that after 50 flips your chance to get the first 50 tail and the next one head.
(...)

In the first situation, you would be absolutely right that the chance to throw the 51st tail would be bigger than 50%. (...)

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.

Oh, and good to hear that everyone's enjoying this - I certainly am


Edit: Yay me! http://forums.civfanatics.com/showthread.php?t=172906

 

[The Great Apple]

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.