Hut luck

[Fleme]

I always seem to get the map. A map of the nearby ocean or tundra.

Some of my more glorious moments include finding techs such as Metal Casting from a hut, and I think I've had a few games in which I've popped three techs from the first three huts I've encountered.

But usually it's the map. Of the ocean.

[Modo44]

Originally posted by Fleme
I always seem to get the map. A map of the nearby ocean or tundra.

That still beats the map of a nearby explored area.

[Unimatrix11]

Originally posted by snoopy369


The above is of course false (it is certainly less likely for someone to hit any odds-determined probability<1 thing twice in a row as compared to once), but the wording is important.

Without knowing what has happened yet, you can accurately say that it is very unlikely for rah and someone else to hit the 1/10000000 chance; but once you know rah hit it, the chance is still 1/10000000 that you or anyone else will hit it.

Yes, thats the one perspective, but still OTOH you have to admit, that in a total number of games it is less likely to occur twice. I´d expect it to happen less. So when i hear it already happened to someone, its kinda valid to say ´damn - thats bad for me´.

[Yosho]

Originally posted by Unimatrix11


Yes, thats the one perspective, but still OTOH you have to admit, that in a total number of games it is less likely to occur twice. I´d expect it to happen less. So when i hear it already happened to someone, its kinda valid to say ´damn - thats bad for me´.

Well, not really. I mean, if I were to predict "Unimatrix will win the lottery twice in his life", that would be a lot less likely then me predicting "Unimatrix will win the lottery once in his life"; but the odds of you winning the lotto once are exactally the same no matter how often or how rarely other people win the lotto during the course of your life.

It's a very common mistake; there seems to be something in the way our minds deal with odds that makes us think that everything will just balance out somehow, but it's not actually true.

[Jonny]

8 techs?

I was ecstatic when I popped 3 techs in a game. I think that's the most that I've ever gotten. The most I remember, anyways.

[Unimatrix11]

Okay, again: If you had to place a bet, on how many times you roll a six out of six times rolling, the safest bet would be on one-time, right ? Cause it´s less likely to happen twice. And very unlikely to happen six times (1:6^6)

When you talk about a single isolated occurance, i do agree that the probabiltiy is always 1:10^8, i stated that more than once now. But it is equally true, that if you look over a certain number of instances, the view on it changes. Now we are talking the spread of probabitlities over the times of a given occurance within the number of tries:

If you roll a dice, you have 1/6 chance of hitting the six. If You roll it twice, you have 1/36 chance of hitting the six twice, but a 10/36 (1/6*5/6+5/6*1/6) chance of htting the six once (and 5/6*5/6=25/36 of hitting no six at all - the sum of all is 1 = 1/36 + 10/36 + 25/36). So hitting it once with two tries is more likely than to hit twice. Now if you roll a six, and now its my turn, i could argue, from this point of view, that my chance to hit now was reduced, because the overall chance of hitting it twice with two roles is a mere 1/36 as opposed to 10/36 of hitting it just once in two rolls - my chances, i could say from this point of view, have dropped by a magnitude of 10, by your hitting the six right before it was my turn. Or rather i should say, that this is ten times less likely to happen - cause ´my´ chances really didnt change. If you roll the dice or i do it, doesnt matter (or at least: shouldnt to my understanding). If you rolled two sixes in a row, i´d say you were lucky. Whats the difference now, if you roll a six first and i have to do the same to you having to do it twice ? As i keep saying: it´s a matter of perspective - of how you look at the problem.

Of course things ´balance out somehow´ - again think of casinos and lotteries. The people who run those, do not take a risk really, just because things do ´balance out somehow´. They know that, say, someone will hit the 1M$ once in a month maybe, but probably it wont happen twice in a month. or a year. or whatever. So after it happened once, they´d say, that that was it for this time probably. Might happen again - but its not likely. But it almost certainly wont happen 3times in a year. The light of the Luxor is living proof, that there is a valid foundation on this train of thoughts.

EDIT: To come back to the 8-tech-huts-in-a-row example, to which we all agreed, the probability is 1:100,000,000, the probability of having that luck twice in a row then is: 1:100,000,000^2. Who runs the experiment does not matter - neither does it matter, if the experiemtator changes during the experiment. When before it happened it was fine to say "that probably wont happen to me", then after it just happened it would be equally fine to say "okay, that was bad ass luck, but now i KNOW it wont happen to me (or anyone - it doesnt matter) AGAIN". In fact it would be more likely to pick the sun out of all stars in the galaxy by blind luck.

If i´d ask you to think of any person on earth, and i´d guess correctly who it was once, you´d say i was lucky. But if´d manage to do it twice in a row, you´d say i can read your thoughts - so slim is the probability of me hitting twice in a row, compared to just once, and that much of a difference it makes. Isn´t that the way, how science ´proves´things BTW ?

EDIT II: When you go hut-popping, and the first is a tech, you say "oh, nice". Then you pop the next: A tech again. You say "wow - i am lucky today". Then the next: "Gosh, thats great - never had that before..." Then the next "Unbelieveable". Then the 5th: "Today must be the luckiest day of my life" and so on... Each time it happens again, you feel more lucky then the time before - and there is a reason for that. Cause you go from 1:10 to 1:100 to 1:1000 and so on of chances of it happening in total. Yes, each time seperately still is 1:10, but hitting a 1:10 8times in a row is pretty unlikely. As is is hitting 1:100.000.000 twice in a row, or within a limited number of tries.

EDIT III: Actually as i think about it, i hold statements like "rah, didnt mess with my comp, so nothing changed for me" to be invalid. It doesnt matter how many comps are involved in the experiment. All that matters is the total number of tries. At least i never heard of any stochastic formulae, that would put the number of experimentators into the equation. Randomness cares not about ownership or name. If the question is: ´How likely is it to occur twice out of x times?´ all that matters is how likely it is to occur once and the x. Who or whose comp conducts the x-es or where the occurances actually take place does not matter in this context. If we were asking how likely it was to happen twice on rah´s computer, that would get less likely only due to the reduced x, the lower number of tries. If his comp was capable of tossing the dice a thousand times faster than any other comp, than the chances of occurance in any given time on his machine would be as high as the chances of occurance on 1000 other comps combined, obviously.

EDIT IV: Now if you had to choose wether or not to change your bet on someone popping 8-techs in a row after someone had actually done so, is almost a matter of faith. You could say that this didnt change anything, because the likelyhood of the isolated occurance is still 1:10^8 nonetheless. But You could also say that it is so much more unlikely to happen again any time soon, because its double-occurance within a certain number of tries is much less likely than its one-time occurance. The statements seem to contradict each other, yet are based on the same logic (the one that made us assess that popping 8 techs in row has a chance of 1:10^8) and thus are equally true. As i see it, you can pick either view or you can, like me, say there is no truth really, both is false and true all the same (be a nihilist about it so to say). But from instinct, i was probably less likely to place my bets on that 1:10^8 occurance to happen in the near future if it just did happen. Just as i tend to stay on the same color, playing roulette, even more-so, when the other had just come up five times in a row (if you double your bet each time you loose, you can hardly ever loose in the long run this way - but if you do, you loose a lot (all you have or the table-limit) - but it is lot more likely, that your color will eventually come up and then you win your initial betting-amount, the one before you started to double).
Look at like this: If You just popped 7 techs in a row, would you accept a 1:10 bet, that the eigth hut will also be a tech (knowing it is all random) ? I wouldnt (but i would, if it was the first hut). But i wouldnt say it was dumb to do so either.
Or like that: You and a buddy are at some carnival. There is a guy with a deck of cards and he says: "Pull a card (for a buck) - if it´s the ace of spades, you win !". Your buddy pulls a card. It´s the ace of spades. Now, would that influence your decision to try yourself (given you know the deck of cards is okay and no cheating whats-o-ever is involvied) ? I´d argue with the guy, that if my buddy won 50$ (for 52-card-deck that would be fair), i want 2500$ if i pull the ace of spades, cause the likelihood of it being drawn twice on a row is 1:52^2. If the guy said, that it doesnt matter that my buddy just pulled it, that the chances are evened out, because i am a different person, i´d ask him, how the cards know ? Of course then he could reply, that the cards do not remember either... highest chances are actually, i´d get us some beer, and we´d have a long philosophical discussion (in which i´d probably point out, that the doubt in the very existence of truth is were wisdom starts to seperate itself from knowledge, IMO) - but i wont give him a buck on a 1:50 deal, as long as 20 or so people didnt miss the AoS before its my turn.

[rah]

Damn, I was figureing that the average response would be. "you had some good luck"

But it is cool to get AH and HORSE from two consecutive huts. I thought that was special. Little did I know just how special it was going to get.

AND ONE FINAL NOTE, I haven't won this game yet, and there have been a couple of moments where it looked like I was going to get buldozed.

[DirtyMartini]

I had a sinking suspicion that when I brought statistics and probability into the discussion it was going to get messy...

Uni --

Please do not play roullette...

I roll a 100 million sided dice. The odds that I roll a 1 are 1 in 100 million (well, really the odds are pretty good this die would be close enough to a sphere to just roll around without ever really stopping, but let's not further confuse things). I roll a 1.

I hand you the die. The odds that you roll a 1 are 1 in 100 million. It doesn't matter how many other people have rolled 1's using their 100 million sided die.

The fact that it happened once does not change the odds that it will happen again. Yes, as you approach an infinite number of throws, the number 1 will have occurred 1 out of every 100 million throws, but steaks of ones can happen.

edit: Snoopy is better at math than me.

[snoopy369]

EDIT: To come back to the 8-tech-huts-in-a-row example, to which we all agreed, the probability is 1:100,000,000, the probability of having that luck twice in a row then is: 1:100,000,000^2. Who runs the experiment does not matter - neither does it matter, if the experiemtator changes during the experiment. When before it happened it was fine to say "that probably wont happen to me", then after it just happened it would be equally fine to say "okay, that was bad ass luck, but now i KNOW it wont happen to me (or anyone - it doesnt matter) AGAIN". In fact it would be more likely to pick the sun out of all stars in the galaxy by blind luck.

You're wrong, unfortunately... you're making a common error in odds calculations. There's an easy explanation for this:

ONCE YOU KNOW SOMETHING HAS OCCURRED, THE PROBABILITY OF IT HAPPENING IS 1.

So, it's 1 in 10^8 chance of happening. 1 in 10^8*1 in 10^8, or 1 in 10^16, of happening twice (in a row).

However, once it happened to rah once, the odds of it happening one of those two times is now 1 (you observed it happening, so it has happened). So, the chance of it happening twice is now (1)*(1 in 10^8) or 1 in 10^8.

[Unimatrix11]

So when the coin-tosser who told you that you win face-up, is tossing one face-down after the other you just go "well it´s always 1:1, so no problem" or would maybe suspect he´s cheating after the 50th face-down ?

EDIT: All you just did there Snoopy, was to isolate the occurance once again - you picked one of the perspectives i offered. Thats fair enough, but i´d rather call that a common mistake (when there is almost always two sides to each story), than denying oneself a look at the other perspective.

Imagine an experiment, where a true random machine would generate a number between 1 and 100,000,000. We will have i do so 100,000,000 times. Given that we all agree on the isolated occurance probabilty of popping 8 techs in a row and we shall estimate the number of all civ games ever played at 100,000,000, that would resemble our problem. Now, we have that random machine store each number at picks and then, after all attempts made, give is the number of picks of, say, ´939´. For that number to have occured, would you, at a fixed rate, rather place your bet on it having been picked once, or twice ? i think, it would be reasonable to place it on ´once´, at least from this perspective it seems so.

But if you did that, before the experiment started, and now, at, say, about half the time the random machine needs to pick all that numbers, by some error, the ´939´ flashes on your screen, then... well what then ? I just pondered this. You could say, that it is more likely to occur twice now, for it wont be zero at least - it seems much more likely to occur twice now, than it appeared before you knew it hit already once. But on the other hand, you could say, that it is the 1 that was ´supposed´ to happen anyways. It just happened to happen in the first half of the experiment. If it is likely to happen, it has to happen somewhen, and why not in the first half ? How does it change the second half ?

Coming back to the example at hand, we now have to place our bets on ´twice´ (or more), since we know rah already popped 8 techs in a row. Even from the former perspective, it still sucks, cause the next 939 has to occur within a smaller amount of picks, while we are still picking from 100,000,000. In the later perspective, it´s a true downer, because, as you might say ´fate chose someone else to be the lucky one already´ or something to that effect...

[Yosho]

Originally posted by Unimatrix11
EDIT: All you just did there Snoopy, was to isolate the occurance once again - you picked one of the perspectives i offered. Thats fair enough, but i´d rather call that a common mistake (when there is almost always two sides to each story), than denying oneself a look at the other perspective.

The thing is, it's not that he's isolating it, it's that it IS isolated.

The fact is, past occurences of this kind of randomness are completly useless in predicting what WILL happen in the future. So, in other words, if you flip a coin twice and get heads both time, you might want to think "Well, if I flip it again, it's got to come up tails, right?" But that's just not true; you can not predict the odds of future events happening based on that, nor do past events change the odds of future events happening.

The same applies here. You gut instint is to think that someone else getting really lucky means it's less likely you'll get really lucky, but that's just not true.

[Unimatrix11]

Yosho, with a lot of effort, i could proof, tho, that the experiment of flipping the coin, if conducted often enough, will result in a bell-curve. What is less likely to happen, will happen less often. It doesnt matter, weather i know about the experiment or not, neither does it matter if some of it was conducted in the past and some will in the future. When i do the flip-the-coin-3-times-experiemt, say, a thousand times, then the result will be very close to the matrix that can be calculated in the primitive fashion i exercised with the dice a couple of posts before. Three times up would occur pretty exactly 62.5 times in a thousand goes. If after 500 goes it already came up 50 times, which is very unlikely by itself.... well maybe there is somekind of mistake here... maybe its not valid to ´split´ an experiment of this kind - i dunno... but at least from the start they are no BS that i pull out of my a**, they have scientific foundation and history. So i am kind of startled that instead of a good discussion, all i get is the same fact again and again, as if i was trying to sell some esotheric idea here... What i am trying to do is to point out the dualty between the mass-experiment as descripted above and the fact that the chances for the single occurance is always the same. You keep repeating the later part, but dont seem to take the former serious at all.

[DirtyMartini]

Originally posted by Unimatrix11
. You keep repeating the later part, but dont seem to take the former serious at all.

Seriously...don't play roulette.

Yes, as you go to an infinite number of trials, the number of occurences of an event will approach their expected distribution. For example, in thousands of trials of flipping 6 coins, yes, the number of 3:3 will be higher than the number of 0:6.

This has absolutely no bearing on an individual trial. You may be keeping track. Your bell curve may look all goofy. It may seem like the universe should start to correct this imbalance. You've just thrown 6 heads, 3 times in a row. It doesn't matter. The new trial is independent with respect to the odds of throwing 6 heads or 6 tails or whatever.

[Unimatrix11]

I agree, DM. I just find the link (´has absolutely no bearing´) odd (note: i didnt say ´wrong´). Arent the two facts that you stated somehow contradictionary by logic (i am asking this really)? I do agree both are equally true, what i am pondering here all the time is: how can that be ?

The infinite number of tries is made up of individual tries after all. So if a certain outcome can be expected from the infinite number, how can it be, that we cant deduce anything for the chances of the individual try this way, even if we already know the outcome for infinity-1. I am well aware that if i roll a dice 6 times, you might well not get all the numbers once, but if i keep rolling it, then they will eventually all come up equally often. Of course in between there will be streaks of a certain number occuring (or not occuring) but then again, i know that the system as whole will approach the gaussian bell-curve. This is the ´balancing out´ and it does happen. But when and how, if the individual chances are unchanged (again: even an infinite number is made up from individual ones) ? It seems more likely to me, that the curve for the experiment at hand will alter its shape towards the ´ideal´ rather than moving away from it. But still all that doesnt tell me anything about whats going to come up next - the chances are unaltered. I find that wierd.

You know, in my mind it looks a bit like your avatar, DM. I know both ideas as scientific facts, but there is a big question mark between them.

EDIT: Coming back to the tech-popping once more. If i tried often enough, i could actually deduce from the bell-curve, the 1:100,000,000 as the real chances of the individual try , with increasing certainity the more tries i run (that would take an awful lot of tries tho, to even reach only a minimum of certainty).

The Roulette-remarks are unnessecary BTW, i am no gambler, and the one time i did play roulette, i did well enough to pay for my drinks, and also saw ´odd´ things happen, like a 2-2-4-2 series, when i had a chip on the 3.

Edit II: According to the perspective, that nothing changes, there is no mistakes to make in Roulette anyways.

[snoopy369]

Uni... you don't understand basic statistics. You are, still, making the basic mistake of statistics, e.g. treating an occurence that has already occurred as being treated by the laws of statistics. It's not.

Chance does not describe the distribution of what has already occurred. Chance describes the distribution of what may occur in the future. The "bell curve", or normal distribution curve, describes only what the chance of something occurring is; and over (very, very long) time, it can be expected that random occurrences may fall in this pattern, but only before the random tosses occur. If you have 100 three-heads in a 500 sample, in your example above, at that point your likely result is 163 (162.5 round up) because it's still 0.125 chance that three heads occurs, or 62.5 in 500. (Your odds are off by half... 1/2*1/2*1/2 is 1/8, or .125)

It does not, however, describe what already has happened. Much of the grunt work of statistics is reconciling 'already happened' with 'what would have been expected to have happened'. You're perfectly right to have said, "Prior to rah hitting 8 techs, the odds of two folks hitting 8 techs is absurdly low". However, once he hit it, that no longer applies; it's 1/10^8 of it happening again, period, and it could easily happen today. It probably won't - but it could, and the 'bell curve' would not have any effect on that. The slot machine that pays out the big jackpot has just as much a chance of paying out again on the next pull as it did of paying out on the pull it paid out on - assuming they're not rigged, anyhow, which they shouldn't be by law; the folks who go to slot machines that didn't pay out for a long time are fooling themselves, it doesn't help a whit (again assuming nothing is rigged).

If every post is starting to sound the same, it's because they're, well, accurate... this is a pretty common theme in basic statistics class, and not really up for debate any more than "1+1=2" is. We're trying to teach you the error of your ways, and you're arguing with basic statistics; you must forgive us if we get a bit impatient with your arguments that are well-known to be false.