5% chance of being poisoned? I don't think so!

[Tauren]

All you need are a few lessons in statistics

Assuming this is aimed at me: Yes I probably do need some lessons, but it still sounds like rubbish to me

 

I'm taking a screenshot of this thread.

Should I also take a screenie of your clown friend there?

[DarElik]

Yes but with many experiments repeated continuously, the overall amount of times a poisoning occurs should be around 5%.

Not necessarily. Some could be a bit more unlucky than others and hit that 5% each time for 30 toads in a row out of 100. The guy sitting next to him could hit it once out of 100. First guy's result: 30% of eaten toads poisoned him. Second guy: 1%. But... Still only a 5% chance of being poisoned per toadstool.

[peino]

 

Just because there are 2 possible events does not mean the odds of being poisoned in the end are 50/50, 50%, 1/2, etc. There is some truth in this, but it is not the correct way to express it.

"There is a 50/50 chance of me being poisoned on the next toad I eat, yet the chance of being poisoned is 5%"

Six of one, half a dozen of the other. Say it whatever way you prefer.

 

May I add once again... wtf

Maybe it's because you're thinking about it in a mathematical way. Try thinking about it in a philosophical way. Remember that odds are one thing, actuality is another. Odds are always predictive and therefore never 100% certain, so regardless of how confident one is in one's odds, one would be foolish to act on them without waiting to see what the actuality turns out to be. One would be reckless to eat lots and lots of toads all at once by fast clicking without looking to see if one is getting poisoned, because one expects based on odds that one will only get poisoned once out of the batch. It's the same thing as saying one would be foolish to place a bet on a horse, and then go and rack up debts in anticipation of the money, without waiting for the horse to finish running the race, no matter how good the odds on that horse were.

 

Predictions contradict probabilities, this is still insufficient to assume the next outcome is going to be one or the other with a 50% chance.

Ah, but that contradicts your own statement, i.e.: "There is a 50/50 chance of me being poisoned on the next toad I eat, yet the chance of being poisoned is 5%" Again, try looking at it philosophically.

 

Also, I have to admit that my statement is only partially applicable to EL probablities and predictions, because the 5% is not...how do I want to say this?...a natural probability. It is an imposed probability, deliberately chosen. If this were RL, and we were discussing toadstool eating, the 5% chance of being poisoned would be a predictive calculation based on observations of the past. We use the past to predict what will happen in the future, and base our choices on those predictions, but there are many ways those predictions can be wrong because so many factors affect what happens, and our data about the past may not be complete. That cannot be said of EL toadstools. The 5% is not a statistical estimate based on what has usually happened before. It is a set standard upon which we can rely. We know that there is no time when the likelihood of poisoning will not be 5% (unless Entropy changes it on purpose). But that still does not change the fact that, at the moment you are about to click on a toadstool, you cannot know whether it will be the one to poison you or not.

 

I guess what I'm saying is, basically, that because of the built-in randomness of toad poisonings, a player might decide that 5% is a reasonable risk to take, but should still take care to watch for those little green droplets. I said before that I'm a toad-eater, and I only have 90 hp. Right now, it is too expensive for me to keep a constant stock of antidotes. So I can't afford to let poisonings stack up on me. So even though I've had many days where I've eaten 100+ toads without one poisoning, I still watch for the green drop on every single toad I click, so I can switch to fruit until it wears off.

[ville-v]

Lol, the point is that when it comes down to individual cases at the moment of decision, the odds come down to 50/50. The horse you bet on either will win or it won't. The toad you clicked on either will poison you or it won't. The chances, odds, rates of occurrence, whatever you call them, is just how we hedge our bets, what we base our decisions on ahead of the fact (since you're not allowed to bet on yesterday's horse race). A 5% rate of poisoning ensures that toads will be safe often enough to be useful. But the random number generator ensures that the uncertainty remains for each individual toad you click. 50/50 -- poisonous or not.

Just because there are 2 possible events does not mean the odds of being poisoned in the end are 50/50, 50%, 1/2, etc. There is some truth in this, but it is not the correct way to express it.

"There is a 50/50 chance of me being poisoned on the next toad I eat, yet the chance of being poisoned is 5%"

To be exact, the chance of being poisoned is varying.

 

Since one either gets poisoned or not, the chance is either 100% or 0% per toadstool.

 

Not 50%.

[Hex]

MUAHAHAHA! Our plan to have players discussing ridiculous topics in forums instead of leveling is working!

[BlackFalcon]

Hex ownz y0

[peino]

Hex wins thread.

[Usl]

Hex wins hands down the match!

 

But, for the more mathematically-oriented, there is some confusion here between descriptive statistics and inferential statistics.

 

Let X_i be the outcome of eating the i-th toadstool (e.g., 0=good, 1=poison), and let us assume each toadstool has the same average mu and finite variance, and that all outcomes are independent (i.e., the random number generator does not "remember" whether you have been poisoned recently or not - in other words, there are no counters), then we can rest assured that, for any epsilon,

 

lim_{n->infinity} P( | avg(X_n)-mu | < epsilon ) = 1

 

which is to say, the average mu will be sufficiently (= up to epsilon) close to the actual average of the population avg(X_n), given enough (n) samples. You think you get poisoned more often than 5%? Eat more toadstool, and your average will in the end get closer to 5%. This is often termed "the weak law of large numbers", although I'm not sure if this is the name used in English.

We could even compute how many toads are enough for a given level of approximation (e.g., which n gives a probability of 90% that the actual average is between 4% and 6%), if Ent had given out his distribution function for the random generator -- which he will probably never produce (also because there is an ergodic source in there, given by players' activity, which is not easily described by analitic functions).

 

Ok, enough ranting for a single day: now go and enjoy the thrill of the game! 8)

Edited December 28, 2007 by Usl

[Tauren]

Yes but with many experiments repeated continuously, the overall amount of times a poisoning occurs should be around 5%.

Not necessarily. Some could be a bit more unlucky than others and hit that 5% each time for 30 toads in a row out of 100. The guy sitting next to him could hit it once out of 100. First guy's result: 30% of eaten toads poisoned him. Second guy: 1%. But... Still only a 5% chance of being poisoned per toadstool.

Yes these 2 guys' luck of toad poisonings are seperate experiments that are in the end combined...

Also refer to -

Eat more toadstool, and your average will in the end get closer to 5%. This is often termed "the weak law of large numbers", although I'm not sure if this is the name used in English.

 

 

 

 

 

Just because there are 2 possible events does not mean the odds of being poisoned in the end are 50/50, 50%, 1/2, etc. There is some truth in this, but it is not the correct way to express it.

"There is a 50/50 chance of me being poisoned on the next toad I eat, yet the chance of being poisoned is 5%"

Six of one, half a dozen of the other. Say it whatever way you prefer.

 

May I add once again... wtf

Maybe it's because you're thinking about it in a mathematical way. Try thinking about it in a philosophical way. Remember that odds are one thing, actuality is another. Odds are always predictive and therefore never 100% certain, so regardless of how confident one is in one's odds, one would be foolish to act on them without waiting to see what the actuality turns out to be. One would be reckless to eat lots and lots of toads all at once by fast clicking without looking to see if one is getting poisoned, because one expects based on odds that one will only get poisoned once out of the batch. It's the same thing as saying one would be foolish to place a bet on a horse, and then go and rack up debts in anticipation of the money, without waiting for the horse to finish running the race, no matter how good the odds on that horse were.

 

Predictions contradict probabilities, this is still insufficient to assume the next outcome is going to be one or the other with a 50% chance.

Ah, but that contradicts your own statement, i.e.: "There is a 50/50 chance of me being poisoned on the next toad I eat, yet the chance of being poisoned is 5%" Again, try looking at it philosophically.

 

Also, I have to admit that my statement is only partially applicable to EL probablities and predictions, because the 5% is not...how do I want to say this?...a natural probability. It is an imposed probability, deliberately chosen. If this were RL, and we were discussing toadstool eating, the 5% chance of being poisoned would be a predictive calculation based on observations of the past. We use the past to predict what will happen in the future, and base our choices on those predictions, but there are many ways those predictions can be wrong because so many factors affect what happens, and our data about the past may not be complete. That cannot be said of EL toadstools. The 5% is not a statistical estimate based on what has usually happened before. It is a set standard upon which we can rely. We know that there is no time when the likelihood of poisoning will not be 5% (unless Entropy changes it on purpose). But that still does not change the fact that, at the moment you are about to click on a toadstool, you cannot know whether it will be the one to poison you or not.

 

I guess what I'm saying is, basically, that because of the built-in randomness of toad poisonings, a player might decide that 5% is a reasonable risk to take, but should still take care to watch for those little green droplets. I said before that I'm a toad-eater, and I only have 90 hp. Right now, it is too expensive for me to keep a constant stock of antidotes. So I can't afford to let poisonings stack up on me. So even though I've had many days where I've eaten 100+ toads without one poisoning, I still watch for the green drop on every single toad I click, so I can switch to fruit until it wears off.

Aha! No wonder why everyone had approached this differently to me

Thanks for explaining this clearly.

 

 

lim_{n->infinity} P( | avg(X_n)-mu | < epsilon ) = 1

ftw