The Law of Averages - Page 2
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MoonBear
Straight outta Johto18973 Posts
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Lemonwalrus
United States5465 Posts
I learned that from a blog once. | ||
EsX_Raptor
United States2801 Posts
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obesechicken13
United States10467 Posts
On May 21 2011 07:59 Lemonwalrus wrote: Remake the blog, the more you try, the more likely you are to get it right sooner or later. I learned that from a blog once. Eh, you guys figured out what I was saying eventually. On May 21 2011 10:24 EsX_Raptor wrote: Do you understand that there is a probability that you will never roll a 6 after an infinite amount of casts? No there isn't ![]() | ||
Sleight
2471 Posts
Two dice, any chance of getting one single 6 is the same as rolling one die twice to get a six. 6 * 6 = 36 Outcomes Winning outcomes = [6 X] and [X 6] with [6 6] only counting once, obviously, so 11 wins. 11 / 36 = .306 You guys need to do better math. Rolling more dice DOES increase the probability of a success. Taking more chances increases the likelihood of a success as a strategy. EDIT for clarification: No single roll EVER has a higher likelihood than 1/6, but you can only examine probability on the large scale. We are looking at combinations of chances, which mean that if you roll 1000 dice, your likelihood of getting a 6 is basically 1, but that says nothing of whether its the first roll or the last roll. Probability theory ONLY applies to SETS. | ||
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Empyrean
16950 Posts
On May 21 2011 10:24 EsX_Raptor wrote: Do you understand that there is a probability that you will never roll a 6 after an infinite amount of casts? The probability is zero, because you will almost surely roll a 6 in an infinite amount of casts. The amount of statistical ignorance in the general population is staggering ![]() EDIT: Before someone replies, just because an event occurs with probability zero doesn't mean it can't occur. And I'm using the term "almost surely" in its technical meaning, in case there were any doubts. | ||
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MoonBear
Straight outta Johto18973 Posts
On May 21 2011 11:21 Sleight wrote: Guys, you really don't understand probability theory. Two dice, any chance of getting one single 6 is the same as rolling one die twice to get a six. 6 * 6 = 36 Outcomes Winning outcomes = [6 X] and [X 6] with [6 6] only counting once, obviously, so 11 wins. 11 / 36 = .306 You guys need to do better math. Rolling more dice DOES increase the probability of a success. Taking more chances increases the likelihood of a success as a strategy. EDIT for clarification: No single roll EVER has a higher likelihood than 1/6, but you can only examine probability on the large scale. We are looking at combinations of chances, which mean that if you roll 1000 dice, your likelihood of getting a 6 is basically 1, but that says nothing of whether its the first roll or the last roll. Probability theory ONLY applies to SETS. I'm not sure what point you are trying to make with your first example of rolling two dice concurrently. But if you are saying that the chance getting a 6 when rolling two dice at the same time is different from the probability of obtaining a 6 when rolling a single die is different then the result is a given. In that instance you are comparing a joint probability distribution to a single variable probability distribution so the results will be skewed as a result. You are misunderstanding the point that Infinity was making. There is nothing wrong with observing probability on a small scale. Statisticians do this all the time. The "Law of Large Numbers" (I do detest the name but no matter) is a statement that a very large number of observations will tend to reflect the underlying probability of the random variable in question. On this instance, I believe we are all in agreement. If you flip a fair coin an infinite number of times, your observations will tend to a 50:50 split. However, you are confusing this with the applications and caveats that come with independence and random sampling. The OP is not making a statement about deducing conclusion from an extremely large sample space. Instead, it is a case of repeated trials and commenting on the results of each observation. In this case, it is a conditional probability function. For example, one example was continuing to hit on women at a party until you achieve success. It would be incorrect to state that we are making observations on a large scale. Instead, you are taking repeated samples from a state space and then commenting on each observation one at a time. The fallacy in his article was "Given that I have made advances on a woman and failed, I expect to have a success because the law of averages should even things out eventually." This is incorrect because independence between events means that the conditional probability of success given failure is still the same as the probability of success in a single event. I would recommend you read the link that Infinity posted and not make claims such as "You don't understand probability theory". | ||
Sleight
2471 Posts
Notice how I explicitly say your single instance probably NEVER CHANGES? Did you read my post before saying the same thing in a different way and trying to sound contradictory? I said nothing about the OP's correctness in regards to his Gambler's Fallacy. I spoke only to the event that increased trials increases chance of success. He is right, statistically you will eventually hit it home, but he is wrong in that it is some magical self-correction. It's just probability, nothing more, nothing less. Like I said and you said and other informed people have said. | ||
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MoonBear
Straight outta Johto18973 Posts
On May 21 2011 12:25 Sleight wrote: I pointed out exactly how the Gambler's fallacy doesn't account for reality, friend. I also said probability only works on SETS as my last statement. Two instances is a set, even if its largely useless. Two hundred instances and we begin to find relevant information to inform a decision, typically. Notice how I explicitly say your single instance probably NEVER CHANGES? Did you read my post before saying the same thing in a different way and trying to sound contradictory? I said nothing about the OP's correctness in regards to his Gambler's Fallacy. I spoke only to the event that increased trials increases chance of success. He is right, statistically you will eventually hit it home, but he is wrong in that it is some magical self-correction. It's just probability, nothing more, nothing less. Like I said and you said and other informed people have said. There are two disagreements with your argument I have. The first is "Rolling more dice DOES increase the probability of a success." If we consider rolling die to be a Bernoulli or Binomial process, then each roll has the same probability. The probability of success on each roll hasn't changed. Increased trials does not "increase the chance of success" as you say. It simply reduces the effect of randomness and chance from your samples in the long run. What repeated samples means is that the distribution of your sample results will converge to the underlying distribution. The second disagreement is that "you can only examine probability on the large scale". You can model any event regardless of how large your sample size is. | ||
Sleight
2471 Posts
Again, for the record. Increasing trials DOES NOT increase the probability of ANY SINGLE INSTANCE. Got it? I've said that each and every post. Rolling a die 10k times does not increase the chance of getting a 6 on any given trial. You are wrong to say that the probability of getting a 6 rolling a dice once is the same as rolling a dice 10k times. Dead wrong. Which is what I have said over and over. You are COMPLETELY WRONG if defining this as a Bernoulli process formally changes ANYTHING from what I've said. Let's define our process as such. If a die rolls a non-6, we score it a 0. If the die is a 6 it is a 1, p = 1/6. Let's run a trial on that for one time. We will say P(1) = (1 choose 1)*.16^1*.84*0 = .16. The chance of getting a 6 in 1 roll. We will ask what are the chances of getting at least 1 6 in 2 trials. P(1)=(2 choose 1)*.16^1*.84^1 = .268. Does this account for all outcomes? NO! We still need to consider 2 successes. P(2)=(2 choose2)*.16^2*.84^1 = .022 P of at least 1 success = .268+.022 = .29 (i rounded .166 to .16, so its marginally lower). You are unequivocally wrong that changing the model somehow stops more trials from increasing chance of success. | ||
obesechicken13
United States10467 Posts
On May 21 2011 12:15 MoonBear wrote: I'm not sure what point you are trying to make with your first example of rolling two dice concurrently. But if you are saying that the chance getting a 6 when rolling two dice at the same time is different from the probability of obtaining a 6 when rolling a single die is different then the result is a given. In that instance you are comparing a joint probability distribution to a single variable probability distribution so the results will be skewed as a result. You are misunderstanding the point that Infinity was making. There is nothing wrong with observing probability on a small scale. Statisticians do this all the time. The "Law of Large Numbers" (I do detest the name but no matter) is a statement that a very large number of observations will tend to reflect the underlying probability of the random variable in question. On this instance, I believe we are all in agreement. If you flip a fair coin an infinite number of times, your observations will tend to a 50:50 split. However, you are confusing this with the applications and caveats that come with independence and random sampling. The OP is not making a statement about deducing conclusion from an extremely large sample space. Instead, it is a case of repeated trials and commenting on the results of each observation. In this case, it is a conditional probability function. For example, one example was continuing to hit on women at a party until you achieve success. It would be incorrect to state that we are making observations on a large scale. Instead, you are taking repeated samples from a state space and then commenting on each observation one at a time. Hmmm... ok... ok The fallacy in his article was "Given that I have made advances on a woman and failed, I expect to have a success because the law of averages should even things out eventually." This is incorrect because independence between events means that the conditional probability of success given failure is still the same as the probability of success in a single event. I would recommend you read the link that Infinity posted and not make claims such as "You don't understand probability theory". Hey I never said that! + Show Spoiler + ;_; Even if it is true And I quote The law of averages is actually not a law at all. It's a truism that has no truth stating that when you've flipped a coin and gotten heads three times in a row, well then tails is more likely to turn up on your next flip. I just think that "The Law of Large Numbers" is a horrible title. My intention wasn't to say that I would have a greater chance of success on my next attempt, I was saying that if I got turned down 20 times, and then approached 50 more women, I would have a higher chance of success with at least one of those 50 women than if I felt discouraged and only approached two women. I'm trying to say don't give up. I understand "independece between events" or whatever | ||
Cambium
United States16368 Posts
<3 TL | ||
infinity21
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Canada6683 Posts
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Empyrean
16950 Posts
On May 21 2011 14:44 infinity21 wrote: You guys are literally arguing over the difference between 'chances of success' and 'chances of a success' lol It's not worth trying. ![]() | ||
xxpack09
United States2160 Posts
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Empyrean
16950 Posts
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Mactator
109 Posts
On May 21 2011 13:30 obesechicken13 wrote: Hmmm... ok... ok Hey I never said that! + Show Spoiler + ;_; Even if it is true And I quote My intention wasn't to say that I would have a greater chance of success on my next attempt, I was saying that if I got turned down 20 times, and then approached 50 more women, I would have a higher chance of success with at least one of those 50 women than if I felt discouraged and only approached two women. I'm trying to say don't give up. I understand "independece between events" or whatever Oh I wish you were right and that success in life was proportional to the number of times you try. The problem though is that if you fuck up badly then the probability to succeed next time you try will decrease. Or the other way around. Real life events usually aren't independent and you can fail if you behave stupidly :-). EDIT: One may say that this is true for sc2 as well. Trying a lot is a good thing but if you don't analyze your games, optimize your build orders and create new ones well.. then there is a chance that you aren't improving or perhaps even get bad habits. | ||
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