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6 months ago ::
Nov 29, 2012 - 5:09PM
#101
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- Volunteer Community Lead
- blame me for the weather
Date Joined:
Feb 27, 2002
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I was a stats major in college and I do understand that the probability of any single coin-flip is always 50/50. I was simply pointing out that over 100 flips that it should be 50/50 heads/tails so if you know that 20 of those flips are heads then you know that statistically speaking that 50 of the remaining 80 flips should be tails so if you bet tails for the next 80 flips then statistically you should win. Now because it is 50/50 and it might take 10000 flips to even out (instead of 100), it isn't a "proven" strategy to beat the system. That and the fact that there is no skill involved. The player has no influence.
I rarely challenge people here on what they claim about their lives, but I'm calling bull. No stats major would make such a basic mistake, let alone repeat it.
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6 months ago ::
Nov 29, 2012 - 7:05PM
#102
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Yeah.....I think we can all agree here that that is just wrong.
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6 months ago ::
Nov 29, 2012 - 9:33PM
#103
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Date Joined:
Aug 17, 2007
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Well, it seems I don't do very well explaining things but this will be my last try.
It all depends on what you determine to be a good enough sample size. But if I tell you the odds of something and then tell you what I have observed after a sample size of X, you should easily be able to tell me what should (statistically) happen over the next X samples. So if I said a coin flip is 50/50 and I have flipped it 817 times and 600 times it came up heads and 217 times it came up tails, you should be able to tell me that if I flipped the coin another 817 times that it should even out (maybe not entirely flip but at least even out) with more tails than heads because after 1634 flips it should be closer to 50/50 than my 73% heads has shown. Therefore with that knowledge if I were to bet on the 2nd set of 817 flips then I should bet tails. Unless of course you don't think that 1634 is a large enough sample size for coin flipping. This only works because I know what the initial sequence was and I know what the overall (absolute) probability is.
Now we all know that in "reality" if I flipped a coin 817 times I would really have 400 ish of each type and the actual numbers I got would in likelihood fall within 1-3 standard deviations based on the number of flips.
I was just using the extreme case (as others have) to basically show that if I know a probability and I know what has come before then I can somewhat predict what will come after. Very similar to how MTG players predict the odds they will draw a land (or any card). I have drawn 6 so far and have 11 left in my deck.
And yes, the probability of any 1 coin flip is and always will be 50%, but depending on what sample size you are willing to call sufficient you can "play the odds" and predict what will happen if you know what has already happened (but only in some of the more extreme cases) and never over an individual coin flip.
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6 months ago ::
Nov 29, 2012 - 9:57PM
#104
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Date Joined:
Dec 14, 2008
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...... and never over an individual coin flip.
and thus since each individual coin flip is independent of anything prior, no predictions can be made about future coin flips outside of the 50/50 probability, regardless of what previously occurred over any sample size.
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6 months ago ::
Nov 30, 2012 - 12:22AM
#105
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Date Joined:
Mar 20, 2003
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urbanjedi, please stop posting, it hurts.
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6 months ago ::
Nov 30, 2012 - 2:48AM
#106
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urbanjedi, you a wrong, and I assume it's because of a misinterpretation of the Law of large numbers. This misinterpretation is also known as the Gambler's fallacy.
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6 months ago ::
Nov 30, 2012 - 3:40AM
#107
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Date Joined:
Nov 25, 2012
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Yeah, the coinflip example is completely wrong. If you would however change it to red cards and black cards in a normal card deck, where you actually KNOW the end result, that is a different story. Then it will obviously get more likely to draw a black card in the end, the more red card that was being drawn earlier on.
Every single coinflip is always going to be 50/50, and the probability of each flip won't change based on what has happened in the past since you don't KNOW what the results will be after your 817 flips. You can predict that it will be 50/50, but randomness might take the end result somewhere else.
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6 months ago ::
Nov 30, 2012 - 7:54AM
#108
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Date Joined:
Mar 26, 2004
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Well, the classic answer, which I already quoted to you in another context, is that the previous flips don't matter a bit (unless, of course, the coin is rigged). So it doesn't matter at all what you bet on, your chances are the same anyway.
This is most commonly talked about in discussions of lottery.
And about our arguments: I, and many others (Nushae for example), argue with your assumptions, not with your data. I feel your model is flawed, since it does not take into account important factors which influence the win/loss percentages. About the only way to resolve our argument is by experiment: change the rule, and see what happens.
That is the answer that most people with a statistical background give. The coin has no memory of previous flips, so either side is equally likely to come up on the next flip. But that answer is wrong. The naive answer of 'bet on heads' turns out to be correct. Because in the scenario described there are 3 possibilities:
1) The coin is fair, but happened to flip 9 heads in a row by chance
2) The coin has two heads, every flip will come up heads
3) The coin has a heads and a tails but is weighted in such a way that causes it to come up heads more often than tails
In scenario one it doesn't matter which side you bet on, but in scenarios two and three the correct answer is 'bet of heads'. Since betting on heads will never hurt you, and can potentially help, it is the correct answer.
Since we're fantasizing: the lottery says bet on tails. Many people will be thinking like you did above, but if the coin is random, then tails are equally likely, but less people bet on it, so your winnings are bigger. In lottery, it's very unlikey you win anyway, so if you do strike lucky, go for the psychologically unappealing numbers.
And I won't even complain that you took a well-known example where we all make hidden assumptions, and then proposed a scenario that does not include to those assumptions, since I saw that one coming. You were talking about real-life coing tossing with no additional data about the coin, I was talking about the statistical coin-toss problem.
50. Doesn't hurt. Yet.
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6 months ago ::
Nov 30, 2012 - 12:47PM
#109
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Date Joined:
Jun 15, 2009
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And I won't even complain that you took a well-known example where we all make hidden assumptions, and then proposed a scenario that does not include those assumptions, since I saw that one coming. You were talking about real-life coing tossing with no additional data about the coin, I was talking about the statistical coin-toss problem.
Perhaps that's why I find RNG discussions on here so trying, because if I flipped a coin 9 times and saw it come up heads 9 times I would jump immediately to questioning whether the coin was fair. While most other people on here would assume the coin is fair, and that they just happened to witness a 1 in 512 occurance.
And to those people I say:
"Sorry, I forgot to introduce myself. I'm Daniel D'Arby and this is my cat."
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6 months ago ::
Nov 30, 2012 - 1:06PM
#110
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Date Joined:
Jul 10, 2007
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Having been halfway observant of my tactics for a few weeks now I would say that mulliganing down to 6 usually has a better outcome than keeping a hand full of high cost mana and 1 land. 6 cradz doesn't seem to make much more difference than 7. 5 cradz seems to be a small disadvantage. I wouldn't go less than 3-4 even if it was no land. Most times if I get 1 one land good hand I take the risk because I have faith in my deck.
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