Probability - You don't have to believe in it for it to work
I think I've finally convinced myself that probability behaves the way that people say it does, by which I mean, essentially, that the odds of flipping heads twice in a row is 1/4, but the odds of flipping heads after already flipping heads once already is 1/2. I have nursed the idea that that second flip is influenced by the first; that there is a force beyond human reckoning that will turn that second coin tails just to maintain the status quo. The problem with that logic is what I think can best be described as believing in "doncha think it's due?": the gambling pitfall that makes you put all your money on 15 black because it's been hours since it's come up and, doncha think it's due?
The reason that line of thinking is so tempting is because it makes sense in a way. If you roll the die a hundred thousand times, you're going to get all six results with a pretty even distribution, so if you find yourself in a streak of rolls with no fives, it stands to some sort of reason that five is going to HAVE to come up soon in order to keep up with the other results. The problem with that is that it assumes that even though the odds of getting a five on your next roll is 1/6, there is some sort of universal probability equality law that increases your odds. Who says that your sample of 100,000 rolls has to have an equal distribution? If I roll six times, should I expect equal distribution? What if I roll a million times? How can you possibly hope to say anything about one single roll? Is the guy rolling dice on the other side of the world "using up" all the five rolls? Probability, in theoretical terms I suppose, is based on infinite sample sizes, and so basing your assumptions on what "is due" on a finite sample seems silly, especially when you consider that it's a sample size based on the number of times a guy can roll dice in one sitting, or on what will come up next.
I don't know if I've explained myself very well, but this will at least spark a discussion amongst the people who aren't sick of this topic already, and I just wanted to put out there that I'm finally happy in thinking that the flip of the coin already finished can do nothing to influence the next flip. Hmm.
1 comment:
I cannot settle on a way to discuss probability.
In World of Warcraft I have a trinket that has a chance of activating whenever one of my spells does damage. After playing around with the trinket I found that is has about a 10% chance of activating. So if I do damage 10 times one of those times will activate the trinket.
Within the context of World of Warcraft I can explain this as the result of programming. The trinket itself is coded to only trigger about 10% of the time.
Within reality? I do not think that coins and dice are programmed to behave in a certain manner as discussing reality in terms of "programming" leads to gigantic quizibucks.
So certainly we can flip coins, tally the results, and then from those results construct a set of rules which we apply to reality. But I do not think that the rules we construct necessarily indicate some structure or programming to reality.
It has a lot to do with free will v causality. But it also has something to do with the structure of reality as we understand it. I do not think that there is some universal force or being or whatever somehow impacting coin flips in a manner which prevents 1,000 flips from coming up heads.
This conversation, when I think about it with myself, usually leads into discussings of causality and reinforcement of the fact that human beings do not have free will. But we don't have to go there.
Suffice it to say that I do not know how to discuss this without the language itself becomming problematic.
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