cyberpainter wrote:
Yeah, however you say the odds are "low", but I don't delve deep enough to understand what that means. Seems like the odds would go down to get all heads repeatedly over time because as each is 50/50, you have 50% chance each time of breaking the streak.
Yes, the odds of getting 6 heads in a row are half of the odds of getting 5 heads in a row and so on.
cyberpainter wrote:
Also, since over time you'd probably break even, it feels like there should be some other kind of statistical factors in play (that are like some kind of magic hocus pocus to the likes of me).
Here's where the essential misunderstanding for most people comes in. Of course, taken from point 0 (before the first flip) you can say that the single most likely scenario is that, 10 flips from now, you will find yourself with a distribution of 5 heads and 5 tails.
But let's assume that you've already flipped 4 straight heads and you're now at point 4, with six flips remaining. Would you then expect that over time, starting from this point on, the most likely scenario will be with you ending (after 10 flips, 100 flips, whatever) at an even distribution of heads and tails for the set taken as a whole (from point 0 until the end)? The answer to this is a resounding "no"...since you already have four heads "in the bag", the odds calculated at point 4 are that, once you have finished flipping, you are more likely to have more heads than tails. There is no "mean reversion" here because each flip is independent of those that came before it.
No hocus pocus here!
Interesting, thanks wracket. But even though each flip is independent, can't you look at odds over a longer span? Let's say you did 100 flips. The first 4 were even. You've already "beaten" the odds. But I thought maybe the odds would get greater as time went on, that it would indeed get close to 50 odd and 50 even. I'm thinking there might be some magic number that would bring the odds back to 50/50?