I have always *hated* statistics and probability, and here is an example of why:
I have a coin. I flip it 9 times, and I get heads 9 times in a row. According to the probability of independent events, the 10th flip has a 50% chance of being heads again, because previous events don’t affect it whatsoever. According to the law of large numbers or whatever, it’s supposed to big-picture even out to 50% over time, so it *should* be more likely I get a tails; if it *didn’t* even out after a million flips it’d be a freakish statistical anomaly, or the coin is weighted and it’s not the 50/50 chance we think it is.
So, small-scale, I have a 50% chance of getting heads again. Big scale, it’s supposed to start leaning toward tails the more heads I get. The previous events don’t matter, and the previous events do matter; opposite statements which are both true.
And that just makes my brain want to crumple up and die. ><
I suppose you could say the previous flips are independent, and the trend over time is for it to even out, and although the results lead to the trend, the trend will never lead to the results. Somehow, math breaks free, math…finds a way.
Nevertheless, in math 2+2=4. There’s no “2+2=4 usually, except sometimes it’s not, because it just didn’t work out that way.” I am *trying* to impose order on the universe, and the universe doesn’t seem to want to comply.
I “love” probabilities and statistics.
Assuming our first 10 flips resulted in heads, our next 10 flips “should” still result in 5 heads and 5 tails. This results in a total of 15 heads and 5 tails and a ratio between the two of 75%/25% after 20 flips. Again, assuming our first 10 flips resulted in heads, our next 100 flips “should” result in 50 heads and 50 tails. This results in a total of 60 heads and 50 tails and a ratio between the two of 54.5%/45.5% after 110 flips.
Expected total
First 10 after 10 more after 100 after 1,000,000
flips flips additional more
Heads 10 15 60 500,010
Tails 0 5 50 500,000
%H/%T 100/0 75/25 54.5/45.5 50.0005/49.9995
Statistically, once we flip 10 heads in a row, we cannot expect to “get them back”. The universe simply continues as it should and drowns the imbalance.
that “drowns the imbalance” is sort of what i meant when i referred to math “finding a way.” i still don’t have to like it :P