“And likewise if you’d rolled several 6s, your next several results will probably go back down to 3.5”. Err…no. The likelihood of rolling a 6 remains 1 in 6 regardless of how many 6s you’ve rolled previously.
Isn't that his point? The expected average of your next several rolls is 3.5 no matter whether you've been rolling 1s or 6s or anything in between. So if you've been doing well, you'll probably start doing worse, and if you've been doing badly, you'll probably start doing better. Makes sense to me.
Thoughtful response, thanks. I guess I’m responding to a fallacy I’ve encountered a lot: that “the Law of Averages” requires that an unusual run of one outcome (eg “heads”) will make the alternative outcome (“tails”) more likely in the future because we know that the expected frequency of each is (theoretically) 50%. Perhaps I misunderstood, but the combination of the words “if” and “probably” seemed to suggest that outcomes in future rolls were somehow conditional on past rolls. Your point that “if you’ve been doing well you’ll probably start doing worse” is exactly the “Reversion to the Mean” idea though, and I see that that could well be what he intended.
Ah yeah, the supposed law of averages would mean that after a run of 6s you'd be likely to get 1s. But he said it'd be 3.5 expected average for the next lot, which is right, not 1 for the next lot (to balance out the 6s and get to 3.5 retrospectively), which would be law of averages stuff. I think it's all fine.
“And likewise if you’d rolled several 6s, your next several results will probably go back down to 3.5”. Err…no. The likelihood of rolling a 6 remains 1 in 6 regardless of how many 6s you’ve rolled previously.
Isn't that his point? The expected average of your next several rolls is 3.5 no matter whether you've been rolling 1s or 6s or anything in between. So if you've been doing well, you'll probably start doing worse, and if you've been doing badly, you'll probably start doing better. Makes sense to me.
Thoughtful response, thanks. I guess I’m responding to a fallacy I’ve encountered a lot: that “the Law of Averages” requires that an unusual run of one outcome (eg “heads”) will make the alternative outcome (“tails”) more likely in the future because we know that the expected frequency of each is (theoretically) 50%. Perhaps I misunderstood, but the combination of the words “if” and “probably” seemed to suggest that outcomes in future rolls were somehow conditional on past rolls. Your point that “if you’ve been doing well you’ll probably start doing worse” is exactly the “Reversion to the Mean” idea though, and I see that that could well be what he intended.
Ah yeah, the supposed law of averages would mean that after a run of 6s you'd be likely to get 1s. But he said it'd be 3.5 expected average for the next lot, which is right, not 1 for the next lot (to balance out the 6s and get to 3.5 retrospectively), which would be law of averages stuff. I think it's all fine.