Is there any scenario where the results of a coin flip (or a series of coin flips) can be considered to be non-random?

No. Absolutely not when you are talking about a SINGLE event. Even if the coin said heads 5 times in a row, the chances of it being heads on the next throw are still 50-50.

I honestly don't understand your question.

When the coin is unfair.

No coinflip is random, given its 2 slices weight differently.
Otherwise, sklanskying does look sometimes so pathetic.

Is it a truly random event if the same person flips each time with the head side (or tail side) of the coin always oriented up on top of the thumb? How about if a machine flipped the coin in an identical manner each time? I get that theoretically, it is a random event. But, in reality, is it really?

If you beleive in a determenistic world then yes, it is not truly random. However, the quantum world tells us differently, and the quantum world almost definatly exists.

Sunday nights my local drinking hole has a "toss the boss" promotion. Every time you order a round of drinks the bar staff flips a coin and if you guess correctly your drinks are on the house.

Now, some pretty girls can't flip a coin same as they can't throw a ball - so they chuck the coin in the air and it doesn't rotate much. I'm pretty sure I've got a 75% success rate with this one girls coin flips, although I've not ordered 10,000 beers so it may be due to variance and not sustainable in the long run.

But nevertheless, if a coin isn't flipped properly you have a scenario where the result won't be 50/50.

Unless they are consciously trying to make one side or the other land by tossing the coin flat, then there is no way this isn't a 50/50.

Huh? Whether or not they mean to do it is irrelevant. The point is that their technique is flawed and thus the coin flipping occurs the same. Ie, it often only flips once or twice etc so it is not always 50/50

Wow it really is an old thread but I wanna ask a question:
If the coinflip is irrelevant from the past (eg if the first 100 times it is heads then on 101st it is 50-50 again) then can't we say the same about the variance on poker?
I mean that if you were for a month on a bad run, it is irrelevant what happens the next month, so it is the same probability to continue to have a bad run for the next month as much as having a good run. So there is no reason talking about variance because it is irrelevant with the past (as with the coin). Am I flawed somewhere?

edit: I saw it is closed so I will repost it in the apropriate section.