I am wondering if we assume "identical flips" when we perform a series of coin toss experiments to get the probability of either heads of tails. The way I understand "identical flips" is that it means each coin toss is done exactly in the same environments although each coin toss is not really experimented each time in the same environments(forces on the coin, angle, distance, and etc) but we just assume each coin toss is done in the same environment.
Nowadays, when we "perform" a series of coin toss experiments, then this is often an idealistic thought experiment, or an an experiment with a random number generator on a computer. We are not performing a coin flip experiment in reality.
The behaviour of the coin flip should be such that, not the environment and conditions of the coin flip, but instead the probability of the outcomes, are identical each time. So the term "identical flips" is not clear and should not be used in statistics. It should be "flips with identical probabilities for the outcomes".
It would not be difficult to create a controlled environment were a coin will be flipped in a identical way such that it lands the same everytime, e.g. heads everytime. That is not the idea of 'identical' coin flips (assuming identical refers to identical probability distribution and not identical flipping).
So if you would want to perform a coin flip experiment for real then you would need to have as much 'randomness' as possible in the flipping. But the factor that you wish to keep the same is the probability of the outcomes. Because this is difficult people have been using all sorts of tricks like using numbers/digits from logarithmic tables (which resemble random behaviour) or constructing special machines to manually generate experiments in a random way.
The typical coin flip experiment relates to identical (and also independent) distribution of the outcomes of the coin tosses. Sometimes one considers the coin tosses to be correlated, or biased (the heads and tails probabilitiea for each coin follows some distribution). So, "when we perform a series of coin toss experiments" is a bit ambiguous and not necessarily refering to identical.