>>12943234Why the shit with limits? You are seriously overcomplicating this. Infinitesimals and limits are only needed to explain why the probability is roughly 1/2 instead of exactly 1/2. Those operations are not needed to explain why previous outcomes of coinflips do not effect future outcomes of coinflips. Your confusing the question with another question
Imagine you are drawing a deck of 52 playing cards. You want to find the jack of hearts. When picking at random, your chance of finding the jack of hearts on your first try is 1 in 52; out of 52 possible choices, only one of them is correct. Imagine on your first attempt you draw the 2 of diamonds and then put it into a discard pile, thereby removing it from play. Because you have taken a possible loser out of the pile, the chance of picking the jack of diamonds will now be 1 in 51. Imagine you keep drawing losing cards and removing them from play. N cards removed from play will make the probability of finding your jack of hearts 1 in 52 - N. In this case, your chances WILL increase because the losing cards are slowly being removed
A coin flip on the other hand does not follow the same rules. No matter how many times you flip a coin, neither the heads nor tails are removed from probability. They are not thrown in the discard pile once they have failed to produce winning results. Throwing heads n times in a row is roughly equal to 1/2^n (where n is greater than or equal to 1). But when evaluated on a single coin flip at a time, the probability is always roughly 1/2 because both heads and tails are always in play.
