Patient, that does not align with probability in mathematics, at all. Probability is defined as a favorable outcome divided by the total number of outcomes. The more flips you have, the more total outcomes you have. If you stick to one "favorable" choice, the lower (or higher) the chance of that choice hitting becomes per turn, depending on the number of times it hit prior.
To put it simply, if you are flipping a coin 100 times (all things considered fair, the way it's flipped, and taking the coin weight distribution out of the equation), and it hit heads the first two times already. If you were asked to guess the total number of times it will now hit heads for the remaining flips, if you answer, "Well, 50% of the time" you'd be wrong. The variable, the equation essentially changed based on the number of flips made, and the number of times it has hit heads. At that point the likelihood of it landing heads would be 48% over time, but right at that point, the likelihood of the coin actually hitting heads a third time is 1/6, or a 16.666% chance.
If you'd like though, we can agree to disagree. Mathematic nerdgasm is fun and all, but other things are cool also, lol =)
Been a while since I've done statistics - but I think both of you are right:
So you have two sperate views of the probably: what is the probability of getting a head on a coin and its always 50% if its a truly independent toss, but the other way of looking at it is what is the probability of getting heads on the third toss GIVEN that the first two were heads. In the second statement you're giving a predictive probability i.e. if you tossed 3 coins in row rather than just looking at the probability of the the coin toss in isolation. If that makes sense.
