What makes WHM special? Nothing anymore.

[winsock]

This is the case each flip is its own separate event, previous or subsequent flips do not effect outcomes. When you flip the coin once, you have a 50/50 chance of getting heads. The next flip is also a 50/50 chance of getting heads, weather you had heads before or not.

The previous flips to not impact subsequent outcomes. This is true. But you're looking at the chance of something occurring within a certain number of attempts
To simplify, let's say AST flips coins. For an encounter, you only have time to flip your coin 3 times. Your possible flips for the encounter are:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT

There is an equal chance for any of the above combinations to be the combination you get during the run. "TTT" has the same chance of appearing as "HTH" or "THT" or "HHH". However, there are 7 outcomes that would allow you to get at least 1 H during the encounter. 7/8 outcomes means you have a 87.5% chance of getting at least 1 H over the course of 3 flips.