On its face, the simple fact that you have a 75% chance of not flipping a coin heads twice in a row is cognitively at odds with the fact that you have a 50% cha

On its face, the simple fact that you have a 75% chance of not flipping a coin heads twice in a row is cognitively at odds with the fact that you have a 50% chance of doing it on the second flip... if you know you flipped heads the first time. If you didn't have the knowledge of what the first flip was, your known odds on the second flip completing two heads would still be 25%. Which seems to intuitively imply that prior knowledge is valuable.