The answer is that the odds of each occurring are precisely same — 1 in 16,384. And, yet, to most people the first outcome is viewed far differently and is, often, seen as a matter of extraordinary skill.
To demonstrate the point, consider one of the more statistically improbable outcomes of the last 14 Super Bowl's — the team from the National Football Conference (NFC) has won the coin toss 14 straight times.
Now, the NFC team has not always called "Heads." In fact, the NFC team only gets to call the coin toss every other year. Therefore, the NFC has only had direct control of its destiny 7 times. And when it does call the flip, the NFC has been just as likely to call "heads" as "tails."
And, yet, the NFC has defied the odds by being on the winning side of the coin toss 14 consecutive times with this random outcome: HTHHTTTHHTHHTT.
My point is that this outcome is no more likely than 14 straight "heads," 14 straight "tails;" or 16,381 other permutations. The NFC's streak is, to be sure, a matter of extraordinary good fortune but it is important to remember that the odds of the NFC team winning the coin toss for a fifteenth straight time next year is only — 50%.