Streak calculation based on skill Is there a difference between how the probability of a winning/losing streak of a certain length occurring for random events vs skill based events? For example if a chess player has a 50% win rate, does he have the same probability of having a 100 game losing streak over 1000 games as a coin toss (if there were no draws in chess).

Not necessarily. A win rate of $50\%$ could have different causes.

If the probability of a win in each game is independent of the other games the answer is yes.

But if he always loses after he wins (overconfidence) and always wins after he loses (he tries harder) then he will have a $50\%$ win rate and no losing streaks at all.

If he's very streaky and always wins or loses $100$ times in a row he will surely have several long losing streaks in $1000$ games.