What happens if a strong chess engine plays with itself many times? If a strong engine (eg. Stockfish) plays with itself many times (say, 100 times), what will be the outcomes in terms of the following:


What will be the proportion of draws? Will there be wins/losses? If so, what could determine wins? Will it tend to be predominantly white (because of opening advantage) or just random?
Will all the games played be along a narrow repertoire? Will there be diversity in games played?
http://tests.stockfishchess.org/tests 


has information on exactly what you want. They are self-playing tests for improving the Stockfish code base.



The draw rate is roughly about 60% - 70%. There're lots of wins and losses. I believe white has more wins but it's not shown on the page.

Chess engines aren't perfect, they do make mistakes. If SF makes a bad move at move 20, the same algorithm might find the win a move later (21) because it can search deeper and further.