Is it possible to make a brilliancy (a brilliant move) with luck? Or is it so rare that it can only be spotted by the best chess players?
Is it possible to make a brilliancy (a brilliant move) with luck?
For adventurous players I think it is not that uncommon. They often make risky moves which they haven't calculated all the way through. Sometimes they work and sometimes they don't. Tal played a lot of brilliant moves which later were found to be unsound but his opponent's couldn't find the refutation over the board. Tal was lucky.
What happens at a lower level is you see what looks like a brilliant move and play it without calculating all the way through to the end. Several moves in your opponent makes a move you hadn't anticipated or seen which seems to refute your sacrifice. You break out into a sweat. You hunker down and start thinking hard trying to find a way out. After 10 or 15 minutes you find the right move and play it. A few moves later your opponent resigns.
Your original move was a brilliancy which you didn't have the ability or patience to calculate all the way through. If you had calculated a little bit further you would have found your opponent's apparent refutation and given up. You were lucky you didn't calculate that far and then you were lucky again when there was a good reply that kept your attack going after your opponent found the tricky move.
Yes. The proof is trivial. For any chess position where a legal "brilliant"1 move exists, then by definition there are at least n >= 1 legal moves. Then even if a player randomly selects a move legal in such a position, there exists the possibility of playing a "brilliant" move.
In cases where a player is not playing random moves, the possibility still exists, though it may be with a low probability.
YouTube videos from chess Twitch streams abound with content where a lower rated player plays an incredibly strong move without knowing why it is so strong, or where a lower rated player plays a move not realizing they checkmate their opponent. Similarly, though maybe less often, strong players may play a move believing it is strong not realizing it leads to disaster.
1. The question is unclear on the definition for a "brilliant" move but the answer holds for any definition that is also a legal move.