1000 is extremely conservative. Every time you play any game with an element of chance - risk, backgammon, poker, scrabble, blackjack, or even just flipping a coin - the odds against you getting the exact sequence of outcomes you do get will be astronomical. So the limiting factor on how many unbelievable outcomes you perceive in a lifetime is how good you are at recognizing patterns as "unusual". Somebody who studied numerology or had "lucky numbers" or paid attention to "lucky streaks" would see them all the time.

In the case at hand, that same series of rolls would be just as unlikely if it had happened at the beginning of the game or in the middle or spread throughout the match and hadn't determined the outcome. Unless there was something special about this particular game that made its outcome matter - perhaps it was being televised, there was a million dollars bet on it, or it was otherwise your last chance to achieve some important outcome - the main thing that makes that sequence of rolls more noteworthy than any other sequence of rolls of equivalent length is selection bias, not degree of unlikeliness.