How to calculate the odds of a highly improbable event? I'd like to calculate the odds of a chess player A to gain 1000 Elo points in a year. Elo rating is an indicator of a player's strength at a given moment (wikipedia - elo). 
a) It doesn't matter what is the actual Elo of the player
b) The event never happened before but it's not impossible, just highly improbable
How do you tackle this kind of problem?
Assume I'm working in a finite set of players (i.e. I can consider only, and all, FIDE
rated players).
So if I have 1000 players and none of them gained 1000 Elo points in a year, maybe with
a 10k or 100k players examined we can find that one out of n players.
Note: 
The problem is more about the odds and less about chess - I intentionally set a highly improbable 
(but not, as per se, impossible) event.
 A: I believe that one of the most accurate ways to calculate that probability is by using agent based simulation.
Sketch of approach:
I assume you already have access to chess databases with a lot of games between players with various ELO ratings. For instance, you may have 100 games of 1200-1300 ELO players VS 1300-1400 ELO players where in 33 white wins, 33 draws and 34 black wins and so on. This data will be your sampling distribution/dataset.
You start by creating your agents: All chess players with their ELO ratings and you start by simulating 1 year of "championship" between them which includes the games that these guys  usually play in a normal year. For instance first game, player 30 (1245) vs player 44 (1333) simulate a result from the above dataset: draw then the new ratings are player 30 1247 and player 44 1330 so +3 for player 30 and -3 for player 44. Next game, Carlsen (player 144) vs Caruana (player 145): Draw and so on..
So you repeat the above process for N years (big number) and then you count how many times k the event occurred (how many payers got more than 1000 ELO points). You then divide that k by the number of years N times the number of players n so $k/nN$ this is your probability.
