What is the probability that a position has been played before?

When reading annotated games from GMs, I sometimes find annotations such as "This was tried by XXX in 1975 vs YYY". Such annotations are sometimes found very deeply in the game, sometimes past move 20.

Depending on the move number, what is the probability that my position has been previously played by someone, somewhere?

• Opening theory consists mostly of "positions that have been played before", so it depends on how theoretical your opening repertoire is. Commented Sep 13, 2015 at 9:06
• I do not know how many positions are possible. The possibility that a position comes up is 1 over this amount (if you look at it in a statistical way). The position after 1. e4 is however 5% and in if you look at all the games ever played it will be even more. Commented Sep 13, 2015 at 12:35
• the answer to your question is entirely dependent on you chess ability, opening knowledgeopenings you play,style, etc. It would be nice if you added this on, though this question seems though to answer. Commented Sep 13, 2015 at 16:56
• In the other direction, many endgame positions have occurred numerous times, often reached by very different routes. Commented Jan 17, 2016 at 5:18
• Fascinating question, because simple to ask, hard to answer. The number of positions is known exactly for up to white's 6th move, oeis.org/A083276. And you could approximate beyond that. The harder question is "how many positions have ever been played by anyone anywhere ever?". Given that we're already at move 6 well beyond the total number of people who have ever lived, prb.org/howmanypeoplehaveeverlivedonearth, ... Commented Oct 4, 2019 at 20:11

I think you cannot accurately calculate the probability a given position has been previously played by someone, somewhere. But you can make a rough estimation with a big game database.

To calculate this probability you need a really big database -I'd say it should contain some million games-. And you should have a good representation of games played by players of different levels and historical periods. Then using a database manager (like Scid), and search how many games in your database contain that position. Dividing the number of games containing the position by the total number of games, you have a rough estimation of the probability it has been previously played.

This is a rough estimation because low-level players are not very well represented in the databases, because there is less information of games played in the past and because non-annotated games (blitz, friendly games) do not appear in the database.

You can't calculate a percentage. But there are some interesting points to make on that topic.

1) The possibility of a position being played before goes down the more moves you make (obviously)

2) However, positions in openings with more book moves (ex. Ruy Lopez and Sicilian) come up more.

3) If an opening was played long ago but with a terrible loss, you might be surprised how few games there are with that opening.

How much of the legal position space has been explored by humans or machines would be the question to ask first, or one would need to specify in which probability space you are asking your question.

With opening theory repertoires aficionados, there is the question of how well distributed have past games been in terms of positions explored.

So I you are asking about some non temporal context and forgetting about historical biases, would be different than using the current distribution over position space of all databases.

Not an answer. Maybe it should be a comment.