7-piece Syzygy tablebases are complete

For some math fun! It seems to me like the extreme upper end of possible positions would be: (64 choose 5) * (10^5) * (59 choose 2) * (2!). Logic:

(64 choose 7) - The number of distinct 7 square selections on the board. This is where our pieces go.

(10^5) - For each piece there are a maximum number of 10 possible choices (queen/rook/pawn/knight/bishop of black or white)

(59 choose 2) - There are 59 remaining squares, we need to pick 2 for the kings to be on.

(2!) - The combinations pieces of the two squares for the kings - obviously just two.

This is mathematically equivalent to (64 choose 7) * (10^5) * (7 choose 2) * (2!) for those that might find that method of counting more intuitive.

This seems to give an extreme upper bound of ~2,609,000,000,000,000 position. Our real number (423,836,835,667,331) is 16.2% of that. That means 83.8% of all possible positions are invalid. Seems just about right.

It's amazing to see the 7-piece tablebase on lichess. But afaik it's not the first free 7-piece tablebase. The Lomonosov tablebase has had a free smartphone application for some time.

This is great!, go Lichess, go!

@OhNoMyPants Your analysis is correct, I think. Only the percentage of illegal positions is probably a lot lower, because the 423 trillion are "unique positions", i.e. excluding all kinds of symmetries. (Or maybe that's what you meant by "invalid" in the first place).

Amazing work.

Now it would be very nice if server-side analysis would use these tables to analyze positions. I outlined it here: lichess.org/forum/lichess-feedback/is-there-a-reason-lichess-does-not-use-gaviota-tables-during-server-analysis

This is a great achievement!
Big congratulations to Bojun Guo & Ronald de Man & congrats LiChess!
It is not clear to me if they were also involved in managing to compress it all into 18.4 Terabytes, but I think that is a pretty major achievement as well.

Well done!

@revoof Yeah, agreed. E.g. we're counting things like 5 black rooks multiple times, since order matters - yet there's only one way to have those 5 black rooks in reality.

Is it not possible to have a 7man position with DTZ 50 which then reaches a 6 man position with DTZ greater than 50?

On first page it needs a correction :
Bojun Guo (also one of the top contributors of computing power for Stockfish testing) started generating the first tables in May, expertly managing two machines, one of them with 384 threads (4 Xeon processors) and more than 1 TB of RAM (later distributed differently).

His system is a 8x Intel Xeon Platinum 8168 8x24c/48t makes 384threads in total!
You can find some benchmarks on my website: http://www.ipmanchess.yolasite.com/amd---intel-chess-bench.php

Ipman.