Yes, I noticed his climate change thread is no longer accessible. He and his forums will probably return tomorrow.
Optimissed seems to be on another long enforced vacation.
Yes, I noticed his climate change thread is no longer accessible. He and his forums will probably return tomorrow.
Optimissed seems to be on another long enforced vacation.
so that's why this post got sent back a couple of pages. knew something was missing. welp we won't be seeing big chunks of text for a solid 3 hours
hes prolly js doin something else while he waits for the, err... i guess uninprisonment works within the context of how this conversation has gone? well yeah im going with that. not gonna use grammar until the big guns come back
Because the number of possible positions is a 45 digit number.
uhhh...didju *poof* that one up ?? i mean whered u get the 45 thingy ? and trust me. i like made up stuff alot (teehee !) but take me thru that 45-zeros count again ? ...for my sake ?
So if you can cut that down somehow to a billionth of that - you've still got a 36 digit number.
they say every little bit helps right ?
Hi L.
Chess.com might have accidentally muted some people just in the last few hours.
@Elroch and his forums will probably re-appear before sunday.
Just guessing though. I don't claim to know.
-------------------------------------------------------------
L- yes - the number of possible chess positions is a 45 digit number.
But its an 'upper bound'. Which is a term in mathematics.
You want some more info on that?
OK.
------------------
Starting out with the fact that each square can only have 13 states -
in other words each square either has to be empty - or have a white piece or a black piece on it.
And there's six types of piece but two possible colours - so you get 12 possibilities.
So add the one to the 12 and you get the 13.
So right away you've got a 'first upper bound' of 13 multiplied by itself 63 times.
Which is written 13^64.
'Thirteen to the sixty-fourth power'. The 64 is an exponent.
And of course is derived from the number of squares on the board.
------------------------------
But a man named John Tromp then did a lot of math on that number.
Taking into account that at least 32 squares of the board have to be empty.
Because there's a max of 32 pieces.
And there's a max of two kings only.
And other math like a max number on various pieces.
So a few years ago he came up with a number of 4.8 x (10^44).
Which is a 45 digit number. A cutdown from 13^64.
Big cutdown but still leaves that Gi-Normous 45-digit number.
Could some of the details be off? Maybe.
I've seen suggestions of 46 digit and 47 digit numbers.
--------------
If you look up John Tromp on the internet or on AI you'll probably see the number mentioned.
If you want to think about it - you could start with 'how many ways to arrange the two kings? Then multiple that by the number of places a bishop could be - and for each added piece you multiply again .... you start to see how you get a very very big number.
WHERE ARE MY PANCAKES?
I said - before Sunday.
My guess proven.
Better than guessing...
Creating an outcome: https://www.chess.com/forum/view/help-support/auto-mute-shenanigans#comment-113867126
That's because a rather accurate number has been calculated by Tromp et al.
This page explains what was done and gives the estimate and uncertainty as:
(4.59 +- 0.38) * 10^44 (with 95% confidence level)
This confidence interval makes the number of digits a very safe bet, since an error over 10 times as big would be required to change the number of digits.
Went to that page: https://github.com/tromp/ChessPositionRanking------------------
This list there is remarkable.
492045 Illegal Both Kings in Check
173401 Illegal Side not to move in Check
102541 Illegal Adjacent Kings
79019 Illegal Bishops Too Monochromatic
53063 Single Check
35584 No Checks
29962 Illegal Triple Check
27415 Illegal Double Check
6256 Discovered Double Check
714 Illegal Double Knight Check
------------------
10 categories. Ranked. Apparently adding up to one million.
Three of the 10 categories are legal.
Notable are the relatively small numbers to the left of those three legal categories.
----------------------------------
Also this paragraph:
"The reason for satisfying ourselves with a mere estimate is that we have no hope of ever determining the number exactly, like we did in the game of Go. Whereas in Go, deciding whether a given position is legal is quite simple, determining the legality of a given chess position is exceedingly hard. It is the essence of so-called retrograde analysis problems that concern the possible past moves rather than the possible future moves that normal chess problems concern themselves with."
There was also a term used - 'proof games'.
Proving that a position could be legally reached.
Connects to 'exceedingly hard'.
-----------------
And the article mentions other results also arriving at figures with over 40 digits in them.
they bounced elrock off ??...think they threw him into restront jail ?
wait a sec....wheres his threads ?? hmmm...heave ho ?