Chess has actually been weakly solved already in the most commonly analysed variations.
This is false. Only small branches have been solved. It's generally almost as far beyond computational capabilities as solving chess. All practical analysis ignores most moves and this is absolutely not good enough for a weak solution. This requires a strategy for each side that addresses EVERY legal opponent response.
so then a 6-piece ending isnt really solved right ?
No, tablebases solve them.
The Syzergy tablebases strongly solve all 7 piece positions in a tiny 18 terrabytes (over 20 positions per byte, via very efficient compression).
and guess what ?...chess can be completely described. trust me. its just out there waiting to be discovered lol !
top engines are unable to play accurately in 6 piece endings
so its the engines not playing best. ok.
and guess what ?...chess can be completely described. trust me. its just out there waiting to be discovered lol !
What's interesting is there are all sorts of "easy" facts out there that for practical reasons we'll never know them... but they exist... we just can't have them
For example, what's the exact population of humans on Earth at any given time?
Yes, others have observed that solving chess is mathematically trivial and practically impossible. The only obstruction is the amount of computation.
if u put 99 bl balls and 1 wh ball in a rabbits hat ?...the chance of pulling the wh ball out in the first 50 tries is ~69%...maybe.
if u put 99 bl balls and 1 wh ball in a rabbits hat ?...the chance of pulling the wh ball out in the first 50 tries is ~69%...maybe.
ur math aint mathing. many ways to show that it is 50%. some are simpler, some are more profound
heres an easy yet very profound to understand way, especially if you think the order you pull out the balls matters.
lets look at the chance of pulling out black balls, one by one.
first ball: 99/100, Second ball: 98/99, Third ball 97/98,... the 49th ball would be 51/52, and the 50th would be 50/51. . multiply those together, and as you can see, the numerator of the Nth ball is canceled by the denominator of the N+1th ball. this leaves only the denominator of the first ball and the numerator of the last (50th) ball, which is 50/100.
another, simpler way to look at it is the balls are randomly arranged in two rows of 50. one row of 50 is chosen. there is a 1/2 chance that the white ball was in the row you chose.
now, the estimated probability of there being a white ball assuming the first 50/100 balls were black is a very different thing. still pretty easy to calculate with a program tho.
There may be infinite chess positions, but you only have to get into the tablebase with the best moves or, much more simply, into a move repetition.
Unless you have significant improvement anywhere in that line, or you think White can somehow win the position in the end, chess is a draw.
meggy try this:
100
Σ 1/n
n=51
meggy try this:
100
Σ 1/n
n=51
probabilities of independent events are multiplicative not additive lmfao.
There may be infinite chess positions, but you only have to get into the tablebase with the best moves or, much more simply, into a move repetition.
Unless you have significant improvement anywhere in that line, or you think White can somehow win the position in the end, chess is a draw.
Newsflash...running Stockfish into one dead position is not a proof of anything.
well, i think the better term would be "non exclusive" events rather than independent for the layman.
iows, in theory ud pull the white ball on ur 63rd try. which is 1/ln e...i think.
iows, in theory ud pull the white ball on ur 63rd try. which is 1/ln e...i think.
again, you are adding probabilities when you are supposed to be multiplying them.
if u put 99 bl balls and 1 wh ball in a rabbits hat ?...the chance of pulling the wh ball out in the first 50 tries is ~69%...maybe.
Well the chance is exactly 50% if you don't replace the balls (you have divided the balls into two equal halves...)
And if you do replace the balls, the chance of not ever getting the white ball is (99/100)^50 = 0.605, so the chance of getting it is 0.395.
(95% confidence interval by John Tromp and Peter Österlund).
so then a 6-piece ending isnt really solved right ?