8 ms·
The upper bound on the number of legal chess positions given in https://en.wikipedia.org/wiki/Shannon_number https://en.wikipedia.org/wiki/Shannon_number is 8.7
by ToValueFunfetti 3y ago
The upper bound on the number of legal chess positions given in https://en.wikipedia.org/wiki/Shannon_number https://en.wikipedia.org/wiki/Shannon_number is 8.7 * 10^45, which gives a lower bound of ln(8.7 * 10^45) = ~106 bits or 14 bytes.
- tromp 3y agoYou need the 2-logarithm rather than the natural logarithm. That gives ~ 152.6 bits, or ~ 19.1 bytes.
- ToValueFunfetti 3y agoThanks, don't know what I was thinking there
- xpe 3y agoDon't worry, that's actually quite a natural error to make
- xpe 3y ago> Recent results improve that estimate, by proving an upper bound of 8.7x10^45, and showing an upper bound 4×10^37 in the absence of promotions. - Wikipedia (link above) You can save 28 bits!... Use log2(4e37) = 124.9 bits for games without piece promotions. Then switch to log2(8.7e45) = 152.6 bits for games with them.