Perfect World released the drop chances of rare, very rare, ultra rare, and cosmically rare items in the 2018 Immortal treasures as for Chinese laws.
A few years ago, China passed a law on loot boxes. The regulation has been effective starting from May 1, 2017, and since then all game developers are required to indicate the drop chance of any item.
Here you can find the full regulation in Chinese.
Dota 2 is played also in China, so Perfect World had to release these info. Of course, we don’t know if the drop chances are exactly the same also in the rest of the world, but there is no reason to assume the opposite. The page now shows also the drop rate of TI7 Immortals, which are exactly the same.
A rough translation of the odds:
Rare: after 10 chests, escalating odds, 1/4 or 25%.
Very Rare: after 10 chests, escalating odds, 1/7 or 14.28%.
Ultra Rare: after 23 chests, escalating odds, 1/10 or 10%.
Cosmically rare: 1/250000, or 0.0004%.
Immortal Treasure: 0.5%.
Codicil of the Veiled Ones - Ultra Rare drop for PA in the Immortal treasure I.
As you might have noticed, the odds aren’t totally accurate because they do not tell us the mathematical formula behind the escalating odds. We don’t know the exact chances to find a rare or very rare item in the first nine chests, neither if and how these improve after the tenth one.
I would appreciate better info on the matter, but most probably with this post they already fulfilled their duty with the Chinese regulation.
Header image: Valve