What is the true shiny rate in Sword and Shield?

Solution 1:

Your calculations seem correct to me; based on serebii, with a 25+ combo and at least 500 of that species battled, you have a 33% chance to get the higher shiny rate. So overall you have a (1/3)X(7/4096)+ (2/3)X(1/4096) chance, about one in 1365. (I'm not entirely sure how the rerolls are worked out - if it simply rolls the 1/4096 chance seven times looking for at least one shiny, the odds are instead one in 1366).

Assuming you were at full odds the whole time, then, the chance of 2000 encounters with no shiny is 23.1%. Not all that unlikely. Once you get up to 6289 encounters you'd be looking at just under 1% chance of still no shiny (still fairly possible).