Since the Games launch Pokemon Sword and Shield got a prediction of how it's shiny encounter chance looks like.
Thanks to data miner Kurt we got this table on Twitter to look at and figure out the shiny chance.
Base chance, since most of the games is 1:4096, but stuff like catch-series and numbers encountered did always influence the odds in an positive favor for the player.
Now since yesterday several news pages started to claim the best chance to encounter an shiny without the shiny charm is 7/4096 e.g. 1:585.
But from what I read you only have a chance of 33% to get a reroll which would provide the additional 6:4096.
So the correct math should be: 1/4096 + 0.33 * 6/4096 which alludes to a chance of roughly 1:1365.
So my question here is: Did I misread or not understand the twitter post? Is the chance of an additional reroll supposed to be another extra reroll after the 7:4096 you get at the start of an encounter (which would still not add up since the chance would be even better)?
To clarify the chances to get a shiny with an shiny charm equipped are calculated as
3/4096 + 0.33 * 6/4096 for at least 500 defeated and a streak of 25+ Pokemon of one species defeated in a row then.
This would mean, the best chance with a shiny charm is around 1:819.
Best Answer
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).