Max Lair runs in the Crown Tundra, with flat odds of 1 in 300 (1 in 100 with the Charm).
Dynamax Adventures are Max Lair runs in the Crown Tundra expansion. You catch up to four Pokémon per run, and at the end you choose one to keep.
These are flat odds: there is no chain to build.
Nothing looks shiny during the run. Shininess is decided on the final screen where you pick a Pokémon to keep, and it is worked out separately for each player, so a shiny for you may not be shiny for a partner. Max Lair shinies always have star sparkles.
Each Legendary at the end of a path can only be kept once. If you decline it, you can try that path again later for a new chance at a shiny.