Suppose sleeping beauty secretly brings a coin into the experiment and flips when she wakes up. There are now six possible combinations of heads and tails, each with their own possibilities:
HH: 1/4
HT: 1/4
THH: 1/8
THT: 1/8
TTH: 1/8
TTT: 1/8
When she wakes up and flips the coin, she notices it lands on heads. This eliminates two of the possibilites. Now renormalizing their values:
HH: 2/5
HT: 0
THH: 1/5
THT: 1/5
TTH: 1/5
TTT: 0
She can conclude that the coin landed on tails with 60% probability, rather than the normal 50% probability. She could flip the coins more times. Doing so, she will asymptotically approach 2/3 probability that it landed on tails.
Perhaps she gets caught with the coin, and has it taken away. This isn't a problem. She can just look at dust specks, or any other thing she can't predict and won't be consistent. For all intents and purposes, she's using SSA. There's a difference if she's woken so many times that it's likely she'll make exactly the same observations more than once, but that takes her being woken order of 10^million times.
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Er, a few species of placental mammal are hardly "widely separated lineages". Trying to draw conclusions for completely alien biologies by looking at convergent evolution inside a clade with a single common ancestor in the last 2-or-3% of the history of life on Earth is absurd. And the fact that the Placentalia start with an unusually high EQ among vertebrates-as-a-whole make it a particularly unsuitable lineage for estimating the possibilities of independent evolution of high animal intelligence.
Parrots and other birds seem to be about that intelligent, and octopi are close.
Perhaps that's an argument for the difficulty of the chimp to human jump: we have (nearly) ape-level intelligence evolving multiple times, so it can't be that hard, but most lineages plateaued there.