This probability is drawing proportional to organism counts, instead of brain cell counts.

Would it not be more representative if the weighting included neuron counts?

In a sense I ascribe to the belief of such a lottery, except that we are all the same "I", we just alternatively wake up as physics evaluating the progress for this or that electron, proton etc in this or that rock or neuron and progressing the state indeterministically according to the rules of physics.

Our identity is a pragmatic illusion (just like the illusion that water is a continuus medium, is a pragmatic one, as it helps summarize the behavior of water).

Imagine an amnesiac elder in an elderly home, still knows the rules of chess, but can't form long term memories any more: its his turn, and he's playing black, there is a small notebook with his plans and strategies, jotted down during the earlier turns, he makes some notes and then a move.

The caretakers turn around the chess board, swap the black notebook with the white notebook and leave the amnesiac bewildered for a few minutes. Then he reads his earlier notes in the white notebook, deliberates his options and makes a move, with a white piece.

The caretakers turn the chess board around again.

This is physics, and the "player" is you, me, everyone, and we are physics.

The notebook is the state of your brain, and your move is indeterminate physics (with deterministic probabilities) evolving the state of the universe.

Does identity exist: yes! as a pragmatic summary, even natural selection latched onto this illusion out of necessity.

Weighting by neurons will be more representative, of universal experience in the earthly biosphere.