It seems to me that, also with the bet you describe, there is no paradox/inconsistency.

To make sure we're talking about the same thing: The bet I'm considering is:

each agent in each room is separately/independently given the option to bet that the coin came up heads. If the agent says "yes, heads", and coin=1, that one agent wins 1 utilon. If the agent says "yes, heads", but coin=0, that one agent loses 3 utilons.

One likely source of confusion that I see here is: If one thinks about {what the agent cares about} in terms of "I", "me", "this agent", or other such concepts which correspond poorly to the Territory (in this kind of dilemma/situation).

To properly deconfuse that, I recommend Tabooing "this", "I", "me", "you", etc. (A trick I found useful for that was to consider variations of the original dilemma, where the agents additionally have numbers tattooed on them; either numbers from 1 to 20, or random UUIDs, or etc.; either visible to the agent or not. Then one can formulate the agent's utility function in terms of "agent with number N tattooed on it", instead of e.g. "instances of me".)

For brevity, below I do use "this" and "I" and etc. Hopefully enough of the idea still comes through to be useful.

If what the agent cares about is something like "utilons gained in total, by computations/agents that are similar to the original agent", then:

• Before the experiment: The agent would want agents in green rooms to accept the bet, and agents in red rooms to reject the bet.

• Upon waking up in a green room: The agent has received no information which would allow it to distinguish between coin-flip-outcomes, and its probability for coin=1 is still 50/50. I.e., the agent is in practically the same situation as before the experiment, and so its answer is still the same: accept the bet. (And conversely if in a red room.)

The above seems consistent/paradox-free to me.(?)

If what the agent cares about is something like "utilons gained, by this particular blob of atoms, and the temporal sort-of-continuation of it, as usually understood by e.g. humans", then:

• Before the experiment: The original description of the dilemma leaves unclear what happens to the original blob of atoms, but here I'll assume that the original blob-of-atoms is destroyed or somehow split 20 ways. In that case, before the experiment, the agent would not care at all how the other copy-agents bet. They're not the same blob-of-atoms, after all. The pre-experiment agent's preferences w.r.t. betting are undefined.

• Upon waking up in a green room: the agent's probability distribution over coin=1 is still 50/50. And it is a new blob-of-atoms, not the original pre-experiment blob-of-atoms. It doesn't care at all how other blobs-of-atoms fare. It rejects the bet.

To the extent that there's an inconsistency between the pre-experiment agent and in-room agents, I think it's due to them being different agents with different utility functions. So it doesn't seem accurate to say that either agent's individual preferences are inconsistent?

A likely objection I anticipate to the above is something like:

"{The total number of utilons (summed over agents) gained by agents using the above probability-update- and decision-algorithm} is less than {the total number of utilons gained by agents that would update their probability for coin=1 to 90% upon seeing green}."

To which I think Blob-of-atoms #N would respond:

"Yes, but Blob #N does not care that Other-blobs-of-atoms-using-the-same-reasoning-algorithm tend to fare poorly. Blob #N isn't trying to cooperate with near-copies of itself. So what if other blobs-of-atoms don't gain utility? That argument doesn't really weigh against Blob #N's reasoning-algorithm, does it?"

Does this make sense to you? If not, what seems (most) wrong/confused?

You appeared to be rejecting any meaning for probability of events such as "I am a copy" [...]

If I can translate "I am a copy" to e.g. "an agent that is currently having observations/thoughts x,y,z is a copy" (or to something else that does not depend on (seemingly-to-me ill-defined) things like "me"), then I do think that probabilities can and should be assignable to those kinds of events. I guess my post/writing was even less clear than I thought.

The fact remains that the indistinguishable copies still need to make decisions, may [...]

I think I'm entirely in agreement with that paragraph.

Declaring that all utilities must be summed or averaged or whatever [...]

I don't understand where that paragraph is coming from. (I'm guessing it's coming from my writing being much less clear or much more prone to misinterpretation than I thought. Feel free to not explain where that paragraph came from.)

I'm confused: Where have I said that probabilities are undefined?

I did say that, if the pre-experiment agent-blob-of-atoms cares only about itself, and not the in-room-agents, then its preferences w.r.t. how the in-room-agents bet are undefined. Because its utility function was (by definition) independent of what happens to the in-room-agents. But I don't think I've implied that any probabilities are undefined.

Did this help clarify things?