Another problem is, do you know how to formulate/​formalize a version of LDT so that we can mathematically derive the game outcomes that you suggest here?
What about a rock with $9 painted on it? The LDT agent in the problem reasons that the best action is to choose $1, so the rock gets $9.
Thus, $9 rock is more rational than LDT in this problem.
The solution above addresses this; by playing probabilistically, the rock gets a payoff somewhat less than $5 in expectation, so it does worse than an LDT agent.
Towards the end of the post in the No agent is rational in every problem section, I provided a more general argument. I was assuming LDT would fall under case 1, but if not case 2 will demonstrate it is irrational.
There is a no free lunch theorem for this. LDT (and everything else) can be irrational
I think your post misses the point made here.
The solution above addresses this; by playing probabilistically, the rock gets a payoff somewhat less than $5 in expectation, so it does worse than an LDT agent.
Towards the end of the post in the No agent is rational in every problem section, I provided a more general argument. I was assuming LDT would fall under case 1, but if not case 2 will demonstrate it is irrational.