gave stronger hardness result user6973

By Theorem 3.1 and the proof's IPS being one-way, that problem
for all real numbers $$\epsilon$$, if ​ $$0<\epsilon$$ ​ then the promise problem

Input: ​ a game as described in my question
must output YES if : ​ ​ ​ the game's value for Player 1 is greater than 1-$$\hspace{.025 in}\epsilon$$
must output ​ NO ​ if : ​ ​ ​ the game's value for Player 1 is less than $$\epsilon$$

remains RE-hard even when

player_to_move is always 1 ​ (i.e., only 1 player is needed)
and
s0 ≠ sa ​ and ​ sa is not in Range(next_state_table)
(i.e., it's literally impossible for the player to lose)
and
p1_info and p2_info and number_of_choices are independent of the state
(i.e., the player's only feedback is whether or not it just won)

. user6973

By Theorem 3.1 and the proof's IPS being one-way, that problem remains RE-hard even when

player_to_move is always 1 ​ (i.e., only 1 player is needed)
and
s0 ≠ sa ​ and ​ sa is not in Range(next_state_table)
(i.e., it's literally impossible for the player to lose)
and
p1_info and p2_info and number_of_choices are independent of the state
(i.e., the player's only feedback is whether or not it just won)

.