By [Theorem 3.1](http://www.cs.ubc.ca/~condon/papers/condon-lipton89.pdf#page=6) and the proof's IPS being one-way, that problem remains [RE](https://complexityzoo.uwaterloo.ca/Complexity_Zoo:R#re)-hard even when

player_to_move is always 1 ​ (i.e., only 1 player is needed)
<br>and<br>
s<sub>0</sub> ≠ s<sub>a</sub> ​ and ​ s<sub>a</sub> is not in Range(next_state_table)
<br>
(i.e., it's literally impossible for the player to lose)
<br>and<br>
p1_info and p2_info and number_of_choices are independent of the state
<br>
(i.e., the player's _only_ feedback is whether or not it just won)

.