Frodo is on the Mordor track.No cap on damage done. As you note, the SP can only assign up to the number of remaining companions, so FP needs to decide how many companions they are taking into Mordor.
When a tile with an eye symbol is pulled, the damage is the # of dice in the hunt box, right?
Is this capped in any manner?
i.e. if the shadow player chooses to put 4 dice in the hunt box and then happens to roll 3 more, does an eye symbol now do 7 damage?
I see that the # of dice the shadow player can place in the box intentionally is capped by the number of companions remaining, but it seems possible you could have a large number of dice in that box.
This also makes the "lidless eye" card very powerful in the late game. Note that the # of dice includes any fellowship dice added to the hunt box as a result of a character action to advance the fellowship on the Mordor track.
If there are 7 eye dice in the hunt box and 4 eye tiles in the pool, FP is almost definitely better off just taking the 1 damage for not moving. SP will have at most 3 action dice for the military game and FP can focus their efforts on delaying the inevitable there.