So, in baksetball, there is the possession arrow. When ambiguous situations happen, the team with the possession arrow gets the ball, then the possession arrow swaps to the other side.

What if Legion was like this? You roll one die at the start to see who gets the choice to have or pass the possession arrow, then everytime you play a card with the same pips, priority goes to the person with the "possession arrow." Then, the possession arrow swaps to the other player.

This leads to less RNG, but is that a good or bad thing? Obviously real battles have some elements of chaos, mistakes, and chance, but in terms of priority, using a possession arrow seems like an intriguing house rule. Or is six rounds too few to really matter?

So I think that at least in the case of determining priority, rolling dice when pips are tied is actually best for the game. As it stands, if battlefield conditions are ripe for playing a 1 pip card, you have to keep in mind that you still might not win priority. By the same token, if you suspect your opponent is going to play a 1 pip card, you might also choose to play a 1 pip card knowing that with luck you can steal priority away, but it isn't guaranteed. However, if you enter the command phase knowing that one player will automatically win priority ties, then this element of calculating risk goes away.

Also, if the possession arrow flipped for every ambiguous situation, then just like in basketball you will have situations where people will try to game it so they can have the possession arrow in their favor. I don't think it would be good for the game if people are actively trying to force an ambiguous situation right before the end of a round so that they can guarantee they will win (or lose) the priority tie-breaker during the next command phase.

As it is, players pass the round counter back and forth at the end of each round, and the person with the round counter is the one to roll the dice. This is reminiscent of the possession arrow without actually creating an entire mini-game centered around winning possession.

Yeah, I agree that the uncertainty is a key element of the game.

You can have the game-winning activation planned out, but if you lose the roll-off and then that unit gets suppressed and then doesn't rally and then you can't claim the objective, them's the breaks. I think that chaos is core to Legion's identity.