My algorithm is so much more complicated than yours. In my area you get rear-ended if you were going straight and you didn't go when someone coming from the opposite direction but also going straight went (your algorithm doesn't allow that).

Assuming cars are already at the intersection, I wait until each of them goes and then take my turn, unless it's someone's turn who wouldn't cause a conflict with me and nobody else could go at the same time and would cause a conflict with me.

When I arrive at the intersection at nearly the exact same time as someone else then some more complicated heuristics come into play (I'm not sure how you handle it when the timing is close enough to be in question). The person on a significantly larger road has priority over smaller road. People going straight have priority over right turners, which have priority over left turners, and if all else is equal, the right-most person should go first.

I guess I could sum it up as "if you can go safely, and nobody who was there before you can go safely, then go. Otherwise wait your turn", but with a lot more nuance around tie-breaking.