And another import thing is, if you look at exact robocode physics, one bullet & wave collide on exact same tick, regardless of bullet_t/wave_t, so probability of bullet shadow will always be fixed.
You are correct that the shadow on bullet_t is always 100%. But I think that the probability of a shadow on bullet_t-1 (when a collision occurs when the wave moves first) is only 25%. Rationale: 50% chance that wave moves before bullet, 50% chance that a collision occurs if either one moves (the other 50% is when both move).
Two things, independent from each other:
1. Enemy bullet in black area: 100% probability of collision.
2. Enemy bullet in gray area: 50% for update order [my bullet, enemy bullet], 50% for update order [enemy bullet, my bullet].
Note that 1 and 2 is completely independent, because there are no intersections between the two areas (event spaces), this can be proved by some geometry.
And note that, probability of bullet collision happens in gray area vs in black area is a complete different thing, which also depends on actual size of area.