A hardware-based traversal coprocessor provides acceleration of tree traversal operations searching for intersections between primitives represented in a tree data structure and a ray. The primitives may include opaque and alpha triangles used in generating a virtual scene. The hardware-based traversal coprocessor is configured to determine primitives intersected by the ray, and return intersection information to a streaming multiprocessor for further processing. The hardware-based traversal coprocessor is configured to provide a deterministic result of intersected triangles regardless of the order that the memory subsystem returns triangle range blocks for processing, while opportunistically eliminating alpha intersections that lie further along the length of the ray than closer opaque intersections.