diff --git a/README.md b/README.md
index ea345b0..2166ade 100644
--- a/README.md
+++ b/README.md
@@ -158,6 +158,9 @@ Throughput benchmark:
 
 ```bash
 flock -n .compute.lock uv run python benchmarks/throughput.py
+
+# Optional CUDA check without making CUDA a project dependency:
+flock -n .compute.lock uv run --with 'jax[cuda12]' python benchmarks/throughput.py
 ```
 
 Measured on 2026-07-04 with CPU JAX backend:
@@ -170,6 +173,17 @@ elapsed_sec=4.655526
 steps_per_sec=450465.14
 ```
 
+Measured on 2026-07-04 with CUDA JAX backend on RTX 3090, using the optional
+`uv run --with 'jax[cuda12]' ...` command:
+
+```text
+backend=gpu
+batch_size=8192
+steps=256
+elapsed_sec=0.530039
+steps_per_sec=3956598.38
+```
+
 ### DECISIONS.md
 
 - Explicit `deck_order` dealing uses the first eight cards for player 0 and