Sampling-based planners such as MPPI and CEM query a learned world model thousands of times per control step, so low-bit world models are an obvious way to make model-based control cheaper on a robot. With round-to-nearest activation quantization and no calibration, we find that planning can collapse, by up to 100 points of success, while the world model's latent one-step prediction error stays no larger than that of a stochastic rounding scheme that plans well. At the same bit width, what decides the outcome is not the size of the rounding error but whether it persists across planner iterations and is shared across candidates. Round-to-nearest leaves an error that persists, and an iterating planner drifts toward the candidates that this error favors; in TD-MPC2, holding the same dither fixed within a step or an episode brings the drift back. Dither shared by all candidates and redrawn at every iteration removes most of the damage at the same bit width and without training: at least half of it in all 19 affected Meta-World cells (task $\times$ bit width) of TD-MPC2 (median 95%), in 4 of 5 DINO-WM cells, and in all 8 affected tasks of a 317M-parameter multi-task TD-MPC2. Captured as CUDA graphs on an Ampere GPU, a W8A4 integer TD-MPC2 world model runs its planning rollouts 1.9-3.3$\times$ and the whole planning step 1.3-1.5$\times$ faster than FP32, though not faster than BF16 with pre-converted weights; shared dither adds at most 2.3% latency. In TD-MPC2, block-scaled NVFP4 removes most of the damage and MXFP4 part of it, which ties the failure to coarse grids with a shared scale. Hypotheses, thresholds and analysis code were fixed before the data that test them, and the hypotheses that failed are reported.