diff --git a/docs/guides/estimator-options.ipynb b/docs/guides/estimator-options.ipynb
index 4f7755869e3..999f42c9dc7 100644
--- a/docs/guides/estimator-options.ipynb
+++ b/docs/guides/estimator-options.ipynb
@@ -250,6 +250,10 @@
     "\n",
     "However, if `precision` is not specified by any PUB or in the run keyword argument (or if they are all `None`), then the precision value from the options is used, most notably `default_precision`.\n",
     "\n",
+    "<Admonition type=\"note\">\n",
+    "These precision parameters are only for specifying _target_ precision, and the results are not guaranteed to reach the specified precision.\n",
+    "</Admonition>\n",
+    "\n",
     "Note that Estimator options contain both `default_shots` and `default_precision`. However, because gate-twirling is enabled by default, the product of `num_randomizations` and `shots_per_randomization` takes precedence over those two options.\n",
     "\n",
     "Specifically, for any Estimator PUB:\n",
@@ -263,6 +267,10 @@
     "For example, if precision is specified in all four places, the one with highest precedence (precision specified in the PUB) is used.\n",
     "\n",
     "<Admonition type=\"note\">\n",
+    "Although precision specified in the PUB and in `run` have higher precedence, the job fails if `twirling` is enabled and the product of `num_randomizations` and `shots_per_randomization` is smaller than the shots needed to achieve the precision. In this scenario, `EstimatorV2` is unable to allocate the shots among the specified `num_randomizations`.\n",
+    "</Admonition>\n",
+    "\n",
+    "<Admonition type=\"note\">\n",
     "Precision scales inversely with usage.  That is, the lower the precision, the more QPU time it takes to run.\n",
     "</Admonition>"
    ]
diff --git a/docs/guides/sampler-options.ipynb b/docs/guides/sampler-options.ipynb
index 754a1747b5a..d2e24d83589 100644
--- a/docs/guides/sampler-options.ipynb
+++ b/docs/guides/sampler-options.ipynb
@@ -144,6 +144,10 @@
     "\n",
     "Thus, if shots are specified in all possible places, the one with highest precedence (shots specified in the PUB) is used.\n",
     "\n",
+    "<Admonition type=\"note\">\n",
+    "Although shots specified in the PUB and in `run` have higher precedence, the job fails if `twirling` is enabled and the product of `num_randomizations` and `shots_per_randomization` is smaller than the `shots` value. In this scenario, `SamplerV2` is unable to allocate the shots among the specified `num_randomizations`.\n",
+    "</Admonition>\n",
+    "\n",
     "Example:"
    ]
   },