diff --git a/random/randao_analysis.ipynb b/random/randao_analysis.ipynb
index 37157c4..0603199 100644
--- a/random/randao_analysis.ipynb
+++ b/random/randao_analysis.ipynb
@@ -318,7 +318,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
@@ -327,7 +327,7 @@
        "7774.15709413154"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -337,6 +337,27 @@
     "1/negbintail(67,2/3,64)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3738.63966703836"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# If we include the bias from 4 epochs above, the number of options might be 10 more.\n",
+    "1/negbintail(67,2/3,74)/172.837461872421"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,