best-of-3 oracle/deployable split: realistic selector loses the overall edge (55.0/27.3 vs oracle 57.8/34.5); paper economics rewritten

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

results-loop/stats_final.json

@@ -322,6 +322,108 @@
    "a_only": 0,
    "b_only": 4,
    "p": 0.125
+  },
+  "bo3-oracle vs loop k=4, overall": {
+   "n": 500,
+   "a_only": 27,
+   "b_only": 48,
+   "p": 0.020298406990107445
+  },
+  "bo3-oracle vs loop k=4, hard": {
+   "n": 55,
+   "a_only": 14,
+   "b_only": 9,
+   "p": 0.4048728942871094
+  },
+  "bo3-oracle vs distill k=1, overall": {
+   "n": 500,
+   "a_only": 27,
+   "b_only": 44,
+   "p": 0.056814677932839015
+  },
+  "bo3-oracle vs distill k=1, hard": {
+   "n": 55,
+   "a_only": 14,
+   "b_only": 10,
+   "p": 0.5412561893463135
+  },
+  "bo3-deployable vs loop k=4, overall": {
+   "n": 500,
+   "a_only": 31,
+   "b_only": 38,
+   "p": 0.4703685318581444
+  },
+  "bo3-deployable vs loop k=4, hard": {
+   "n": 55,
+   "a_only": 16,
+   "b_only": 7,
+   "p": 0.0931396484375
+  },
+  "bo3-deployable vs distill k=1, overall": {
+   "n": 500,
+   "a_only": 31,
+   "b_only": 34,
+   "p": 0.8043170001933986
+  },
+  "bo3-deployable vs distill k=1, hard": {
+   "n": 55,
+   "a_only": 15,
+   "b_only": 7,
+   "p": 0.13380050659179688
+  }
+ },
+ "best-of-3 ORACLE (any-pass)": {
+  "overall": {
+   "acc": 0.578,
+   "n": 500,
+   "ci": [
+    0.534,
+    0.621
+   ]
+  },
+  "hard": {
+   "acc": 0.34545454545454546,
+   "n": 55,
+   "ci": [
+    0.234,
+    0.477
+   ]
+  }
+ },
+ "best-of-3 oracle (selector run)": {
+  "overall": {
+   "acc": 0.578,
+   "n": 500,
+   "ci": [
+    0.534,
+    0.621
+   ]
+  },
+  "hard": {
+   "acc": 0.34545454545454546,
+   "n": 55,
+   "ci": [
+    0.234,
+    0.477
+   ]
+  }
+ },
+ "best-of-3 DEPLOYABLE (logprob-selected)": {
+  "overall": {
+   "acc": 0.55,
+   "n": 500,
+   "ci": [
+    0.506,
+    0.593
+   ]
+  },
+  "hard": {
+   "acc": 0.2727272727272727,
+   "n": 55,
+   "ci": [
+    0.173,
+    0.402
+   ]
   }
  },
  "pooled_hard_loop": {