{
  "parameters": {
    "alpha": "1/20",
    "alternative_for_lr": "3/4",
    "monitoring": "after every observation from the first"
  },
  "rows": [
    {
      "horizon": 20,
      "p": "1/2",
      "rule": "fixed_binomial",
      "rejection_probability": 0.020694732666015625,
      "probability_exact": "5425/262144",
      "expected_observations": 20.0
    },
    {
      "horizon": 20,
      "p": "1/2",
      "rule": "peek_binomial",
      "rejection_probability": 0.0986785888671875,
      "probability_exact": "6467/65536",
      "expected_observations": 19.018890380859375
    },
    {
      "horizon": 20,
      "p": "1/2",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.021137237548828125,
      "probability_exact": "5541/262144",
      "expected_observations": 19.854290008544922
    },
    {
      "horizon": 20,
      "p": "3/5",
      "rule": "fixed_binomial",
      "rejection_probability": 0.12559897272303747,
      "probability_exact": "11978051445297/95367431640625",
      "expected_observations": 20.0
    },
    {
      "horizon": 20,
      "p": "3/5",
      "rule": "peek_binomial",
      "rejection_probability": 0.2951284736395837,
      "probability_exact": "1125825781401/3814697265625",
      "expected_observations": 17.241749056867008
    },
    {
      "horizon": 20,
      "p": "3/5",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.10695537146163364,
      "probability_exact": "2040011815293/19073486328125",
      "expected_observations": 19.305180060494436
    },
    {
      "horizon": 20,
      "p": "3/4",
      "rule": "fixed_binomial",
      "rejection_probability": 0.6171726543871046,
      "probability_exact": "169647127461/274877906944",
      "expected_observations": 20.0
    },
    {
      "horizon": 20,
      "p": "3/4",
      "rule": "peek_binomial",
      "rejection_probability": 0.7740480938809924,
      "probability_exact": "13298044995/17179869184",
      "expected_observations": 12.164162645698525
    },
    {
      "horizon": 20,
      "p": "3/4",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.5285200232683565,
      "probability_exact": "72639238887/137438953472",
      "expected_observations": 16.347185894097493
    },
    {
      "horizon": 50,
      "p": "1/2",
      "rule": "fixed_binomial",
      "rejection_probability": 0.03245432353613609,
      "probability_exact": "4567539980747/140737488355328",
      "expected_observations": 50.0
    },
    {
      "horizon": 50,
      "p": "1/2",
      "rule": "peek_binomial",
      "rejection_probability": 0.1578822453198061,
      "probability_exact": "88879802648837/562949953421312",
      "expected_observations": 45.01982109300513
    },
    {
      "horizon": 50,
      "p": "1/2",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.03759043021723407,
      "probability_exact": "21161530939879/562949953421312",
      "expected_observations": 48.88639636526021
    },
    {
      "horizon": 50,
      "p": "3/5",
      "rule": "fixed_binomial",
      "rejection_probability": 0.3356132635690677,
      "probability_exact": "29808445806717615681153654222450009/88817841970012523233890533447265625",
      "expected_observations": 50.0
    },
    {
      "horizon": 50,
      "p": "3/5",
      "rule": "peek_binomial",
      "rejection_probability": 0.5571409294627921,
      "probability_exact": "9896811005610433013665331064437829/17763568394002504646778106689453125",
      "expected_observations": 33.96524786972791
    },
    {
      "horizon": 50,
      "p": "3/5",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.25194888058587456,
      "probability_exact": "4475511172079552563088255216090181/17763568394002504646778106689453125",
      "expected_observations": 43.50469458482532
    },
    {
      "horizon": 50,
      "p": "3/4",
      "rule": "fixed_binomial",
      "rejection_probability": 0.9712668401644692,
      "probability_exact": "76951687057266565332102960729/79228162514264337593543950336",
      "expected_observations": 50.0
    },
    {
      "horizon": 50,
      "p": "3/4",
      "rule": "peek_binomial",
      "rejection_probability": 0.9880552276453942,
      "probability_exact": "313127200595830952599450062759/316912650057057350374175801344",
      "expected_observations": 14.345448718527386
    },
    {
      "horizon": 50,
      "p": "3/4",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.9157748263364397,
      "probability_exact": "290220627069822595612176947583/316912650057057350374175801344",
      "expected_observations": 22.80489337078866
    },
    {
      "horizon": 100,
      "p": "1/2",
      "rule": "fixed_binomial",
      "rejection_probability": 0.04431304005703379,
      "probability_exact": "7021681478279557518621742225/158456325028528675187087900672",
      "expected_observations": 100.0
    },
    {
      "horizon": 100,
      "p": "1/2",
      "rule": "peek_binomial",
      "rejection_probability": 0.20205809786793333,
      "probability_exact": "8004345907601874773458582909/39614081257132168796771975168",
      "expected_observations": 85.88590435284839
    },
    {
      "horizon": 100,
      "p": "1/2",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.04088964341296718,
      "probability_exact": "12958445253891527919585381637/316912650057057350374175801344",
      "expected_observations": 96.89061431483694
    },
    {
      "horizon": 100,
      "p": "3/5",
      "rule": "fixed_binomial",
      "rejection_probability": 0.6225326761221724,
      "probability_exact": "4910916904153958803014246672181688575426320019162501663320906559318257/7888609052210118054117285652827862296732064351090230047702789306640625",
      "expected_observations": 100.0
    },
    {
      "horizon": 100,
      "p": "3/5",
      "rule": "peek_binomial",
      "rejection_probability": 0.7819150464838488,
      "probability_exact": "6168222113751784990573702096684006474610872516856728756261882425436401/7888609052210118054117285652827862296732064351090230047702789306640625",
      "expected_observations": 49.817991977986175
    },
    {
      "horizon": 100,
      "p": "3/5",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.3485727322100315,
      "probability_exact": "549950802133133568796171745330834677022968853464757540819503987856637/1577721810442023610823457130565572459346412870218046009540557861328125",
      "expected_observations": 78.10052771961536
    },
    {
      "horizon": 100,
      "p": "3/4",
      "rule": "fixed_binomial",
      "rejection_probability": 0.9998529257015585,
      "probability_exact": "200837713121686496239102905332255012151825229931674468250133/200867255532373784442745261542645325315275374222849104412672",
      "expected_observations": 100.0
    },
    {
      "horizon": 100,
      "p": "3/4",
      "rule": "peek_binomial",
      "rejection_probability": 0.9999454446417539,
      "probability_exact": "200856297147288319888661715124718148050295275668681248816597/200867255532373784442745261542645325315275374222849104412672",
      "expected_observations": 14.458262270737265
    },
    {
      "horizon": 100,
      "p": "3/4",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.993448809246945,
      "probability_exact": "399102671650677132808522880691905565539246572567465076461575/401734511064747568885490523085290650630550748445698208825344",
      "expected_observations": 24.283249393236826
    },
    {
      "horizon": 200,
      "p": "1/2",
      "rule": "fixed_binomial",
      "rejection_probability": 0.03841881606563018,
      "probability_exact": "7717082143906205388823421413947098632655431311000408565791/200867255532373784442745261542645325315275374222849104412672",
      "expected_observations": 200.0
    },
    {
      "horizon": 200,
      "p": "1/2",
      "rule": "peek_binomial",
      "rejection_probability": 0.24462730236319022,
      "probability_exact": "196550459415928773262390452540183273490262288343349636699971/803469022129495137770981046170581301261101496891396417650688",
      "expected_observations": 163.29925806824258
    },
    {
      "horizon": 200,
      "p": "1/2",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.0411580655751116,
      "probability_exact": "33069230700376555067421243302288544571061266838933507146551/803469022129495137770981046170581301261101496891396417650688",
      "expected_observations": 192.78086381928617
    },
    {
      "horizon": 200,
      "p": "3/5",
      "rule": "fixed_binomial",
      "rejection_probability": 0.8603356670716591,
      "probability_exact": "10707764000551582937012436503220487020880800596632985848771445248322651017049052217950552750317033439817090426460788544891014674699879418413/12446030555722283414288128107560248481180504337442334266202233229579397668070766882367889646251427233913933179110244964249432086944580078125",
      "expected_observations": 200.0
    },
    {
      "horizon": 200,
      "p": "3/5",
      "rule": "peek_binomial",
      "rejection_probability": 0.9451468968892407,
      "probability_exact": "11763327158329588037824863333146639328633548811393695486759359947148777052464308794884282787454772773421854187590815161500764837435964885549/12446030555722283414288128107560248481180504337442334266202233229579397668070766882367889646251427233913933179110244964249432086944580078125",
      "expected_observations": 61.687490094114175
    },
    {
      "horizon": 200,
      "p": "3/5",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.411580767000326,
      "probability_exact": "25612734011168354647081037902461330621413425485100015710949559471774638070549846411469875043084464760758759044318832538040137683392020460257/62230152778611417071440640537801242405902521687211671331011166147896988340353834411839448231257136169569665895551224821247160434722900390625",
      "expected_observations": 139.5932692154574
    },
    {
      "horizon": 200,
      "p": "3/4",
      "rule": "fixed_binomial",
      "rejection_probability": 0.9999999961037178,
      "probability_exact": "322781233503216789172665640607986051975998948266064211542762554791020459697070159719163054585709248182136878032894880479/322781234760863573706989896500376484291213224103652939103832419567580952752105149328705669160017228929487896496593436672",
      "expected_observations": 200.0
    },
    {
      "horizon": 200,
      "p": "3/4",
      "rule": "peek_binomial",
      "rejection_probability": 0.9999999993087197,
      "probability_exact": "645562469075462582154183784278570306299625226916507069955165505540931211380069502081309513050366837440746335503432182759/645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344",
      "expected_observations": 14.458794420519602
    },
    {
      "horizon": 200,
      "p": "3/4",
      "rule": "likelihood_ratio",
      "rejection_probability": 0.9999123915803735,
      "probability_exact": "1291011825628004340287259804289090072624389771767712609880627790851721098238856116537231943692278492706185196912417289369/1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688",
      "expected_observations": 24.43777192404113
    }
  ],
  "null_horizon_100": {
    "fixed_binomial": 0.04431304005703379,
    "peek_binomial": 0.20205809786793333,
    "likelihood_ratio": 0.04088964341296718
  },
  "peeking_to_fixed_ratio_horizon_100": 4.559788667350994,
  "oracle_checks_passed": 18,
  "row_count": 36,
  "synthetic_only": true
}