{
  "version": "2026-09-27",
  "engineSHA256": "afb1d832177fc96c3cd43984841d24e7c07109b4ebdfc61ce65f4b2fad04c972",
  "sourceURL": "https://wizardofodds.com/games/blackjack/expected-return-infinite-deck/",
  "toleranceEVPerOriginalDollar": 5.1e-7,
  "passed": true,
  "evChecks": [
    {
      "hand": "Hard 11",
      "cards": [
        "5",
        "6"
      ],
      "up": "2",
      "expected": [
        -0.292784,
        0.238351,
        0.470641
      ],
      "actual": [
        -0.29278372720927737,
        0.23835074945762985,
        0.47064092333946894
      ],
      "maxError": 2.72790722621874e-7,
      "pass": true,
      "bestAction": "double",
      "referenceAction": "double"
    },
    {
      "hand": "Hard 11",
      "cards": [
        "5",
        "6"
      ],
      "up": "6",
      "expected": [
        -0.153699,
        0.33369,
        0.66738
      ],
      "actual": [
        -0.15369901583000456,
        0.3336900474537847,
        0.6673800949075694
      ],
      "maxError": 9.490756947005963e-8,
      "pass": true,
      "bestAction": "double",
      "referenceAction": "double"
    },
    {
      "hand": "Hard 11",
      "cards": [
        "5",
        "6"
      ],
      "up": "T",
      "expected": [
        -0.54043,
        0.119482,
        0.179689
      ],
      "actual": [
        -0.540430333994985,
        0.1194822307637135,
        0.17968872741114605
      ],
      "maxError": 3.3399498500230607e-7,
      "pass": true,
      "bestAction": "double",
      "referenceAction": "double"
    },
    {
      "hand": "Hard 11",
      "cards": [
        "5",
        "6"
      ],
      "up": "A",
      "expected": [
        -0.666951,
        0.143001,
        0.109061
      ],
      "actual": [
        -0.6669507746855105,
        0.14300128216153024,
        0.10906077977909712
      ],
      "maxError": 2.821615302517344e-7,
      "pass": true,
      "bestAction": "hit",
      "referenceAction": "hit"
    },
    {
      "hand": "Hard 16",
      "cards": [
        "T",
        "6"
      ],
      "up": "2",
      "expected": [
        -0.292784,
        -0.470995,
        -0.94199
      ],
      "actual": [
        -0.29278372720927737,
        -0.47099499297916814,
        -0.9419899859583363
      ],
      "maxError": 2.72790722621874e-7,
      "pass": true,
      "bestAction": "stand",
      "referenceAction": "stand"
    },
    {
      "hand": "Hard 16",
      "cards": [
        "T",
        "6"
      ],
      "up": "6",
      "expected": [
        -0.153699,
        -0.430927,
        -0.861853
      ],
      "actual": [
        -0.15369901583000456,
        -0.4309265027291166,
        -0.8618530054582332
      ],
      "maxError": 4.972708834150019e-7,
      "pass": true,
      "bestAction": "stand",
      "referenceAction": "stand"
    },
    {
      "hand": "Hard 16",
      "cards": [
        "T",
        "6"
      ],
      "up": "T",
      "expected": [
        -0.54043,
        -0.539826,
        -1.079653
      ],
      "actual": [
        -0.540430333994985,
        -0.5398263462810868,
        -1.0796526925621737
      ],
      "maxError": 3.4628108680490044e-7,
      "pass": true,
      "bestAction": "hit",
      "referenceAction": "hit"
    },
    {
      "hand": "Hard 16",
      "cards": [
        "T",
        "6"
      ],
      "up": "A",
      "expected": [
        -0.666951,
        -0.517149,
        -1.034297
      ],
      "actual": [
        -0.6669507746855105,
        -0.5171486532514871,
        -1.0342973065029741
      ],
      "maxError": 3.467485129027281e-7,
      "pass": true,
      "bestAction": "hit",
      "referenceAction": "hit"
    },
    {
      "hand": "Soft 18",
      "cards": [
        "A",
        "7"
      ],
      "up": "2",
      "expected": [
        0.121742,
        0.062905,
        0.11975
      ],
      "actual": [
        0.12174190222088777,
        0.06290506947151775,
        0.11974956336724496
      ],
      "maxError": 4.366327550353599e-7,
      "pass": true,
      "bestAction": "stand",
      "referenceAction": "stand"
    },
    {
      "hand": "Soft 18",
      "cards": [
        "A",
        "7"
      ],
      "up": "6",
      "expected": [
        0.283444,
        0.190753,
        0.381506
      ],
      "actual": [
        0.28344391604689845,
        0.19075324103939656,
        0.3815064820787931
      ],
      "maxError": 4.820787931070214e-7,
      "pass": true,
      "bestAction": "double",
      "referenceAction": "double"
    },
    {
      "hand": "Soft 18",
      "cards": [
        "A",
        "7"
      ],
      "up": "T",
      "expected": [
        -0.178301,
        -0.143808,
        -0.346892
      ],
      "actual": [
        -0.17830123379648954,
        -0.14380812317405367,
        -0.3468919804643883
      ],
      "maxError": 2.337964895571254e-7,
      "pass": true,
      "bestAction": "hit",
      "referenceAction": "hit"
    },
    {
      "hand": "Soft 18",
      "cards": [
        "A",
        "7"
      ],
      "up": "A",
      "expected": [
        -0.100199,
        -0.092935,
        -0.362813
      ],
      "actual": [
        -0.10019887561319057,
        -0.09293549176928406,
        -0.36281276808253127
      ],
      "maxError": 4.917692840583632e-7,
      "pass": true,
      "bestAction": "hit",
      "referenceAction": "hit"
    }
  ],
  "dealerChecks": [
    {
      "rule": "S17",
      "up": "A",
      "actual": [
        0.18891729969077328,
        0.18891729969077328,
        0.18891729969077328,
        0.18891729969077328,
        0.07780618857966215,
        0.16652461265724486
      ],
      "expected": [
        0.18891729969077325,
        0.18891729969077325,
        0.18891729969077325,
        0.18891729969077325,
        0.07780618857966215,
        0.16652461265724483
      ],
      "maxError": 2.7755575615628914e-17,
      "pass": true
    },
    {
      "rule": "S17",
      "up": "2",
      "actual": [
        0.1398091395277353,
        0.13490735037469445,
        0.1296554334250078,
        0.12402645577124112,
        0.11799348450596005,
        0.35360813639536137
      ],
      "expected": [
        0.1398091395277353,
        0.13490735037469445,
        0.1296554334250078,
        0.1240264557712411,
        0.11799348450596006,
        0.35360813639536137
      ],
      "maxError": 1.3877787807814457e-17,
      "pass": true
    },
    {
      "rule": "S17",
      "up": "3",
      "actual": [
        0.13503398781113995,
        0.13048232645474486,
        0.125580537301704,
        0.12032862035201736,
        0.11469964269825067,
        0.3738748853821433
      ],
      "expected": [
        0.13503398781113995,
        0.13048232645474486,
        0.125580537301704,
        0.12032862035201736,
        0.11469964269825067,
        0.3738748853821433
      ],
      "maxError": 0,
      "pass": true
    },
    {
      "rule": "S17",
      "up": "4",
      "actual": [
        0.13048973584959825,
        0.12593807449320316,
        0.12138641313680808,
        0.1164846239837672,
        0.11123270703408057,
        0.39446844550254284
      ],
      "expected": [
        0.13048973584959822,
        0.12593807449320316,
        0.12138641313680806,
        0.11648462398376722,
        0.11123270703408057,
        0.3944684455025429
      ],
      "maxError": 5.551115123125783e-17,
      "pass": true
    },
    {
      "rule": "S17",
      "up": "5",
      "actual": [
        0.1222512852705508,
        0.1222512852705508,
        0.11769962391415573,
        0.11314796255776065,
        0.10824617340471979,
        0.4164036695822624
      ],
      "expected": [
        0.1222512852705508,
        0.1222512852705508,
        0.11769962391415573,
        0.11314796255776063,
        0.10824617340471979,
        0.4164036695822624
      ],
      "maxError": 1.3877787807814457e-17,
      "pass": true
    },
    {
      "rule": "S17",
      "up": "6",
      "actual": [
        0.16543817650334638,
        0.1062665788702103,
        0.1062665788702103,
        0.10171491751381523,
        0.09716325615742014,
        0.4231504920849978
      ],
      "expected": [
        0.1654381765033464,
        0.1062665788702103,
        0.1062665788702103,
        0.10171491751381523,
        0.09716325615742014,
        0.4231504920849978
      ],
      "maxError": 2.7755575615628914e-17,
      "pass": true
    },
    {
      "rule": "S17",
      "up": "7",
      "actual": [
        0.36856619379423866,
        0.13779696302500788,
        0.07862536539187177,
        0.07862536539187177,
        0.07407370403547668,
        0.26231240836153336
      ],
      "expected": [
        0.36856619379423866,
        0.13779696302500785,
        0.07862536539187177,
        0.07862536539187177,
        0.07407370403547668,
        0.26231240836153336
      ],
      "maxError": 2.7755575615628914e-17,
      "pass": true
    },
    {
      "rule": "S17",
      "up": "8",
      "actual": [
        0.12856654444917004,
        0.3593357752184008,
        0.12856654444917004,
        0.06939494681603392,
        0.06939494681603392,
        0.24474124225119143
      ],
      "expected": [
        0.12856654444917004,
        0.3593357752184008,
        0.12856654444917,
        0.06939494681603392,
        0.06939494681603392,
        0.24474124225119143
      ],
      "maxError": 2.7755575615628914e-17,
      "pass": true
    },
    {
      "rule": "S17",
      "up": "9",
      "actual": [
        0.11999544148589202,
        0.11999544148589202,
        0.3507646722551228,
        0.11999544148589202,
        0.060823843852755924,
        0.2284251594344453
      ],
      "expected": [
        0.11999544148589202,
        0.11999544148589202,
        0.3507646722551228,
        0.11999544148589202,
        0.060823843852755924,
        0.2284251594344453
      ],
      "maxError": 0,
      "pass": true
    },
    {
      "rule": "S17",
      "up": "T",
      "actual": [
        0.12070970006616517,
        0.12070970006616517,
        0.12070970006616517,
        0.37070970006616516,
        0.037376366732831845,
        0.22978483300250746
      ],
      "expected": [
        0.12070970006616517,
        0.12070970006616517,
        0.12070970006616517,
        0.37070970006616516,
        0.037376366732831845,
        0.22978483300250746
      ],
      "maxError": 0,
      "pass": true
    },
    {
      "rule": "H17",
      "up": "A",
      "actual": [
        0.0830458104209385,
        0.20685063100162077,
        0.20685063100162077,
        0.20685063100162077,
        0.09573951989050963,
        0.20066277668368984
      ],
      "expected": [
        0.08304581042093848,
        0.2068506310016207,
        0.2068506310016207,
        0.2068506310016207,
        0.09573951989050962,
        0.20066277668368976
      ],
      "maxError": 8.326672684688674e-17,
      "pass": true
    },
    {
      "rule": "H17",
      "up": "2",
      "actual": [
        0.13013408258322726,
        0.1365461863146987,
        0.13129426936501204,
        0.12566529171124535,
        0.11963232044596428,
        0.35672784957985254
      ],
      "expected": [
        0.13013408258322723,
        0.1365461863146987,
        0.13129426936501204,
        0.12566529171124535,
        0.11963232044596431,
        0.3567278495798525
      ],
      "maxError": 5.551115123125783e-17,
      "pass": true
    },
    {
      "rule": "H17",
      "up": "3",
      "actual": [
        0.12632803105865642,
        0.13195700871242308,
        0.12705521955938223,
        0.12180330260969562,
        0.1161743249559289,
        0.3766821131039139
      ],
      "expected": [
        0.1263280310586564,
        0.13195700871242308,
        0.12705521955938223,
        0.1218033026096956,
        0.11617432495592891,
        0.37668211310391386
      ],
      "maxError": 5.551115123125783e-17,
      "pass": true
    },
    {
      "rule": "H17",
      "up": "4",
      "actual": [
        0.12240563315086352,
        0.12730742230390438,
        0.1227557609475093,
        0.11785397179446844,
        0.1126020548447818,
        0.39707515695847273
      ],
      "expected": [
        0.1224056331508635,
        0.12730742230390435,
        0.12275576094750927,
        0.11785397179446842,
        0.1126020548447818,
        0.39707515695847273
      ],
      "maxError": 2.7755575615628914e-17,
      "pass": true
    },
    {
      "rule": "H17",
      "up": "5",
      "actual": [
        0.11835893952671557,
        0.12291060088311065,
        0.11835893952671557,
        0.11380727817032049,
        0.10890548901727963,
        0.41765875287585824
      ],
      "expected": [
        0.11835893952671556,
        0.12291060088311065,
        0.11835893952671557,
        0.11380727817032048,
        0.10890548901727963,
        0.4176587528758583
      ],
      "maxError": 5.551115123125783e-17,
      "pass": true
    },
    {
      "rule": "H17",
      "up": "6",
      "actual": [
        0.11483768183348829,
        0.11483768183348829,
        0.11483768183348829,
        0.11028602047709322,
        0.10573435912069813,
        0.4394665749017439
      ],
      "expected": [
        0.1148376818334883,
        0.1148376818334883,
        0.1148376818334883,
        0.11028602047709321,
        0.10573435912069815,
        0.4394665749017439
      ],
      "maxError": 1.3877787807814457e-17,
      "pass": true
    },
    {
      "rule": "H17",
      "up": "7",
      "actual": [
        0.36856619379423866,
        0.13779696302500788,
        0.07862536539187177,
        0.07862536539187177,
        0.07407370403547668,
        0.26231240836153336
      ],
      "expected": [
        0.36856619379423866,
        0.13779696302500785,
        0.07862536539187177,
        0.07862536539187177,
        0.07407370403547668,
        0.26231240836153336
      ],
      "maxError": 2.7755575615628914e-17,
      "pass": true
    },
    {
      "rule": "H17",
      "up": "8",
      "actual": [
        0.12856654444917004,
        0.3593357752184008,
        0.12856654444917004,
        0.06939494681603392,
        0.06939494681603392,
        0.24474124225119143
      ],
      "expected": [
        0.12856654444917004,
        0.3593357752184008,
        0.12856654444917,
        0.06939494681603392,
        0.06939494681603392,
        0.24474124225119143
      ],
      "maxError": 2.7755575615628914e-17,
      "pass": true
    },
    {
      "rule": "H17",
      "up": "9",
      "actual": [
        0.11999544148589202,
        0.11999544148589202,
        0.3507646722551228,
        0.11999544148589202,
        0.060823843852755924,
        0.2284251594344453
      ],
      "expected": [
        0.11999544148589202,
        0.11999544148589202,
        0.3507646722551228,
        0.11999544148589202,
        0.060823843852755924,
        0.2284251594344453
      ],
      "maxError": 0,
      "pass": true
    },
    {
      "rule": "H17",
      "up": "T",
      "actual": [
        0.12070970006616517,
        0.12070970006616517,
        0.12070970006616517,
        0.37070970006616516,
        0.037376366732831845,
        0.22978483300250746
      ],
      "expected": [
        0.12070970006616517,
        0.12070970006616517,
        0.12070970006616517,
        0.37070970006616516,
        0.037376366732831845,
        0.22978483300250746
      ],
      "maxError": 0,
      "pass": true
    }
  ],
  "finiteDiagnostics": [
    {
      "decks": 1,
      "rule": "S17",
      "up": "A",
      "model": [
        0.18632826508082484,
        0.19056603102489905,
        0.19056603102489905,
        0.19056603102489905,
        0.07628031673918478,
        0.1656933251052931
      ],
      "exact": [
        0.18378593840602184,
        0.1908901660115011,
        0.18867989934595686,
        0.19169199620884192,
        0.0751370569466739,
        0.16981494308100437
      ],
      "maxErrorPercentagePoints": 0.4121617975711256,
      "bustErrorPercentagePoints": -0.4121617975711256
    },
    {
      "decks": 6,
      "rule": "S17",
      "up": "A",
      "model": [
        0.18848721143107522,
        0.18918750132044132,
        0.18918750132044132,
        0.18918750132044132,
        0.07755959434369714,
        0.16639069026390385
      ],
      "exact": [
        0.1880705682688244,
        0.1892349021455324,
        0.18890566655043814,
        0.18936239067956367,
        0.07739348450184845,
        0.16703298785379297
      ],
      "maxErrorPercentagePoints": 0.06422975898891237,
      "bustErrorPercentagePoints": -0.06422975898891237
    },
    {
      "decks": 1,
      "rule": "S17",
      "up": "2",
      "model": [
        0.1382489498039504,
        0.13316542845320023,
        0.13056490381458757,
        0.12489693605184549,
        0.11882151984991651,
        0.3543022620264998
      ],
      "exact": [
        0.13897583298169436,
        0.1317622707617926,
        0.1318154534260218,
        0.12394809967438508,
        0.12052579999851118,
        0.35297254315759496
      ],
      "maxErrorPercentagePoints": 0.17042801485946668,
      "bustErrorPercentagePoints": 0.13297188689048167
    },
    {
      "decks": 6,
      "rule": "S17",
      "up": "2",
      "model": [
        0.13954450567912113,
        0.13462218054445552,
        0.1298068307843887,
        0.12417145408174085,
        0.11813145743096799,
        0.353723571479326
      ],
      "exact": [
        0.13965640029513784,
        0.13438862674532268,
        0.13001965464336276,
        0.12401888321248336,
        0.11841272954673111,
        0.3535037055569623
      ],
      "maxErrorPercentagePoints": 0.02812721157631204,
      "bustErrorPercentagePoints": 0.02198659223636712
    },
    {
      "decks": 1,
      "rule": "S17",
      "up": "3",
      "model": [
        0.13231847276747624,
        0.12977484217788432,
        0.12476856755263857,
        0.12180580524123638,
        0.11611317841375818,
        0.3752191338470063
      ],
      "exact": [
        0.13031318483158127,
        0.1309463861235466,
        0.12376109486546644,
        0.12334456949789817,
        0.11604681572217115,
        0.37558794895933634
      ],
      "maxErrorPercentagePoints": 0.2005287935894967,
      "bustErrorPercentagePoints": -0.03688151123300565
    },
    {
      "decks": 6,
      "rule": "S17",
      "up": "3",
      "model": [
        0.13459403251244148,
        0.1303667344932112,
        0.12541058062840282,
        0.12057311165154891,
        0.11493452547614985,
        0.374121015238246
      ],
      "exact": [
        0.13429575365167448,
        0.1305388238768863,
        0.1252260120622163,
        0.1208174086547274,
        0.11492790457954435,
        0.3741940971749512
      ],
      "maxErrorPercentagePoints": 0.02982788607669984,
      "bustErrorPercentagePoints": -0.007308193670524377
    },
    {
      "decks": 1,
      "rule": "S17",
      "up": "4",
      "model": [
        0.13013158402363734,
        0.11599735366393797,
        0.11957931174212579,
        0.11666507787615187,
        0.11362750593146748,
        0.40399916676267966
      ],
      "exact": [
        0.13097265148876247,
        0.11416293951400722,
        0.12067875418066623,
        0.11628648799961815,
        0.11509609619105546,
        0.4028030706258905
      ],
      "maxErrorPercentagePoints": 0.18344141499307548,
      "bustErrorPercentagePoints": 0.11960961367891709
    },
    {
      "decks": 6,
      "rule": "S17",
      "up": "4",
      "model": [
        0.13042894080901926,
        0.12433062791693057,
        0.12109252735440075,
        0.11651197077904293,
        0.11162397870123761,
        0.3960119544393691
      ],
      "exact": [
        0.1305557228204866,
        0.12406151628064824,
        0.12127156506562764,
        0.11644067621301624,
        0.11186560158556608,
        0.3958049180346553
      ],
      "maxErrorPercentagePoints": 0.02691116362823348,
      "bustErrorPercentagePoints": 0.02070364047138118
    },
    {
      "decks": 1,
      "rule": "S17",
      "up": "5",
      "model": [
        0.12250872301104417,
        0.12233156473565936,
        0.11743880364380946,
        0.10329648461474827,
        0.10651466734400362,
        0.42790975665073516
      ],
      "exact": [
        0.1196872903844351,
        0.12348305862492073,
        0.11690947571246704,
        0.10469365813771475,
        0.10632136429637964,
        0.4289051528440827
      ],
      "maxErrorPercentagePoints": 0.2821432626609069,
      "bustErrorPercentagePoints": -0.09953961933475419
    },
    {
      "decks": 6,
      "rule": "S17",
      "up": "5",
      "model": [
        0.1222913971083492,
        0.12226281212433263,
        0.11765552219793361,
        0.11155700927823801,
        0.10796557951531809,
        0.4182676797758286
      ],
      "exact": [
        0.12184345848442756,
        0.12243712207542727,
        0.11757537804257884,
        0.11179292356038388,
        0.10794517554193274,
        0.4184059422952498
      ],
      "maxErrorPercentagePoints": 0.04479386239216454,
      "bustErrorPercentagePoints": -0.013826251942117285
    },
    {
      "decks": 1,
      "rule": "S17",
      "up": "6",
      "model": [
        0.16660540908326815,
        0.10674332959738149,
        0.10622833250808149,
        0.1013834922233508,
        0.09649745705994034,
        0.4225419795279778
      ],
      "exact": [
        0.1669476681205939,
        0.10645402905927319,
        0.10719186053213837,
        0.10070493166664622,
        0.09787847663196508,
        0.42082303398938326
      ],
      "maxErrorPercentagePoints": 0.17189455385945296,
      "bustErrorPercentagePoints": 0.17189455385945296
    },
    {
      "decks": 6,
      "rule": "S17",
      "up": "6",
      "model": [
        0.16563716541893692,
        0.1063001759362991,
        0.10626523300798356,
        0.10166216980295635,
        0.09705626351452178,
        0.42307899231930246
      ],
      "exact": [
        0.16570661089303823,
        0.10619404424062566,
        0.10643123825273719,
        0.10155092255566608,
        0.09727557969585647,
        0.4228416043620765
      ],
      "maxErrorPercentagePoints": 0.023738795722594297,
      "bustErrorPercentagePoints": 0.023738795722594297
    },
    {
      "decks": 1,
      "rule": "S17",
      "up": "7",
      "model": [
        0.37387706166421086,
        0.13846232675833003,
        0.07823470011427319,
        0.07808496034928422,
        0.07360387070743835,
        0.25773708040646337
      ],
      "exact": [
        0.3723448664078644,
        0.13858338154873423,
        0.0773344312748226,
        0.07889666587161125,
        0.07298698778514386,
        0.25985366711182367
      ],
      "maxErrorPercentagePoints": 0.21165867053603016,
      "bustErrorPercentagePoints": -0.21165867053603016
    },
    {
      "decks": 6,
      "rule": "S17",
      "up": "7",
      "model": [
        0.3694422267167717,
        0.1379118239083624,
        0.07856745084949955,
        0.07854375486392674,
        0.07395200866670183,
        0.26158273499473794
      ],
      "exact": [
        0.3692080352605309,
        0.13793092270091056,
        0.07842801423089622,
        0.0786815762773251,
        0.07381577566212824,
        0.261935675868209
      ],
      "maxErrorPercentagePoints": 0.03529408734710415,
      "bustErrorPercentagePoints": -0.03529408734710415
    },
    {
      "decks": 1,
      "rule": "S17",
      "up": "8",
      "model": [
        0.1308152603857155,
        0.36457150798279353,
        0.1292773903357347,
        0.06905922386884038,
        0.06891968625569332,
        0.23735693117122256
      ],
      "exact": [
        0.13085746416975672,
        0.36298936571236573,
        0.12944463829318345,
        0.06828976376242757,
        0.06979142147145628,
        0.23862734659081025
      ],
      "maxErrorPercentagePoints": 0.15821422704278,
      "bustErrorPercentagePoints": -0.1270415419587695
    },
    {
      "decks": 6,
      "rule": "S17",
      "up": "8",
      "model": [
        0.12893535036307702,
        0.360198467990066,
        0.12868721397077337,
        0.06934431863197095,
        0.06932221440273335,
        0.2435124346413795
      ],
      "exact": [
        0.1289399921401881,
        0.35995491386458023,
        0.12872316780058843,
        0.06921887942591434,
        0.06947014881836389,
        0.24369289795036514
      ],
      "maxErrorPercentagePoints": 0.02435541254857676,
      "bustErrorPercentagePoints": -0.018046330898563445
    },
    {
      "decks": 1,
      "rule": "S17",
      "up": "9",
      "model": [
        0.12338003684683549,
        0.10377219370958059,
        0.3586741544938943,
        0.12184216679685472,
        0.06174461758878242,
        0.23058683056405246
      ],
      "exact": [
        0.12188622720133381,
        0.10392095413558577,
        0.35739125005537214,
        0.1222502790817221,
        0.06110882959412565,
        0.2334424599318605
      ],
      "maxErrorPercentagePoints": 0.28556293678080324,
      "bustErrorPercentagePoints": -0.28556293678080324
    },
    {
      "decks": 6,
      "rule": "S17",
      "up": "9",
      "model": [
        0.12054726479958917,
        0.11733183071598788,
        0.3520585188188818,
        0.12029912840728553,
        0.060975381857599806,
        0.22878787540065593
      ],
      "exact": [
        0.12030985477727106,
        0.11734847635517628,
        0.35185420678249657,
        0.12036839279403887,
        0.06087717596906466,
        0.22924189332195266
      ],
      "maxErrorPercentagePoints": 0.045401792129673435,
      "bustErrorPercentagePoints": -0.045401792129673435
    },
    {
      "decks": 1,
      "rule": "S17",
      "up": "T",
      "model": [
        0.124143704386313,
        0.124143704386313,
        0.124143704386313,
        0.35818625757780237,
        0.0390373214075896,
        0.230345307855669
      ],
      "exact": [
        0.12415591134597795,
        0.12248568110693409,
        0.12442090777303304,
        0.3568688095231401,
        0.03956963453399546,
        0.23249905571691937
      ],
      "maxErrorPercentagePoints": 0.21537478612503602,
      "bustErrorPercentagePoints": -0.21537478612503602
    },
    {
      "decks": 6,
      "rule": "S17",
      "up": "T",
      "model": [
        0.1212694575763801,
        0.1212694575763801,
        0.1212694575763801,
        0.36865621715826163,
        0.037645764196589146,
        0.22988964591600902
      ],
      "exact": [
        0.1212726718472115,
        0.12100690986281365,
        0.12130582749005003,
        0.3684471169558061,
        0.0377289341781858,
        0.23023853966593302
      ],
      "maxErrorPercentagePoints": 0.03488937499240008,
      "bustErrorPercentagePoints": -0.03488937499240008
    },
    {
      "decks": 1,
      "rule": "H17",
      "up": "A",
      "model": [
        0.08188495751021443,
        0.2056347821245993,
        0.20877127026645811,
        0.20877127026645811,
        0.09448555598074385,
        0.20045216385152614
      ],
      "exact": [
        0.08177626410416156,
        0.2053864526767092,
        0.20616117986950738,
        0.2094601518048742,
        0.09264215991509313,
        0.20457379162965447
      ],
      "maxErrorPercentagePoints": 0.41216277781283284,
      "bustErrorPercentagePoints": -0.41216277781283284
    },
    {
      "decks": 6,
      "rule": "H17",
      "up": "A",
      "model": [
        0.08285314934222736,
        0.20664833020510134,
        0.20716531076900455,
        0.20716531076900455,
        0.09553740379226035,
        0.20063049512240202
      ],
      "exact": [
        0.08284238468340382,
        0.20659330689639774,
        0.20675720302309306,
        0.20726229490776277,
        0.0952641196263742,
        0.20128069086296843
      ],
      "maxErrorPercentagePoints": 0.0650195740566406,
      "bustErrorPercentagePoints": -0.0650195740566406
    },
    {
      "decks": 1,
      "rule": "H17",
      "up": "2",
      "model": [
        0.12866794656013125,
        0.13480893860072377,
        0.13195050805851208,
        0.126570403511994,
        0.12049498731006507,
        0.35750721595857377
      ],
      "exact": [
        0.12977908864888707,
        0.13310821611252655,
        0.1331718043742539,
        0.1256225411662847,
        0.12197327963417637,
        0.35634507006387134
      ],
      "maxErrorPercentagePoints": 0.17007224881972205,
      "bustErrorPercentagePoints": 0.11621458947024266
    },
    {
      "decks": 6,
      "rule": "H17",
      "up": "2",
      "model": [
        0.12989112546821935,
        0.13626074757398482,
        0.13140304296748118,
        0.1258149143691532,
        0.11977491771838034,
        0.35685525190278133
      ],
      "exact": [
        0.13007092130803208,
        0.13597754635791987,
        0.13160749596331034,
        0.12566171004477972,
        0.12002180115157297,
        0.3566605251743851
      ],
      "maxErrorPercentagePoints": 0.02832012160649544,
      "bustErrorPercentagePoints": 0.019472672839621064
    },
    {
      "decks": 1,
      "rule": "H17",
      "up": "3",
      "model": [
        0.12533021927402407,
        0.13097729635255448,
        0.1259694517956114,
        0.12281855067778254,
        0.11733597224470432,
        0.3775685096553231
      ],
      "exact": [
        0.12352724035820142,
        0.1319356634798044,
        0.12494940518711889,
        0.12420981014185288,
        0.11730261320931372,
        0.37807526762370863
      ],
      "maxErrorPercentagePoints": 0.18029789158226506,
      "bustErrorPercentagePoints": -0.050675796838550724
    },
    {
      "decks": 6,
      "rule": "H17",
      "up": "3",
      "model": [
        0.1261669341953348,
        0.1317978824864142,
        0.12684142317981625,
        0.12196697885440062,
        0.11636964172126464,
        0.37685713956276967
      ],
      "exact": [
        0.1258997289947967,
        0.13193044549228247,
        0.12665628448381486,
        0.12218466869538952,
        0.11637065647629996,
        0.3769582158574165
      ],
      "maxErrorPercentagePoints": 0.026720520053810648,
      "bustErrorPercentagePoints": -0.01010762946468402
    },
    {
      "decks": 1,
      "rule": "H17",
      "up": "4",
      "model": [
        0.12179448621018885,
        0.11743568585206622,
        0.12101585039548271,
        0.11810006786120646,
        0.11483801099312382,
        0.4068158986879319
      ],
      "exact": [
        0.12278573638969786,
        0.11537400253927901,
        0.12190728991606226,
        0.11778986776657273,
        0.11634754819543619,
        0.40579555519295196
      ],
      "maxErrorPercentagePoints": 0.20616833127872075,
      "bustErrorPercentagePoints": 0.1020343494979925
    },
    {
      "decks": 6,
      "rule": "H17",
      "up": "4",
      "model": [
        0.12230345407452137,
        0.1257111823223055,
        0.12247280691721467,
        0.11789196415927954,
        0.11296831930983861,
        0.39865227321684044
      ],
      "exact": [
        0.1224579962259538,
        0.1254051093671251,
        0.12262001698325395,
        0.11783040839134942,
        0.11321659941806522,
        0.3984698696142525
      ],
      "maxErrorPercentagePoints": 0.030607295518039757,
      "bustErrorPercentagePoints": 0.018240360258792165
    },
    {
      "decks": 1,
      "rule": "H17",
      "up": "5",
      "model": [
        0.11848853097491341,
        0.12301252426828725,
        0.11811897755618857,
        0.10397581128960418,
        0.10719308033133451,
        0.42921107557967214
      ],
      "exact": [
        0.11665639069801104,
        0.12383758785566946,
        0.11744780982502048,
        0.10523910332781669,
        0.1068581592178635,
        0.42996094907561877
      ],
      "maxErrorPercentagePoints": 0.1832140276902372,
      "bustErrorPercentagePoints": -0.07498734959466291
    },
    {
      "decks": 6,
      "rule": "H17",
      "up": "5",
      "model": [
        0.11837789178399834,
        0.12292569654243563,
        0.11831828414621098,
        0.11221963930564212,
        0.10862806744145999,
        0.41953042078025315
      ],
      "exact": [
        0.11808926947126741,
        0.12304232692219871,
        0.11821618921554142,
        0.11243495699810203,
        0.1085857085970396,
        0.4196315487958509
      ],
      "maxErrorPercentagePoints": 0.028862231273092676,
      "bustErrorPercentagePoints": -0.01011280155977512
    },
    {
      "decks": 1,
      "rule": "H17",
      "up": "6",
      "model": [
        0.11545028881443833,
        0.11544452401897994,
        0.11495022106722293,
        0.11006738936023544,
        0.105170537369881,
        0.4389170393692424
      ],
      "exact": [
        0.11610640037698705,
        0.11380968670932058,
        0.1160555577223928,
        0.10961530679418723,
        0.1066571641785224,
        0.4377558842185899
      ],
      "maxErrorPercentagePoints": 0.16348373096593538,
      "bustErrorPercentagePoints": 0.11611551506525153
    },
    {
      "decks": 6,
      "rule": "H17",
      "up": "6",
      "model": [
        0.11494485675581001,
        0.11489331624462458,
        0.11485769346246177,
        0.11025230220655535,
        0.10564468607679525,
        0.4394071452537532
      ],
      "exact": [
        0.11506400423891709,
        0.1145743026041491,
        0.11504290978496369,
        0.11017741773403981,
        0.10588222415390315,
        0.43925914148402734
      ],
      "maxErrorPercentagePoints": 0.03190136404754851,
      "bustErrorPercentagePoints": 0.014800376972584628
    },
    {
      "decks": 1,
      "rule": "H17",
      "up": "7",
      "model": [
        0.37387706166421086,
        0.13846232675833003,
        0.07823470011427319,
        0.07808496034928422,
        0.07360387070743835,
        0.25773708040646337
      ],
      "exact": [
        0.3723448664078644,
        0.13858338154873423,
        0.0773344312748226,
        0.07889666587161125,
        0.07298698778514386,
        0.25985366711182367
      ],
      "maxErrorPercentagePoints": 0.21165867053603016,
      "bustErrorPercentagePoints": -0.21165867053603016
    },
    {
      "decks": 6,
      "rule": "H17",
      "up": "7",
      "model": [
        0.3694422267167717,
        0.1379118239083624,
        0.07856745084949955,
        0.07854375486392674,
        0.07395200866670183,
        0.26158273499473794
      ],
      "exact": [
        0.3692080352605309,
        0.13793092270091056,
        0.07842801423089622,
        0.0786815762773251,
        0.07381577566212824,
        0.261935675868209
      ],
      "maxErrorPercentagePoints": 0.03529408734710415,
      "bustErrorPercentagePoints": -0.03529408734710415
    },
    {
      "decks": 1,
      "rule": "H17",
      "up": "8",
      "model": [
        0.1308152603857155,
        0.36457150798279353,
        0.1292773903357347,
        0.06905922386884038,
        0.06891968625569332,
        0.23735693117122256
      ],
      "exact": [
        0.13085746416975672,
        0.36298936571236573,
        0.12944463829318345,
        0.06828976376242757,
        0.06979142147145628,
        0.23862734659081025
      ],
      "maxErrorPercentagePoints": 0.15821422704278,
      "bustErrorPercentagePoints": -0.1270415419587695
    },
    {
      "decks": 6,
      "rule": "H17",
      "up": "8",
      "model": [
        0.12893535036307702,
        0.360198467990066,
        0.12868721397077337,
        0.06934431863197095,
        0.06932221440273335,
        0.2435124346413795
      ],
      "exact": [
        0.1289399921401881,
        0.35995491386458023,
        0.12872316780058843,
        0.06921887942591434,
        0.06947014881836389,
        0.24369289795036514
      ],
      "maxErrorPercentagePoints": 0.02435541254857676,
      "bustErrorPercentagePoints": -0.018046330898563445
    },
    {
      "decks": 1,
      "rule": "H17",
      "up": "9",
      "model": [
        0.12338003684683549,
        0.10377219370958059,
        0.3586741544938943,
        0.12184216679685472,
        0.06174461758878242,
        0.23058683056405246
      ],
      "exact": [
        0.12188622720133381,
        0.10392095413558577,
        0.35739125005537214,
        0.1222502790817221,
        0.06110882959412565,
        0.2334424599318605
      ],
      "maxErrorPercentagePoints": 0.28556293678080324,
      "bustErrorPercentagePoints": -0.28556293678080324
    },
    {
      "decks": 6,
      "rule": "H17",
      "up": "9",
      "model": [
        0.12054726479958917,
        0.11733183071598788,
        0.3520585188188818,
        0.12029912840728553,
        0.060975381857599806,
        0.22878787540065593
      ],
      "exact": [
        0.12030985477727106,
        0.11734847635517628,
        0.35185420678249657,
        0.12036839279403887,
        0.06087717596906466,
        0.22924189332195266
      ],
      "maxErrorPercentagePoints": 0.045401792129673435,
      "bustErrorPercentagePoints": -0.045401792129673435
    },
    {
      "decks": 1,
      "rule": "H17",
      "up": "T",
      "model": [
        0.124143704386313,
        0.124143704386313,
        0.124143704386313,
        0.35818625757780237,
        0.0390373214075896,
        0.230345307855669
      ],
      "exact": [
        0.12415591134597795,
        0.12248568110693409,
        0.12442090777303304,
        0.3568688095231401,
        0.03956963453399546,
        0.23249905571691937
      ],
      "maxErrorPercentagePoints": 0.21537478612503602,
      "bustErrorPercentagePoints": -0.21537478612503602
    },
    {
      "decks": 6,
      "rule": "H17",
      "up": "T",
      "model": [
        0.1212694575763801,
        0.1212694575763801,
        0.1212694575763801,
        0.36865621715826163,
        0.037645764196589146,
        0.22988964591600902
      ],
      "exact": [
        0.1212726718472115,
        0.12100690986281365,
        0.12130582749005003,
        0.3684471169558061,
        0.0377289341781858,
        0.23023853966593302
      ],
      "maxErrorPercentagePoints": 0.03488937499240008,
      "bustErrorPercentagePoints": -0.03488937499240008
    }
  ],
  "splitChecks": [
    {
      "pair": "A,A",
      "up": "6",
      "model": 0.6673800949075694,
      "reference": 0.66738,
      "error": 9.490756947005963e-8,
      "matchedRules": true,
      "note": "One card to split aces; no resplit."
    },
    {
      "pair": "A,A",
      "up": "T",
      "model": 0.17968872741114617,
      "reference": 0.179689,
      "error": -2.725888538224197e-7,
      "matchedRules": true,
      "note": "One card to split aces; no resplit."
    },
    {
      "pair": "8,8",
      "up": "6",
      "model": 0.3255333973851646,
      "reference": 0.409329,
      "error": -0.08379560261483537,
      "matchedRules": false,
      "note": "Diagnostic only: engine has no resplits; reference allows up to four hands."
    },
    {
      "pair": "8,8",
      "up": "T",
      "model": -0.4894876231609265,
      "reference": -0.480686,
      "error": -0.008801623160926475,
      "matchedRules": false,
      "note": "Diagnostic only: engine has no resplits; reference allows up to four hands."
    }
  ],
  "insurance": {
    "actual": -0.07692307692307687,
    "expected": -0.07692307692307693
  },
  "limitations": [
    "Not external certification. Independent verifier is authored in this repository.",
    "EV reference cases use infinite proportions; visible cards are not removed.",
    "Finite-deck diagnostics cover dealer outcomes only, before player cards are known, conditioned on no dealer blackjack. They do not validate finite-deck player EV.",
    "No depleted-shoe, full-game house-edge, resplit, surrender, or natural-blackjack payout certification."
  ]
}
