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정밀 확장 탐측과 정밀 고정 탐측의 확률 계산 및 데이터 분석


nga 본문에선 독립 시행과 Pseudo Random Distribution 2가지 경우를 비교하는데

Pseudo Random Distribution (유사 무작위 분포, 의사 난수 분포, PRD)는 

간단히 설명하면 운 없는 사람들을 위한 또 하나의 천장 같은 것으로

특정 회차 이후에도 발생하지 않는 경우 확률이 점점 올라가는 시스템


실제로 적용된 게임에는 워크래프트3가 있는데

크리티컬 확률 25%의 첫 공격은 25%보다 낮은 8.475%에서 시작 

크리티컬이 발생하지 않으면 8.475%p만큼 증가하며 최종적으로 크리티컬이 발생한 경우 다시 8.475% 시작


해당 PRD의 평균 확률은 24.9%로 기존의 25%와 비슷하고 독립 시행에 비해 표준편차가 줄어들어

10만원 무과금 50만원 무과금 같은 운빨좆망겜과 같은 극단적인 분산이 줄어듬 


모바일 게임 중에는 원신 기본 0.6% 확률업 구간인 캐릭터 74회 이후 6%p씩 올라가는 경우가 바로 이 경우

에테르 게이저에선 PRD를 가챠에 적용시켰는지 확인하기엔 표본 획득에 어려움이 많아

결과값은 다르지만 결론은 동일하기 때문에 별도로 설명하지 않음 궁금한 사람은 가서 보면 됨


정밀 확장 탐측 표
시행 횟수
S 확률
누적 미등장 확률
정확한 S  확률기대값
1

0.016

0.984

0.016

0.016

2

0.016

0.968256

0.015744

0.031488

3

0.016

0.952763904

0.015492096

0.046476288

4

0.016

0.937519682

0.015244222

0.06097689

5

0.016

0.922519367

0.015000315

0.075001575

6

0.016

0.907759057

0.01476031

0.088561859

7

0.016

0.893234912

0.014524145

0.101669014

8

0.016

0.878943153

0.014291759

0.114334069

9

0.016

0.864880063

0.01406309

0.126567814

10

0.016

0.851041982

0.013838081

0.13838081

11

0.016

0.83742531

0.013616672

0.149783389

12

0.016

0.824026505

0.013398805

0.16078566

13

0.016

0.810842081

0.013184424

0.171397513

14

0.016

0.797868608

0.012973473

0.181628626

15

0.016

0.78510271

0.012765898

0.191488466

16

0.016

0.772541067

0.012561643

0.200986294

17

0.016

0.76018041

0.012360657

0.21013117

18

0.016

0.748017523

0.012162887

0.218931958

19

0.016

0.736049243

0.01196828

0.227397327

20

0.016

0.724272455

0.011776788

0.235535758

21

0.016

0.712684096

0.011588359

0.243355545

22

0.016

0.70128115

0.011402946

0.250864802

23

0.016

0.690060652

0.011220498

0.258071463

24

0.016

0.679019681

0.01104097

0.26498329

25

0.016

0.668155366

0.010864315

0.271607872

26

0.016

0.65746488

0.010690486

0.277952632

27

0.016

0.646945442

0.010519438

0.284024828

28

0.016

0.636594315

0.010351127

0.289831558

29

0.016

0.626408806

0.010185509

0.295379762

30

0.016

0.616386265

0.010022541

0.300676227

31

0.016

0.606524085

0.00986218

0.305727588

32

0.016

0.5968197

0.009704385

0.310540332

33

0.016

0.587270585

0.009549115

0.315120801

34

0.016

0.577874255

0.009396329

0.319475198

35

0.016

0.568628267

0.009245988

0.323609583

36

0.016

0.559530215

0.009098052

0.327529882

37

0.016

0.550577731

0.008952483

0.331241887

38

0.016

0.541768488

0.008809244

0.334751261

39

0.016

0.533100192

0.008668296

0.338063536

40

0.016

0.524570589

0.008529603

0.341184123

41

0.016

0.516177459

0.008393129

0.344118306

42

0.016

0.50791862

0.008258839

0.346871253

43

0.016

0.499791922

0.008126698

0.349448011

44

0.016

0.491795251

0.007996671

0.351853513

45

0.016

0.483926527

0.007868724

0.354092581

46

0.016

0.476183703

0.007742824

0.356169924

47

0.016

0.468564764

0.007618939

0.358090145

48

0.016

0.461067727

0.007497036

0.359857738

49

0.016

0.453690644

0.007377084

0.361477098

50

0.016

0.446431593

0.00725905

0.362952515

51

0.016

0.439288688

0.007142905

0.36428818

52

0.016

0.432260069

0.007028619

0.365488188

53

0.016

0.425343908

0.006916161

0.366556538

54

0.016

0.418538405

0.006805503

0.367497136

55

0.016

0.411841791

0.006696614

0.368313797

56

0.016

0.405252322

0.006589469

0.369010245

57

0.016

0.398768285

0.006484037

0.369590118

58

0.016

0.392387992

0.006380293

0.370056969

59

0.016

0.386109785

0.006278208

0.370414265

60

0.016

0.379932028

0.006177757

0.370665393

61

0.016

0.373853116

0.006078912

0.370813659

62

0.016

0.367871466

0.00598165

0.370862291

63

0.016

0.361985522

0.005885943

0.370814437

64

0.016

0.356193754

0.005791768

0.370673175

65

0.016

0.350494654

0.0056991

0.370441504

66

0.016

0.344886739

0.005607914

0.370122355

67

0.016

0.339368552

0.005518188

0.369718585

68

0.016

0.333938655

0.005429897

0.369232984

69

0.016

0.328595636

0.005343018

0.368668275

70

1

0

0.328595636

23.00169454


정밀 고정 탐측 표

S 등장 확률 1.6%

90회 이전 등장 시 픽업 확률 55% 

종합 픽업 확률 = 0.88%

시행 횟수픽업 등장 확률누적 미등장 확률정확한 픽업 확률픽업 기대값
1

0.0088

0.9912

0.0088

0.0088

2

0.0088

0.98247744

0.00872256

0.01744512

3

0.0088

0.973831639

0.008645801

0.025937404

4

0.0088

0.96526192

0.008569718

0.034278874

5

0.0088

0.956767615

0.008494305

0.042471524

6

0.0088

0.94834806

0.008419555

0.05051733

7

0.0088

0.940002597

0.008345463

0.058418241

8

0.0088

0.931730574

0.008272023

0.066176183

9

0.0088

0.923531345

0.008199229

0.073793061

10

0.0088

0.91540427

0.008127076

0.081270758

11

0.0088

0.907348712

0.008055558

0.088611133

12

0.0088

0.899364043

0.007984669

0.095816024

13

0.0088

0.89144964

0.007914404

0.102887247

14

0.0088

0.883604883

0.007844757

0.109826596

15

0.0088

0.87582916

0.007775723

0.116635845

16

0.0088

0.868121863

0.007707297

0.123316746

17

0.0088

0.860482391

0.007639472

0.129871031

18

0.0088

0.852910146

0.007572245

0.136300411

19

0.0088

0.845404537

0.007505609

0.142606576

20

0.0088

0.837964977

0.00743956

0.148791198

21

0.0088

0.830590885

0.007374092

0.154855928

22

0.0088

0.823281685

0.0073092

0.160802395

23

0.0088

0.816036806

0.007244879

0.166632213

24

0.0088

0.808855682

0.007181124

0.172346973

25

0.0088

0.801737752

0.00711793

0.17794825

26

0.0088

0.79468246

0.007055292

0.183437598

27

0.0088

0.787689254

0.006993206

0.188816553

28

0.0088

0.780757589

0.006931665

0.194086632

29

0.0088

0.773886922

0.006870667

0.199249337

30

0.0088

0.767076717

0.006810205

0.204306147

31

0.0088

0.760326442

0.006750275

0.209258528

32

0.0088

0.75363557

0.006690873

0.214107926

33

0.0088

0.747003577

0.006631993

0.218855769

34

0.0088

0.740429945

0.006573631

0.22350347

35

0.0088

0.733914162

0.006515784

0.228052423

36

0.0088

0.727455717

0.006458445

0.232504006

37

0.0088

0.721054107

0.00640161

0.236859581

38

0.0088

0.71470883

0.006345276

0.241120493

39

0.0088

0.708419393

0.006289438

0.245288071

40

0.0088

0.702185302

0.006234091

0.249363626

41

0.0088

0.696006071

0.006179231

0.253348457

42

0.0088

0.689881218

0.006124853

0.257243844

43

0.0088

0.683810263

0.006070955

0.261051053

44

0.0088

0.677792733

0.00601753

0.264771334

45

0.0088

0.671828157

0.005964576

0.268405922

46

0.0088

0.665916069

0.005912088

0.271956038

47

0.0088

0.660056008

0.005860061

0.275422886

48

0.0088

0.654247515

0.005808493

0.278807658

49

0.0088

0.648490137

0.005757378

0.282111528

50

0.0088

0.642783424

0.005706713

0.28533566

51

0.0088

0.637126929

0.005656494

0.2884812

52

0.0088

0.631520212

0.005606717

0.291549283

53

0.0088

0.625962835

0.005557378

0.294541027

54

0.0088

0.620454362

0.005508473

0.297457539

55

0.0088

0.614994363

0.005459998

0.300299911

56

0.0088

0.609582413

0.00541195

0.303069222

57

0.0088

0.604218088

0.005364325

0.305766538

58

0.0088

0.598900968

0.005317119

0.308392912

59

0.0088

0.59363064

0.005270329

0.310949383

60

0.0088

0.58840669

0.00522395

0.313436978

61

0.0088

0.583228711

0.005177979

0.315856711

62

0.0088

0.578096299

0.005132413

0.318209585

63

0.0088

0.573009051

0.005087247

0.320496588

64

0.0088

0.567966572

0.00504248

0.322718698

65

0.0088

0.562968466

0.004998106

0.324876879

66

0.0088

0.558014343

0.004954122

0.326972085

67

0.0088

0.553103817

0.004910526

0.329005257

68

0.0088

0.548236504

0.004867314

0.330977324

69

0.0088

0.543412022

0.004824481

0.332889205

70

0.0088

0.538629996

0.004782026

0.334741806

71

0.0088

0.533890053

0.004739944

0.336536022

72

0.0088

0.52919182

0.004698232

0.338272737

73

0.0088

0.524534932

0.004656888

0.339952825

74

0.0088

0.519919025

0.004615907

0.341577148

75

0.0088

0.515343737

0.004575287

0.343146556

76

0.0088

0.510808712

0.004535025

0.344661891

77

0.0088

0.506313596

0.004495117

0.346123983

78

0.0088

0.501858036

0.00445556

0.347533652

79

0.0088

0.497441685

0.004416351

0.348891707

80

0.0088

0.493064198

0.004377487

0.350198946

81

0.0088

0.488725234

0.004338965

0.351456161

82

0.0088

0.484424451

0.004300782

0.352664129

83

0.0088

0.480161516

0.004262935

0.353823619

84

0.0088

0.475936095

0.004225421

0.354935393

85

0.0088

0.471747857

0.004188238

0.356000199

86

0.0088

0.467596476

0.004151381

0.357018778

87

0.0088

0.463481627

0.004114849

0.357991862

88

0.0088

0.459402989

0.004078638

0.358920172

89

0.0088

0.455360243

0.004042746

0.359804421

90

1

0

0.455360243

40.98242183



S 확률
종합s 확률S 기대값
코스모늄 소모값종합 픽업 확률
픽업 S 기대값픽업 코스모늄 소모값
확장(70)0.160.02364548742.291368378,458.273670.015763663.4370525512,687.41051
고정(90)0.160.02361102442.353097158,470.619430.01603945962.3462417712,469.24835



7090
S 기대값
42.2942.35
픽업 S 기대값63.4462.35
Ω 11 기대값697.84685.85