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 확률 | 기대값 |
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 횟수 | 픽업 등장 확률 | 누적 미등장 확률 | 정확한 픽업 확률 | 픽업 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 확률 | S 기대값 | 코스모늄 소모값 | 종합 픽업 확률 | 픽업 S 기대값 | 픽업 코스모늄 소모값 | |
확장(70) | 0.16 | 0.023645487 | 42.29136837 | 8,458.27367 | 0.0157636 | 63.43705255 | 12,687.41051 |
고정(90) | 0.16 | 0.023611024 | 42.35309715 | 8,470.61943 | 0.016039459 | 62.34624177 | 12,469.24835 |
70 | 90 | |
S 기대값 | 42.29 | 42.35 |
픽업 S 기대값 | 63.44 | 62.35 |
Ω 11 기대값 | 697.84 | 685.85 |