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TRPGコラム

確率の話(D10系)

1D10～10D10の出目合計(出現率)

[表部分はスクロールが可能です]

値1D102D103D104D105D106D107D108D109D1010D10
110%---------
210%1%--------
310%2%0.1%-------
410%3%0.3%0.01%------
510%4%0.6%0.04%0.001%-----
610%5%1.0%0.10%0.005%0.000%----
710%6%1.5%0.20%0.015%0.001%0.000%---
810%7%2.1%0.35%0.035%0.002%0.000%0.000%--
910%8%2.8%0.56%0.070%0.006%0.000%0.000%0.000%-
1010%9%3.6%0.84%0.126%0.013%0.001%0.000%0.000%0.000%
11-10%4.5%1.20%0.210%0.025%0.002%0.000%0.000%0.000%
12-9%5.5%1.65%0.330%0.046%0.005%0.000%0.000%0.000%
13-8%6.3%2.20%0.495%0.079%0.009%0.001%0.000%0.000%
14-7%6.9%2.82%0.715%0.129%0.017%0.002%0.000%0.000%
15-6%7.3%3.48%0.996%0.200%0.030%0.003%0.000%0.000%
16-5%7.5%4.15%1.340%0.300%0.050%0.006%0.001%0.000%
17-4%7.5%4.80%1.745%0.433%0.080%0.011%0.001%0.000%
18-3%7.3%5.40%2.205%0.606%0.123%0.019%0.002%0.000%
19-2%6.9%5.92%2.710%0.823%0.184%0.032%0.004%0.000%
20-1%6.3%6.33%3.246%1.087%0.265%0.050%0.008%0.001%
21--5.5%6.60%3.795%1.399%0.373%0.077%0.013%0.002%
22--4.5%6.70%4.335%1.758%0.510%0.114%0.020%0.003%
23--3.6%6.60%4.840%2.158%0.681%0.164%0.032%0.005%
24--2.8%6.33%5.280%2.593%0.889%0.231%0.048%0.008%
25--2.1%5.92%5.631%3.049%1.136%0.319%0.071%0.013%
26--1.5%5.40%5.875%3.513%1.421%0.429%0.102%0.020%
27--1.0%4.80%6.000%3.966%1.742%0.566%0.145%0.030%
28--0.6%4.15%6.000%4.392%2.095%0.732%0.200%0.044%
29--0.3%3.48%5.875%4.771%2.474%0.930%0.271%0.064%
30--0.1%2.82%5.631%5.088%2.869%1.159%0.361%0.091%
31---2.20%5.280%5.326%3.269%1.419%0.472%0.126%
32---1.65%4.840%5.475%3.661%1.709%0.606%0.172%
33---1.20%4.335%5.525%4.033%2.024%0.766%0.231%
34---0.84%3.795%5.475%4.370%2.359%0.952%0.304%
35---0.56%3.246%5.326%4.658%2.707%1.165%0.395%
36---0.35%2.710%5.088%4.886%3.059%1.403%0.504%
37---0.20%2.205%4.771%5.043%3.406%1.666%0.634%
38---0.10%1.745%4.392%5.124%3.736%1.950%0.786%
39---0.04%1.340%3.966%5.124%4.039%2.251%0.961%
40---0.01%0.996%3.513%5.043%4.304%2.561%1.159%
41----0.715%3.049%4.886%4.521%2.876%1.379%
42----0.495%2.593%4.658%4.683%3.186%1.620%
43----0.330%2.158%4.370%4.782%3.484%1.878%
44----0.210%1.758%4.033%4.816%3.759%2.149%
45----0.126%1.399%3.661%4.782%4.005%2.430%
46----0.070%1.087%3.269%4.683%4.213%2.714%
47----0.035%0.823%2.869%4.521%4.375%2.995%
48----0.015%0.606%2.474%4.304%4.487%3.266%
49----0.005%0.433%2.095%4.039%4.543%3.520%
50----0.001%0.300%1.742%3.736%4.543%3.749%
51-----0.200%1.421%3.406%4.487%3.947%
52-----0.129%1.136%3.059%4.375%4.108%
53-----0.079%0.889%2.707%4.213%4.227%
54-----0.046%0.681%2.359%4.005%4.300%
55-----0.025%0.510%2.024%3.759%4.325%
56-----0.013%0.373%1.709%3.484%4.300%
57-----0.006%0.265%1.419%3.186%4.227%
58-----0.002%0.184%1.159%2.876%4.108%
59-----0.001%0.123%0.930%2.561%3.947%
60-----0.000%0.080%0.732%2.251%3.749%
61------0.050%0.566%1.950%3.520%
62------0.030%0.429%1.666%3.266%
63------0.017%0.319%1.403%2.995%
64------0.009%0.231%1.165%2.714%
65------0.005%0.164%0.952%2.430%
66------0.002%0.114%0.766%2.149%
67------0.001%0.077%0.606%1.878%
68------0.000%0.050%0.472%1.620%
69------0.000%0.032%0.361%1.379%
70------0.000%0.019%0.271%1.159%
71-------0.011%0.200%0.961%
72-------0.006%0.145%0.786%
73-------0.003%0.102%0.634%
74-------0.002%0.071%0.504%
75-------0.001%0.048%0.395%
76-------0.000%0.032%0.304%
77-------0.000%0.020%0.231%
78-------0.000%0.013%0.172%
79-------0.000%0.008%0.126%
80-------0.000%0.004%0.091%
81--------0.002%0.064%
82--------0.001%0.044%
83--------0.001%0.030%
84--------0.000%0.020%
85--------0.000%0.013%
86--------0.000%0.008%
87--------0.000%0.005%
88--------0.000%0.003%
89--------0.000%0.002%
90--------0.000%0.001%
91---------0.000%
92---------0.000%
93---------0.000%
94---------0.000%
95---------0.000%
96---------0.000%
97---------0.000%
98---------0.000%
99---------0.000%
100---------0.000%

1D10～10D10の出目合計(以下が出る確率)

[表部分はスクロールが可能です]

値1D102D103D104D105D106D107D108D109D1010D10
1以下10%---------
2以下20%1%--------
3以下30%3%0.1%-------
4以下40%6%0.4%0.01%------
5以下50%10%1.0%0.05%0.001%-----
6以下60%15%2.0%0.15%0.006%0.000%----
7以下70%21%3.5%0.35%0.021%0.001%0.000%---
8以下80%28%5.6%0.70%0.056%0.003%0.000%0.000%--
9以下90%36%8.4%1.26%0.126%0.008%0.000%0.000%0.000%-
10以下100%45%12.0%2.10%0.252%0.021%0.001%0.000%0.000%0.000%
11以下-55%16.5%3.30%0.462%0.046%0.003%0.000%0.000%0.000%
12以下-64%22.0%4.95%0.792%0.092%0.008%0.000%0.000%0.000%
13以下-72%28.3%7.15%1.287%0.172%0.017%0.001%0.000%0.000%
14以下-79%35.2%9.97%2.002%0.300%0.034%0.003%0.000%0.000%
15以下-85%42.5%13.45%2.998%0.501%0.064%0.006%0.001%0.000%
16以下-90%50.0%17.60%4.338%0.800%0.114%0.013%0.001%0.000%
17以下-94%57.5%22.40%6.083%1.233%0.194%0.024%0.002%0.000%
18以下-97%64.8%27.80%8.288%1.840%0.318%0.044%0.005%0.000%
19以下-99%71.7%33.72%10.998%2.663%0.501%0.076%0.009%0.001%
20以下-100%78.0%40.05%14.244%3.750%0.767%0.126%0.017%0.002%
21以下--83.5%46.65%18.039%5.149%1.140%0.202%0.029%0.004%
22以下--88.0%53.35%22.374%6.907%1.650%0.316%0.050%0.006%
23以下--91.6%59.95%27.214%9.065%2.331%0.480%0.081%0.011%
24以下--94.4%66.28%32.494%11.658%3.221%0.711%0.129%0.020%
25以下--96.5%72.20%38.125%14.707%4.357%1.030%0.200%0.032%
26以下--98.0%77.60%44.000%18.220%5.777%1.459%0.302%0.052%
27以下--99.0%82.40%50.000%22.186%7.519%2.026%0.447%0.082%
28以下--99.6%86.55%56.000%26.578%9.614%2.758%0.647%0.127%
29以下--99.9%90.03%61.875%31.349%12.088%3.688%0.918%0.191%
30以下--100.0%92.85%67.506%36.437%14.957%4.846%1.280%0.282%
31以下---95.05%72.786%41.763%18.225%6.265%1.752%0.408%
32以下---96.70%77.626%47.237%21.887%7.974%2.358%0.580%
33以下---97.90%81.961%52.763%25.920%9.998%3.124%0.811%
34以下---98.74%85.756%58.237%30.290%12.357%4.076%1.116%
35以下---99.30%89.002%63.564%34.948%15.063%5.240%1.510%
36以下---99.65%91.712%68.651%39.833%18.123%6.643%2.014%
37以下---99.85%93.917%73.422%44.876%21.528%8.310%2.648%
38以下---99.95%95.662%77.814%50.000%25.264%10.260%3.435%
39以下---99.99%97.002%81.780%55.124%29.302%12.511%4.396%
40以下---100.00%97.998%85.293%60.167%33.606%15.072%5.555%
41以下----98.713%88.342%65.052%38.127%17.948%6.934%
42以下----99.208%90.935%69.710%42.810%21.134%8.554%
43以下----99.538%93.093%74.080%47.592%24.618%10.432%
44以下----99.748%94.851%78.113%52.408%28.377%12.581%
45以下----99.874%96.250%81.775%57.190%32.382%15.011%
46以下----99.944%97.337%85.043%61.873%36.595%17.725%
47以下----99.979%98.160%87.912%66.394%40.970%20.721%
48以下----99.994%98.767%90.386%70.698%45.457%23.987%
49以下----99.999%99.200%92.481%74.736%50.000%27.506%
50以下----100.000%99.500%94.223%78.472%54.543%31.255%
51以下-----99.700%95.643%81.878%59.030%35.202%
52以下-----99.828%96.779%84.937%63.405%39.311%
53以下-----99.908%97.669%87.643%67.618%43.538%
54以下-----99.954%98.350%90.002%71.623%47.838%
55以下-----99.979%98.860%92.026%75.382%52.162%
56以下-----99.992%99.233%93.735%78.866%56.462%
57以下-----99.997%99.499%95.154%82.052%60.689%
58以下-----99.999%99.682%96.312%84.928%64.798%
59以下-----100.000%99.806%97.242%87.489%68.745%
60以下-----100.000%99.886%97.974%89.740%72.494%
61以下------99.936%98.541%91.690%76.013%
62以下------99.966%98.970%93.357%79.279%
63以下------99.983%99.289%94.760%82.275%
64以下------99.992%99.520%95.924%84.989%
65以下------99.997%99.684%96.876%87.419%
66以下------99.999%99.798%97.642%89.568%
67以下------100.000%99.874%98.248%91.446%
68以下------100.000%99.924%98.720%93.066%
69以下------100.000%99.956%99.082%94.445%
70以下------100.000%99.976%99.353%95.604%
71以下-------99.987%99.553%96.565%
72以下-------99.994%99.698%97.352%
73以下-------99.997%99.800%97.986%
74以下-------99.999%99.871%98.490%
75以下-------100.000%99.919%98.884%
76以下-------100.000%99.950%99.189%
77以下-------100.000%99.971%99.420%
78以下-------100.000%99.983%99.592%
79以下-------100.000%99.991%99.718%
80以下-------100.000%99.995%99.809%
81以下--------99.998%99.873%
82以下--------99.999%99.918%
83以下--------99.999%99.948%
84以下--------100.000%99.968%
85以下--------100.000%99.980%
86以下--------100.000%99.989%
87以下--------100.000%99.994%
88以下--------100.000%99.996%
89以下--------100.000%99.998%
90以下--------100.000%99.999%
91以下---------100.000%
92以下---------100.000%
93以下---------100.000%
94以下---------100.000%
95以下---------100.000%
96以下---------100.000%
97以下---------100.000%
98以下---------100.000%
99以下---------100.000%
100以下---------100.000%

10の目がn個出る確率

EXCEL数式=9^(ダイス数-出現数)*COMBIN(ダイス数,出現数)

[表部分はスクロールが可能です]

個数0個1個2個3個4個5個6個7個8個9個10個
1D1090%10%---------
2D1081%18%1%--------
3D1072.9%24.3%2.7%0.1%-------
4D1065.61%29.16%4.86%0.36%0.01%------
5D1059.049%32.805%7.290%0.810%0.045%0.001%-----
6D1053.144%35.429%9.842%1.458%0.122%0.005%0.000%----
7D1047.830%37.201%12.400%2.296%0.255%0.017%0.001%0.000%---
8D1043.047%38.264%14.880%3.307%0.459%0.041%0.002%0.000%0.000%--
9D1038.742%38.742%17.219%4.464%0.744%0.083%0.006%0.000%0.000%0.000%-
10D1034.868%38.742%19.371%5.740%1.116%0.149%0.014%0.001%0.000%0.000%0.000%

10の目がn個以上出る確率

　「フレイムギア」などの、10が2個以上出るとクリティカル、というゲームなどでの確率を求めるときに役立つと思います。

[表部分はスクロールが可能です]

個数1個以上2個以上3個以上4個以上5個以上6個以上7個以上8個以上9個以上10個以上
1D1010%---------
2D1019%1%--------
3D1027.1%2.8%0.1%-------
4D1034.39%5.23%0.37%0.01%------
5D1040.951%8.146%0.856%0.046%0.001%-----
6D1046.856%11.427%1.585%0.127%0.006%0.000%----
7D1052.170%14.969%2.569%0.273%0.018%0.001%0.000%---
8D1056.953%18.690%3.809%0.502%0.043%0.002%0.000%0.000%--
9D1061.258%22.516%5.297%0.833%0.089%0.006%0.000%0.000%0.000%-
10D1065.132%26.390%7.019%1.280%0.163%0.015%0.001%0.000%0.000%0.000%

3D10を振って高い出目2つを採用する場合

　フレイムギアなどで使えると思います。
　ちなみに期待値は13.475です。

[表部分はスクロールが可能です]

出目出現率以下が出る率
20.1%0.1%
30.3%0.4%
40.7%1.1%
51.2%2.3%
61.9%4.2%
72.7%6.9%
83.7%10.6%
94.8%15.4%
106.1%21.5%
117.5%29%
128.8%37.8%
139.6%47.4%
1410%57.4%
159.9%67.3%
169.4%76.7%
178.4%85.1%
187%92.1%
195.1%97.2%
202.8%100%

2D10 vs 2D10 勝敗率表

　算出方法は6面体のページを参照してください。
　ここではクリティカル値「20」、ファンブル値「2」のみを求めます。

[表部分はスクロールが可能です]

実力差勝利敗北引き分け
攻 +17 > 防98.01%1.97%0.02%
攻 +16 > 防97.97%1.97%0.06%
攻 +15 > 防97.85%2.01%0.14%
攻 +14 > 防97.6%2.13%0.27%
攻 +13 > 防97.16%2.38%0.46%
攻 +12 > 防96.46%2.82%0.72%
攻 +11 > 防95.42%3.52%1.06%
攻 +10 > 防93.95%4.56%1.49%
攻 +9 > 防91.95%6.03%2.02%
攻 +8 > 防89.31%8.03%2.66%
攻 +7 > 防85.99%10.67%3.34%
攻 +6 > 防81.98%13.99%4.03%
攻 +5 > 防77.3%18%4.7%
攻 +4 > 防72%22.68%5.32%
攻 +3 > 防66.16%27.98%5.86%
攻 +2 > 防59.89%33.82%6.29%
攻 +1 > 防53.33%40.09%6.58%
攻(±0)=防46.65%46.65%6.7%
攻 -1 < 防40.09%53.33%6.58%
攻 -2 < 防33.82%59.89%6.29%
攻 -3 < 防27.98%66.16%5.86%
攻 -4 < 防22.68%72%5.32%
攻 -5 < 防18%77.3%4.7%
攻 -6 < 防13.99%81.98%4.03%
攻 -7 < 防10.67%85.99%3.34%
攻 -8 < 防8.03%89.31%2.66%
攻 -9 < 防6.03%91.95%2.02%
攻 -10 < 防4.56%93.95%1.49%
攻 -11 < 防3.52%95.42%1.06%
攻 -12 < 防2.82%96.46%0.72%
攻 -13 < 防2.38%97.16%0.46%
攻 -14 < 防2.13%97.6%0.27%
攻 -15 < 防2.01%97.85%0.14%
攻 -16 < 防1.97%97.97%0.06%
攻 -17 < 防1.97%98.01%0.02%

ダブルクロスの期待値

[表部分はスクロールが可能です]

クリティカル値1098765432
1D106.1117.0008.28610.16713.00017.50025.33341.50090.971
2D108.3339.95812.19815.34519.93327.03139.13763.750138.310
3D109.69511.93114.89118.93424.71433.54348.47778.686169.919
4D1010.69013.43716.95321.66428.32638.44155.48989.891193.618
5D1011.48714.66318.61923.85431.21642.35861.09698.854212.571
6D1012.16215.69820.01225.67733.62245.62165.769106.323228.361
7D1012.75116.59321.20627.23835.68248.41769.774112.725241.891
8D1013.27617.38022.24928.60237.48550.86473.279118.326253.726
9D1013.75118.08023.17329.81439.08853.03976.394123.306264.243
10D1014.18518.71024.00430.90440.53054.99779.198127.787273.705
11D1014.58519.28224.75731.89541.84256.77681.746131.861282.305
12D1014.95619.80425.44832.80543.04458.40884.083135.596290.185
13D1015.30120.28526.08533.64444.15459.91386.240139.043297.457
14D1015.62420.73026.67734.42445.18561.31288.242142.244304.207
15D1015.92621.14427.22935.15146.14762.61790.111145.232310.506
16D1016.21121.53127.74735.83447.04863.84091.864148.033316.409
17D1016.48021.89528.23536.47647.89764.99293.513150.669321.963
18D1016.73322.23828.69637.08348.69866.07995.070153.158327.207
19D1016.97422.56229.13337.65749.45867.11096.546155.517332.173
20D1017.20222.87029.54938.20350.17968.08997.948157.758336.890
21D1017.41823.16329.94538.72350.86669.02199.283159.892341.381
22D1017.62523.44330.32339.21951.52269.911100.557161.929345.666
23D1017.82223.71030.68439.69352.14970.762101.776163.877349.764
24D1018.01023.96731.03140.14852.75071.577102.945165.744353.689
25D1018.18924.21331.36440.58453.32772.360104.066167.537357.457
26D1018.36224.45031.68441.00453.88273.113105.144169.261361.078
27D1018.52724.67931.99241.40854.41673.838106.183170.920364.565
28D1018.68524.89932.28941.79854.93274.538107.184172.521367.925
29D1018.83825.11232.57642.17455.42975.213108.151174.066371.169
30D1018.98425.31932.85342.53855.91075.865109.085175.560374.304

ダブルクロスの中央値(50%点)

　出目がいくつのときに出現率が50%に到達するかを求めています。平均値よりもこっちのほうが実用的な値になると思います。
　ぴったりにならない場合、次の値との差を比べて、相加平均で算出しています。
　これを見ると、《イベイジョン》は強いなぁ、と感じますね。

[表部分はスクロールが可能です]

クリティカル値1098765432
1D105.0005.0005.0005.0005.00011.66712.85722.23451.592
2D107.0677.0677.23312.67114.13821.86131.45551.060101.662
3D107.9297.92913.11914.83621.74224.44241.40062.159131.982
4D108.36712.04314.68516.05523.62532.62543.52672.509161.452
5D108.65613.51615.67021.90624.81334.01152.29082.348181.410
6D108.88314.53116.34423.17531.26541.57353.72091.867201.028
7D1010.96815.27316.84524.10332.44842.71761.986101.214211.419
8D1011.69215.84017.77224.80333.34943.58462.943102.331221.628
9D1012.57716.27621.75725.35134.06744.45963.999111.362231.700
10D1013.29316.63022.54925.80334.62951.37971.864112.249241.664
11D1013.88816.94123.20726.45035.22352.14172.574121.110251.540
12D1014.37417.17623.75431.22441.01952.77473.258121.827261.340
13D1014.79817.37424.22131.88341.68453.31273.993122.547271.076
14D1015.16017.55124.61832.44242.26353.77981.611131.207271.764
15D1015.46617.71324.98132.94142.76754.31482.161131.779281.404
16D1015.74617.86325.27533.36443.20854.91082.635132.352281.999
17D1016.00420.01125.54233.74743.59561.42783.096132.913291.566
18D1016.20720.54725.79034.09343.95361.90083.630141.401301.096
19D1016.39521.04226.01834.38844.25762.31291.118141.849301.602
20D1016.57021.47426.20034.66444.53562.68991.549142.311311.077
21D1016.73421.87926.37034.92244.79563.03991.952142.766311.535
22D1016.88822.23826.53035.14545.07363.34192.305151.179311.966
23D1017.02822.56726.68035.34545.49163.62592.633151.553321.385
24D1017.13822.87826.82235.53345.88763.89392.943151.905321.782
25D1017.24223.15726.95735.71151.24264.22693.312152.278331.163
26D1017.34023.41127.25035.88151.57264.59493.679152.646331.532
27D1017.43223.65227.60436.09651.88564.944101.026152.995331.883
28D1017.52123.88227.94236.44052.16971.258101.335161.305341.226
29D1017.60524.09131.24536.76852.43171.553101.629161.599341.556
30D1017.68524.27831.53141.07552.68171.835101.911161.881341.871

人事を尽くして天命を待つ。

[最終更新日　2015.7.15]