第1問についてさらに考える
というわけで第1問題について、
前回までの考えをさらにおし進めてみる。
しつこいようだけど、問題内容はここ参照
前回は必要MPを算出し、
それをもとに必要なクリスタル数を割り出そうとしてた。
その際、「結局何パーセントの確立でクリスタルが引ければOKなのよ？」
といういまさら的な疑問が浮かんだ。
この疑問は避けて通れそうになさそうなので今のうちに片付けておくことにする。
まず、
前回リドローできるんだから60%ぐらいあればいんじゃね？
と、比較的無責任なことを言っていたが冷静になって考えてみると
確率論的には何回引きなおそうが、60%なら60%なのである。
前回の結果は考慮しないのが鉄則であるべきだったのを忘れてた。
そうなると、60%じゃ足りないかな･････と思う。
少なくとも80%はほしいはず・・・・・・
参考程度に枚数とパーセンテージを載せておこう。
【40枚デッキから8枚ドローしたときにクリスタルが2枚含まれる確率】
クリスタル10枚：65.92%
クリスタル11枚：72.09%
クリスタル12枚：77.48%
クリスタル13枚：82.10%
クリスタル14枚：85.99%
クリスタル15枚：89.22%
クリスタル16枚：91.84%
クリスタル17枚：93.94%
クリスタル18枚：95.59%
クリスタル19枚：96.86%
クリスタル20枚：97.82%
こんな結果になった。
見にくくてごめんね。所詮メモ書き程度のものだから。
80%を維持するなら13枚で良いようだ。
関係ないが、
上記の表を見ると10枚～15枚は1枚増やすごとに4%～6%増加するが、
16枚以降は1枚増やすごとに2%程度しか増加していない。
ということは
16枚を17枚にしてもあまり意味がないようだ。やるなら18枚とか、20枚にすべきだと。
ホントに関係ないな。
というわけで、とりあえずMPのみを考慮したらこんな感じ。
でいいのかなぁ・・・・・
まぁいっか。
今日はここまで。
------------------------------------------------------------
いちいち計算するの面倒なんで確率表置いておきますね。
40枚デッキ限定ですけど。
■40枚デッキからN枚ドローして1枚以上含まれる確率
| 3MP | 1ﾀｰﾝ | 2ﾀｰﾝ | 3ﾀｰﾝ | 4ﾀｰﾝ | 5ﾀｰﾝ | 6ﾀｰﾝ | 7ﾀｰﾝ |
| ｸﾘｽﾀﾙ＼ﾄﾞﾛｰ | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 8枚 | 76.39% | 81.95% | 86.32% | 89.74% | 92.39% | 94.42% | 95.96% |
| 9枚 | 80.82% | 85.90% | 89.74% | 92.63% | 94.77% | 96.34% | 97.47% |
| 10枚 | 84.53% | 89.08% | 92.39% | 94.77% | 96.46% | 97.64% | 98.45% |
| 11枚 | 87.62% | 91.63% | 94.42% | 96.34% | 97.64% | 98.50% | 99.07% |
| 12枚 | 90.18% | 93.65% | 95.96% | 97.47% | 98.45% | 99.07% | 99.46% |
| 13枚 | 92.29% | 95.24% | 97.11% | 98.29% | 99.00% | 99.44% | 99.69% |
| 14枚 | 94.00% | 96.47% | 97.97% | 98.86% | 99.37% | 99.67% | 99.83% |
| 15枚 | 95.39% | 97.42% | 98.59% | 99.25% | 99.61% | 99.81% | 99.91% |
| 16枚 | 96.49% | 98.14% | 99.04% | 99.52% | 99.77% | 99.89% | 99.95% |
| 17枚 | 97.37% | 98.69% | 99.36% | 99.70% | 99.87% | 99.94% | 99.98% |
| 18枚 | 98.06% | 99.09% | 99.58% | 99.82% | 99.92% | 99.97% | 99.99% |
| 19枚 | 98.59% | 99.38% | 99.74% | 99.89% | 99.96% | 99.98% | 99.99% |
| 20枚 | 98.99% | 99.58% | 99.84% | 99.94% | 99.98% | 99.99% | 100.00% |
| 21枚 | 99.29% | 99.73% | 99.90% | 99.97% | 99.99% | 100.00% | 100.00% |
| 22枚 | 99.52% | 99.83% | 99.94% | 99.98% | 99.99% | 100.00% | 100.00% |
| 23枚 | 99.68% | 99.90% | 99.97% | 99.99% | 100.00% | 100.00% | 100.00% |
| 24枚 | 99.79% | 99.94% | 99.98% | 100.00% | 100.00% | 100.00% | 100.00% |
| 25枚 | 99.87% | 99.97% | 99.99% | 100.00% | 100.00% | 100.00% | 100.00% |
■40枚デッキからN枚ドローして2枚以上含まれる確率
| 4MP | 1ﾀｰﾝ | 2ﾀｰﾝ | 3ﾀｰﾝ | 4ﾀｰﾝ | 5ﾀｰﾝ | 6ﾀｰﾝ | 7ﾀｰﾝ |
| ｸﾘｽﾀﾙ＼ﾄﾞﾛｰ | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 8枚 | 34.42% | 43.06% | 51.31% | 58.97% | 65.92% | 72.09% | 77.48% |
| 9枚 | 40.98% | 50.35% | 58.97% | 66.66% | 73.36% | 79.07% | 83.83% |
| 10枚 | 47.40% | 57.23% | 65.92% | 73.36% | 79.58% | 84.64% | 88.67% |
| 11枚 | 53.59% | 63.60% | 72.09% | 79.07% | 84.64% | 88.97% | 92.26% |
| 12枚 | 59.46% | 69.40% | 77.48% | 83.83% | 88.67% | 92.26% | 94.84% |
| 13枚 | 64.95% | 74.60% | 82.10% | 87.73% | 91.82% | 94.69% | 96.66% |
| 14枚 | 70.01% | 79.18% | 85.99% | 90.86% | 94.21% | 96.45% | 97.89% |
| 15枚 | 74.62% | 83.17% | 89.22% | 93.32% | 96.00% | 97.69% | 98.71% |
| 16枚 | 78.78% | 86.59% | 91.84% | 95.22% | 97.30% | 98.53% | 99.24% |
| 17枚 | 82.47% | 89.48% | 93.94% | 96.65% | 98.23% | 99.10% | 99.56% |
| 18枚 | 85.71% | 91.88% | 95.59% | 97.71% | 98.87% | 99.47% | 99.76% |
| 19枚 | 88.51% | 93.85% | 96.86% | 98.48% | 99.30% | 99.69% | 99.87% |
| 20枚 | 90.91% | 95.43% | 97.82% | 99.02% | 99.58% | 99.83% | 99.94% |
| 21枚 | 92.93% | 96.67% | 98.53% | 99.39% | 99.76% | 99.91% | 99.97% |
| 22枚 | 94.61% | 97.64% | 99.03% | 99.63% | 99.87% | 99.96% | 99.99% |
| 23枚 | 95.97% | 98.37% | 99.39% | 99.79% | 99.93% | 99.98% | 99.99% |
| 24枚 | 97.06% | 98.91% | 99.63% | 99.88% | 99.97% | 99.99% | 100.00% |
| 25枚 | 97.91% | 99.29% | 99.78% | 99.94% | 99.98% | 100.00% | 100.00% |
■40枚デッキからN枚ドローして3枚以上含まれる確率
| 5MP | 1ﾀｰﾝ | 2ﾀｰﾝ | 3ﾀｰﾝ | 4ﾀｰﾝ | 5ﾀｰﾝ | 6ﾀｰﾝ | 7ﾀｰﾝ |
| ｸﾘｽﾀﾙ＼ﾄﾞﾛｰ | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 8枚 | 8.19% | 12.82% | 18.32% | 24.50% | 31.17% | 38.12% | 45.15% |
| 9枚 | 11.47% | 17.54% | 24.50% | 32.04% | 39.86% | 47.68% | 55.25% |
| 10枚 | 15.28% | 22.83% | 31.17% | 39.86% | 48.51% | 56.79% | 64.47% |
| 11枚 | 19.56% | 28.57% | 38.12% | 47.68% | 56.79% | 65.15% | 72.54% |
| 12枚 | 24.25% | 34.61% | 45.15% | 55.25% | 64.47% | 72.54% | 79.34% |
| 13枚 | 29.28% | 40.82% | 52.08% | 62.40% | 71.39% | 78.88% | 84.88% |
| 14枚 | 34.57% | 47.08% | 58.75% | 68.97% | 77.44% | 84.15% | 89.24% |
| 15枚 | 40.02% | 53.25% | 65.04% | 74.86% | 82.60% | 88.41% | 92.57% |
| 16枚 | 45.56% | 59.23% | 70.84% | 80.03% | 86.89% | 91.75% | 95.02% |
| 17枚 | 51.09% | 64.93% | 76.09% | 84.46% | 90.36% | 94.29% | 96.78% |
| 18枚 | 56.55% | 70.27% | 80.75% | 88.17% | 93.10% | 96.17% | 97.99% |
| 19枚 | 61.85% | 75.18% | 84.80% | 91.21% | 95.19% | 97.52% | 98.80% |
| 20枚 | 66.93% | 79.63% | 88.24% | 93.63% | 96.76% | 98.45% | 99.31% |
| 21枚 | 71.73% | 83.58% | 91.12% | 95.52% | 97.89% | 99.07% | 99.62% |
| 22枚 | 76.19% | 87.02% | 93.46% | 96.94% | 98.68% | 99.47% | 99.81% |
| 23枚 | 80.28% | 89.97% | 95.32% | 97.99% | 99.21% | 99.71% | 99.91% |
| 24枚 | 83.97% | 92.44% | 96.75% | 98.73% | 99.55% | 99.85% | 99.96% |
| 25枚 | 87.25% | 94.46% | 97.83% | 99.23% | 99.76% | 99.93% | 99.98% |
■40枚デッキからN枚ドローして4枚以上含まれる確率
| 6MP | 1ﾀｰﾝ | 2ﾀｰﾝ | 3ﾀｰﾝ | 4ﾀｰﾝ | 5ﾀｰﾝ | 6ﾀｰﾝ | 7ﾀｰﾝ |
| ｸﾘｽﾀﾙ＼ﾄﾞﾛｰ | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 8枚 | 0.95% | 2.02% | 3.65% | 5.94% | 8.94% | 12.64% | 17.04% |
| 9枚 | 1.63% | 3.37% | 5.94% | 9.42% | 13.80% | 19.01% | 24.94% |
| 10枚 | 2.58% | 5.20% | 8.94% | 13.80% | 19.69% | 26.41% | 33.74% |
| 11枚 | 3.85% | 7.55% | 12.64% | 19.01% | 26.41% | 34.51% | 42.96% |
| 12枚 | 5.48% | 10.45% | 17.04% | 24.94% | 33.74% | 42.96% | 52.14% |
| 13枚 | 7.49% | 13.90% | 22.06% | 31.44% | 41.43% | 51.41% | 60.88% |
| 14枚 | 9.91% | 17.89% | 27.62% | 38.32% | 49.19% | 59.55% | 68.88% |
| 15枚 | 12.75% | 22.38% | 33.60% | 45.39% | 56.80% | 67.12% | 75.93% |
| 16枚 | 16.03% | 27.32% | 39.89% | 52.46% | 64.02% | 73.93% | 81.92% |
| 17枚 | 19.72% | 32.64% | 46.34% | 59.36% | 70.69% | 79.87% | 86.83% |
| 18枚 | 23.81% | 38.25% | 52.81% | 65.90% | 76.68% | 84.89% | 90.73% |
| 19枚 | 28.27% | 44.07% | 59.16% | 71.98% | 81.90% | 88.99% | 93.70% |
| 20枚 | 33.07% | 50.00% | 65.26% | 77.47% | 86.33% | 92.24% | 95.88% |
| 21枚 | 38.15% | 55.93% | 71.01% | 82.32% | 89.98% | 94.73% | 97.42% |
| 22枚 | 43.45% | 61.75% | 76.30% | 86.49% | 92.89% | 96.56% | 98.47% |
| 23枚 | 48.91% | 67.36% | 81.07% | 89.97% | 95.14% | 97.85% | 99.14% |
| 24枚 | 54.44% | 72.68% | 85.26% | 92.80% | 96.82% | 98.73% | 99.54% |
| 25枚 | 59.98% | 77.62% | 88.85% | 95.02% | 98.01% | 99.29% | 99.78% |
■40枚デッキからN枚ドローして5枚以上含まれる確率
| 7MP | 1ﾀｰﾝ | 2ﾀｰﾝ | 3ﾀｰﾝ | 4ﾀｰﾝ | 5ﾀｰﾝ | 6ﾀｰﾝ | 7ﾀｰﾝ |
| ｸﾘｽﾀﾙ＼ﾄﾞﾛｰ | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 8枚 | 0.05% | 0.15% | 0.38% | 0.79% | 1.45% | 2.45% | 3.86% |
| 9枚 | 0.10% | 0.33% | 0.79% | 1.59% | 2.86% | 4.68% | 7.15% |
| 10枚 | 0.20% | 0.62% | 1.45% | 2.86% | 4.98% | 7.92% | 11.74% |
| 11枚 | 0.36% | 1.08% | 2.45% | 4.68% | 7.92% | 12.23% | 17.61% |
| 12枚 | 0.60% | 1.75% | 3.86% | 7.15% | 11.74% | 17.61% | 24.60% |
| 13枚 | 0.95% | 2.68% | 5.74% | 10.33% | 16.46% | 23.95% | 32.47% |
| 14枚 | 1.43% | 3.93% | 8.16% | 14.24% | 22.01% | 31.07% | 40.89% |
| 15枚 | 2.09% | 5.54% | 11.15% | 18.87% | 28.28% | 38.74% | 49.50% |
| 16枚 | 2.94% | 7.56% | 14.74% | 24.17% | 35.12% | 46.68% | 57.96% |
| 17枚 | 4.03% | 10.03% | 18.93% | 30.07% | 42.35% | 54.63% | 65.95% |
| 18枚 | 5.39% | 12.98% | 23.70% | 36.43% | 49.74% | 62.31% | 73.21% |
| 19枚 | 7.07% | 16.42% | 28.99% | 43.13% | 57.09% | 69.50% | 79.58% |
| 20枚 | 9.09% | 20.37% | 34.74% | 50.00% | 64.18% | 75.99% | 84.96% |
| 21枚 | 11.49% | 24.82% | 40.84% | 56.87% | 70.82% | 81.68% | 89.33% |
| 22枚 | 14.29% | 29.73% | 47.19% | 63.57% | 76.87% | 86.49% | 92.74% |
| 23枚 | 17.53% | 35.07% | 53.66% | 69.93% | 82.21% | 90.40% | 95.28% |
| 24枚 | 21.22% | 40.77% | 60.11% | 75.83% | 86.78% | 93.47% | 97.10% |
| 25枚 | 25.38% | 46.75% | 66.40% | 81.13% | 90.54% | 95.77% | 98.32% |
■40枚デッキからN枚ドローして6枚以上含まれる確率
| 8MP | 1ﾀｰﾝ | 2ﾀｰﾝ | 3ﾀｰﾝ | 4ﾀｰﾝ | 5ﾀｰﾝ | 6ﾀｰﾝ | 7ﾀｰﾝ |
| ｸﾘｽﾀﾙ＼ﾄﾞﾛｰ | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 8枚 | 0.00% | 0.00% | 0.02% | 0.05% | 0.12% | 0.26% | 0.48% |
| 9枚 | 0.00% | 0.01% | 0.05% | 0.14% | 0.33% | 0.67% | 1.22% |
| 10枚 | 0.01% | 0.03% | 0.12% | 0.33% | 0.74% | 1.44% | 2.56% |
| 11枚 | 0.01% | 0.07% | 0.26% | 0.67% | 1.44% | 2.74% | 4.70% |
| 12枚 | 0.02% | 0.14% | 0.48% | 1.22% | 2.56% | 4.70% | 7.82% |
| 13枚 | 0.04% | 0.26% | 0.85% | 2.07% | 4.20% | 7.47% | 12.02% |
| 14枚 | 0.08% | 0.44% | 1.39% | 3.29% | 6.47% | 11.13% | 17.32% |
| 15枚 | 0.13% | 0.71% | 2.17% | 4.98% | 9.46% | 15.73% | 23.66% |
| 16枚 | 0.21% | 1.09% | 3.25% | 7.20% | 13.22% | 21.25% | 30.90% |
| 17枚 | 0.32% | 1.63% | 4.68% | 10.03% | 17.79% | 27.61% | 38.79% |
| 18枚 | 0.48% | 2.36% | 6.54% | 13.51% | 23.13% | 34.66% | 47.06% |
| 19枚 | 0.71% | 3.33% | 8.88% | 17.68% | 29.18% | 42.20% | 55.38% |
| 20枚 | 1.01% | 4.57% | 11.76% | 22.53% | 35.82% | 50.00% | 63.45% |
| 21枚 | 1.41% | 6.15% | 15.20% | 28.02% | 42.91% | 57.80% | 70.97% |
| 22枚 | 1.94% | 8.12% | 19.25% | 34.10% | 50.26% | 65.34% | 77.74% |
| 23枚 | 2.63% | 10.52% | 23.91% | 40.64% | 57.65% | 72.39% | 83.57% |
| 24枚 | 3.51% | 13.41% | 29.16% | 47.54% | 64.88% | 78.75% | 88.39% |
| 25枚 | 4.61% | 16.83% | 34.96% | 54.61% | 71.72% | 84.27% | 92.20% |
■40枚デッキからN枚ドローして7枚以上含まれる確率
| 9MP | 1ﾀｰﾝ | 2ﾀｰﾝ | 3ﾀｰﾝ | 4ﾀｰﾝ | 5ﾀｰﾝ | 6ﾀｰﾝ | 7ﾀｰﾝ |
| ｸﾘｽﾀﾙ＼ﾄﾞﾛｰ | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 8枚 | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.01% | 0.03% |
| 9枚 | 0.00% | 0.00% | 0.00% | 0.01% | 0.02% | 0.05% | 0.11% |
| 10枚 | 0.00% | 0.00% | 0.00% | 0.02% | 0.06% | 0.15% | 0.33% |
| 11枚 | 0.00% | 0.00% | 0.01% | 0.05% | 0.15% | 0.37% | 0.78% |
| 12枚 | 0.00% | 0.00% | 0.03% | 0.11% | 0.33% | 0.78% | 1.59% |
| 13枚 | 0.00% | 0.01% | 0.06% | 0.23% | 0.65% | 1.48% | 2.92% |
| 14枚 | 0.00% | 0.02% | 0.12% | 0.44% | 1.17% | 2.59% | 4.94% |
| 15枚 | 0.00% | 0.03% | 0.22% | 0.77% | 1.99% | 4.23% | 7.80% |
| 16枚 | 0.00% | 0.06% | 0.37% | 1.27% | 3.18% | 6.53% | 11.61% |
| 17枚 | 0.00% | 0.10% | 0.61% | 2.01% | 4.86% | 9.60% | 16.43% |
| 18枚 | 0.00% | 0.17% | 0.97% | 3.06% | 7.11% | 13.51% | 22.26% |
| 19枚 | 0.00% | 0.27% | 1.47% | 4.48% | 10.02% | 18.32% | 29.03% |
| 20枚 | 0.00% | 0.42% | 2.18% | 6.37% | 13.67% | 24.01% | 36.55% |
| 21枚 | 0.00% | 0.62% | 3.14% | 8.79% | 18.10% | 30.50% | 44.62% |
| 22枚 | 0.00% | 0.91% | 4.41% | 11.83% | 23.32% | 37.69% | 52.94% |
| 23枚 | 0.00% | 1.31% | 6.06% | 15.54% | 29.31% | 45.37% | 61.21% |
| 24枚 | 0.00% | 1.86% | 8.16% | 19.97% | 35.98% | 53.32% | 69.10% |
| 25枚 | 0.00% | 2.58% | 10.78% | 25.14% | 43.20% | 61.26% | 76.34% |
■40枚デッキからN枚ドローして8枚以上含まれる確率
| 10MP | 1ﾀｰﾝ | 2ﾀｰﾝ | 3ﾀｰﾝ | 4ﾀｰﾝ | 5ﾀｰﾝ | 6ﾀｰﾝ | 7ﾀｰﾝ |
| ｸﾘｽﾀﾙ＼ﾄﾞﾛｰ | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 8枚 | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% |
| 9枚 | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.01% |
| 10枚 | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.01% | 0.02% |
| 11枚 | 0.00% | 0.00% | 0.00% | 0.00% | 0.01% | 0.03% | 0.07% |
| 12枚 | 0.00% | 0.00% | 0.00% | 0.01% | 0.02% | 0.07% | 0.19% |
| 13枚 | 0.00% | 0.00% | 0.00% | 0.01% | 0.06% | 0.17% | 0.44% |
| 14枚 | 0.00% | 0.00% | 0.00% | 0.03% | 0.12% | 0.37% | 0.90% |
| 15枚 | 0.00% | 0.00% | 0.01% | 0.06% | 0.24% | 0.71% | 1.68% |
| 16枚 | 0.00% | 0.00% | 0.02% | 0.12% | 0.45% | 1.27% | 2.90% |
| 17枚 | 0.00% | 0.00% | 0.03% | 0.21% | 0.79% | 2.15% | 4.72% |
| 18枚 | 0.00% | 0.00% | 0.06% | 0.37% | 1.32% | 3.44% | 7.26% |
| 19枚 | 0.00% | 0.00% | 0.10% | 0.61% | 2.11% | 5.27% | 10.67% |
| 20枚 | 0.00% | 0.00% | 0.16% | 0.98% | 3.24% | 7.76% | 15.04% |
| 21枚 | 0.00% | 0.00% | 0.26% | 1.52% | 4.81% | 11.01% | 20.42% |
| 22枚 | 0.00% | 0.00% | 0.42% | 2.29% | 6.90% | 15.11% | 26.79% |
| 23枚 | 0.00% | 0.00% | 0.64% | 3.35% | 9.64% | 20.13% | 34.05% |
| 24枚 | 0.00% | 0.00% | 0.96% | 4.78% | 13.11% | 26.07% | 42.04% |
| 25枚 | 0.00% | 0.00% | 1.41% | 6.68% | 17.40% | 32.88% | 50.50% |
| 固定リンク
コメント
ちょっと参考になるかわかりませんが、雑感をば
第1問で追究すべきは「最適クリスタル枚数」なので、
次回考察はクリスタル以外の要素も考慮してはいかがでしょう
自分のここまでの考えを述べますと、
例えば、炎速攻系のデッキだと、「2ターン目までにクリーチャー2体並べ、以後除去と援軍召喚の繰り返し」という理想の展開（※）がありますが、
それを達成する可能性を最大にするクリスタル枚数、クリーチャー枚数、除去枚数のバランスが、デッキ構築の肝かと私は思っています。
※本体ダメージ系やドローは一旦無視と仮定
これでいうと、「クリスタルを○ターン目に○枚引く確率」と「MPが○以下のクリーチャーを○ターン目に○枚引く確率」「除去（ry）」の兼ね合いで、クリスタルの投入枚数の適正値が決まってくるかと。
（もちろんクリスタルを置けることが最重要なので、そこも考慮すべきですが）
デッキのコンセプトごとに上記の考えを用いて数式化すると、
かなり第1問の答えに近づく。かも
長文失礼致しました。
PS 大変遅くなりましたが、
ドラフト大会運営ありがとうございました！
（次回あれば全敗で終わった決勝のリベンジを）
投稿： だんぱ | 2007年2月21日 (水) 22時00分
コメントありがとうございます。
貴重な意見であり、早速回答したいのですが非常に長くなりそうなので記事にて回答させていただきます。
ドラフト大会はFFTの合間を縫ってやっていこうと思ってます。まったりと。
2回目もやるつもりなんでふるってリベンジをどぞどぞ。
投稿： itachi | 2007年2月22日 (木) 10時40分