 Re: ダイヤ級＋アイテムの必要宝石数期待値完全版 ( No.1 ) |
- 日時： 2003/03/18 17:59
- 名前： にゅ？ ID:
- 別のアプローチで+3失敗で+3のままという条件で。
ダイヤ+3の武器にダイヤ7個入れたらどうなるか？
＿＿+4
+3<
＿＿+3
こんな感じでノートに取り見てみました。
+10 1/128
+9 1/128
+8 7/128
+7 7/128
+6 21/128
+5 21/128
+4 35/128
+3 35/128
ダイヤ強化は恐ろしいですね。+3からダイヤ7個使って+3～+6の間が一番確率的に大きくなりますね。
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| Re: ダイヤ級＋アイテムの必要宝石数期待値完全版 ( No.2 ) |
- 日時： 2003/03/18 19:42
- 名前： うろたん ID:
- この議論が出てから、いろいろとシミュレートしています＾＾；
上のシミュレーション結果を掲示して頂いた方とは別人ですが、
結果として面白いものが出てきますね。
とりあえず、強化に必要な宝石数は、のれーんさんの
予測通りの結果が出ました。
以下、解析で求めた、仮想1000万人の強化職人のデータを載せます♪
+0→+1の強化に必要な宝石数の期待値をE(1)、
+1→+2の強化宝石数の期待値をE(2)…として表記。
また、+0→+2までに必要な宝石数をT(2)…として表記したものが下の結果です。
E(1)＝1 T(1)＝1
E(2)＝2.00022 T(2)＝3.00022
E(3)＝2.00026 T(3)＝5.00047
E(4)＝1.99982 T(4)＝7.00030
E(5)＝3.99988 T(5)＝11.0002
E(6)＝5.99975 T(6)＝16.9999
E(7)＝8.00296 T(7)＝25.0029
E(8)＝9.99801 T(8)＝35.0009
E(9)＝12.0108 T(9)＝47.0117
E(10)＝14.0071 T(10)＝61.0188
ここで気になるのが、仮想1000万人の強化職人中、
+0→+10に強化するのに使った宝石が最も多かった職人…
なっ！なんと！！その数792個！！（＠一人）
そして、見事10個で成功させた職人は19,485人…
20個以内で+10にした職人が1,114,746人であった結果から
考えると、10人に一人くらいは20個以内で+10に、
50人に一人は10個で+10に成功するという事になります＾＾；
まぁ…1000万人中の一人(792個)には成りたくないものですね…（＞＜）
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| Re: ダイヤ級＋アイテムの必要宝石数期待値完全版 ( No.3 ) |
- 日時： 2003/03/18 20:47
- 名前： にゅ？ ID:
+3にダイヤ8個投入
+10 3/256 (2は7個目で+10成功）
+9 7/256
+8 8/256
+7 28/256
+6 28/256
+5 56/256
+4 56/256
+3 70/256
+3にダイヤ9個投入
+10 13/512(6は8個目までに+10成功）
+9 8/512
+8 35/512
+7 36/512
+6 84/512
+5 84/512
+4 126/512
+3 126/512
+3にダイヤ10個投入
+10 34/1024(26は9個目までに+10成功）
+9 35/1024
+8 44/1024
+7 119/1024
+6 120/1024
+5 210/1024
+4 210/1024
+3 252/1024
+3にダイヤ11個投入
+10 103/2048(68は10個目までに+10成功）
+9 44/2048
+8 154/2048
+7 164/2048
+6 329/2048
+5 330/2048
+4 462/2048
+3 462/2048
数使っても+3.+4の確率が一番大きいですね。
+5.+6に為ったら諦めるのも手だと思います。
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| Re: ダイヤ級＋アイテムの必要宝石数期待値完全版 ( No.4 ) |
- 日時： 2003/03/18 20:54
- 名前： のれーん ID:
- スレが伸びてる!!
うれしい；；
なんというかコンピュータというか
シミュレーションという手段の威力もすごいですね。
私はなぜか機転が効かないというか、
発想が貧困というか
こういう問題に直面するとゴリゴリ計算してしまうんですねぇ・・
はじめの投稿では一時間くらいは
紙と鉛筆で手がゴリゴリ頭がキシャーって
なってました；；
学校などでの問題と違い、
遊びに直結してる問題なので楽しいことは楽しいのですが。
そもそもこういう問題は基礎的な計算による結果と
シミュレーション結果は表裏一体と考えたほうが
よさそうですね。
どちらも欠かせないというか。
あってるかなさん、うろたんさんには
勉強させていただきました。
しかしにゅさんの計算結果おそろしいですね；；
もっと多くのダイヤを投入した時の結果も
聞きたいような聞きたくないような・・
コツコツエメ強化からはじめようかな・・
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| Re: ダイヤ級＋アイテムの必要宝石数期待値完全版 ( No.5 ) |
- 日時： 2003/03/19 10:31
- 名前： うろたん ID:
- 私も、紙とペンで計算しました＾＾；
意外と大変ですね…
∑k(1/2)^k
これを導出するのに、えらく時間かかりました…
数学を使わなくなって久しいので、脳みそが錆付いているらすぃ＾＾；
それはさておき、シミュレーションによる結果第二弾。
+0→+x(x＝2～10)に必要とした宝石数の確率分布です。
以下をテキストにコピペして、*.csv形式で保存して
Excelで開いてみませう♪
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| Re: ダイヤ級＋アイテムの必要宝石数期待値完全版 ( No.6 ) |
- 日時： 2003/03/19 10:32
- 名前： うろたん ID:
- ---------------------以下コピペ-----------------
Num.Jewel,確率+0to+2,確率+0to+3,確率+0to+4,確率+0to+5,確率+0to+6,確率+0to+7,確率+0to+8,確率+0to+9,確率+0to+10
1,0,0,0,0,0,0,0,0,0
2,0.4999904,0,0,0,0,0,0,0,0
3,0.2500261,0.2498648,0,0,0,0,0,0,0
4,0.1249333,0.2500185,0.1248857,0,0,0,0,0,0
5,0.0625408,0.1875209,0.1874642,0.062503,0,0,0,0,0
6,0.0312016,0.1249973,0.1875921,0.0936281,0.0311776,0,0,0,0
7,0.0156613,0.0782722,0.1562462,0.1094548,0.0468081,0.0156473,0,0,0
8,0.0077942,0.0468303,0.11729,0.1094049,0.0626505,0.0233692,0.0077898,0,0
9,0.0039129,0.0273159,0.0820854,0.1016272,0.0664367,0.0351755,0.0116567,0.0039108,0
10,0.0019738,0.0156303,0.0545696,0.089849,0.0682731,0.0390951,0.0195573,0.0058148,0.0019485
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| Re: ダイヤ級＋アイテムの必要宝石数期待値完全版 ( No.7 ) |
- 日時： 2003/03/19 10:33
- 名前： うろたん ID:
- 11,0.0009792,0.008799,0.0351463,0.0772014,0.0654914,0.0439132,0.0224913,0.0107453,0.0029087
12,0.0004951,0.0048668,0.021991,0.0648835,0.06215,0.043921,0.0273693,0.0126961,0.0058443
13,0.0002486,0.0026952,0.0134486,0.0539543,0.0570264,0.044655,0.028312,0.0166627,0.0070823
14,0.0001245,0.0014644,0.0080727,0.0443724,0.0524478,0.0427996,0.0305949,0.0176738,0.0099147
15,0.0000583,0.0008133,0.0047402,0.0363986,0.047625,0.0417489,0.0301741,0.0202234,0.0107758
16,0.0000312,0.000429,0.0027681,0.029589,0.0433824,0.0393703,0.0309754,0.0204834,0.013053
17,0.0000147,0.0002284,0.0016115,0.0241463,0.0390153,0.0377732,0.0299173,0.021925,0.0134669
18,0.0000079,0.0001201,0.0009078,0.0196107,0.0353953,0.0353611,0.0298948,0.0217236,0.0150694
19,0.0000034,0.0000651,0.0005199,0.0158579,0.0318793,0.0336014,0.0285609,0.0224776,0.0151165
20,0.0000014,0.0000321,0.0002951,0.0128525,0.02871,0.0313887,0.0280519,0.021881,0.0162945
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| Re: ダイヤ級＋アイテムの必要宝石数期待値完全版 ( No.8 ) |
- 日時： 2003/03/19 10:33
- 名前： うろたん ID:
- 21,0.0000005,0.0000157,0.0001669,0.0103748,0.0259164,0.0296618,0.0267884,0.0221194,0.0160736
22,0.0000006,0.0000109,0.0000899,0.0085025,0.0233094,0.0278728,0.0261455,0.0214224,0.0167002
23,0.0000001,0.0000051,0.0000502,0.0068446,0.0210107,0.02618,0.0250211,0.0215142,0.0164535
24,0,0.0000019,0.0000275,0.0054995,0.019021,0.0246472,0.024227,0.0207044,0.0168573
25,0.0000001,0.0000014,0.0000141,0.0044827,0.0170609,0.0232073,0.0230519,0.0205823,0.0164688
26,0,0.0000009,0.0000076,0.003645,0.01541,0.0217659,0.0222411,0.0198758,0.0167201
27,0,0.0000003,0.0000044,0.0029196,0.0138257,0.020488,0.0213139,0.0195083,0.0162324
28,0,0.0000001,0.0000023,0.0023671,0.0124626,0.019137,0.0205276,0.0188997,0.0162987
29,0,0.0000001,0.0000015,0.001901,0.0112722,0.0179924,0.0196203,0.0185394,0.0158554
30,0,0,0.0000007,0.0015557,0.0101178,0.0169745,0.0189253,0.0178441,0.0158958
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[318] ダイヤ級＋アイテムの必要宝石数期待値完全版