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*製錬/試算 [#title]
#contents

** 平均製錬回数 [#frequency]

製錬成功率がpのとき、製錬が成功するまでの回数Xは幾何分布に従い、期待値は E[X] = 1/p で分散は V[X] = (1-p)/p² ~
リペアパウダーの必要回数の平均値は E[X] -1 
- 成功率が33%のときE[X] ≒ 3.03 なので平均して2.03回程度のリペアパウダーが必要になる。~
- リペアパウダーの個数は1回あたり(製錬Lv)個必要です。

標準偏差σ は、分散の平方根 σ = √V[X] = (1/p)√(1-p)
- p が小さい時、σ ≒ (1/p) = E[X]

f(t) = P(X≦E[X]+tσ) とし、p,f(t)を%表示で表すと以下の表のようになる。

*** 1～40% [#p1]
|~p|~E[X]|~σ|~f(0)|~f(1)|~f(2)|~ |~p|~E[X]|~σ|~f(0)|~f(1)|~f(2)|
|RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:||RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:|c
|1|100.00|99.50|63.40|86.47|95.00||21|4.76|4.23|61.05|84.83|95.33|
|2|50.00|49.50|63.58|86.47|94.97||22|4.55|4.01|62.98|86.30|94.93|
|3|33.33|32.83|63.40|86.61|94.95||23|4.35|3.82|64.85|87.64|94.36|
|4|25.00|24.49|63.96|86.47|94.92||24|4.17|3.63|66.64|85.35|95.11|
|5|20.00|19.49|64.15|86.47|94.90||25|4.00|3.46|68.36|86.65|94.37|
|6|16.67|16.16|62.84|86.19|94.87||26|3.85|3.31|59.48|87.85|95.08|
|7|14.29|13.78|63.80|86.89|94.90||27|3.70|3.16|61.10|84.87|95.70|
|8|12.50|11.99|63.23|86.48|95.03||28|3.57|3.03|62.68|86.07|94.80|
|9|11.11|10.60|64.56|86.20|95.11||29|3.45|2.91|64.21|87.19|95.42|
|10|10.00|9.49|65.13|86.49|94.77||30|3.33|2.79|65.70|88.24|94.24|
|11|9.09|8.58|64.96|86.21|95.17||31|3.23|2.68|67.15|84.36|94.86|
|12|8.33|7.82|64.04|87.07|94.71||32|3.13|2.58|68.56|85.46|95.43|
|13|7.69|7.17|62.27|85.77|95.33||33|3.03|2.48|69.92|86.50|93.94|
|14|7.14|6.62|65.21|85.92|95.10||34|2.94|2.39|56.44|87.48|94.54|
|15|6.67|6.15|62.29|85.78|94.64||35|2.86|2.30|57.75|88.40|95.10|
|16|6.25|5.73|64.87|85.31|94.84||36|2.78|2.22|59.04|89.26|95.60|
|17|5.88|5.36|60.61|87.12|94.93||37|2.70|2.15|60.31|84.25|93.75|
|18|5.56|5.03|62.93|86.26|94.90||38|2.63|2.07|61.56|85.22|94.32|
|19|5.26|4.74|65.13|87.84|94.77||39|2.56|2.00|62.79|86.15|94.85|
|20|5.00|4.47|67.23|86.58|94.50||40|2.50|1.94|64.00|87.04|95.33|
~

*** 41～80% [#p41]
|~p|~E[X]|~σ|~f(0)|~f(1)|~f(2)|~ |~p|~E[X]|~σ|~f(0)|~f(1)|~f(2)|
|RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:||RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:|c
|41|2.44|1.87|65.19|87.88|95.78||61|1.64|1.02|61.00|84.79|94.07|
|42|2.38|1.81|66.36|88.68|96.19||62|1.61|0.99|62.00|85.56|94.51|
|43|2.33|1.76|67.51|89.44|93.98||63|1.59|0.97|63.00|86.31|94.93|
|44|2.27|1.70|68.64|82.44|94.49||64|1.56|0.94|64.00|87.04|95.33|
|45|2.22|1.65|69.75|83.36|94.97||65|1.54|0.91|65.00|87.75|95.71|
|46|2.17|1.60|70.84|84.25|95.41||66|1.52|0.88|66.00|88.44|96.07|
|47|2.13|1.55|71.91|85.11|95.82||67|1.49|0.86|67.00|89.11|96.41|
|48|2.08|1.50|72.96|85.94|96.20||68|1.47|0.83|68.00|89.76|96.72|
|49|2.04|1.46|73.99|86.73|93.23||69|1.45|0.81|69.00|90.39|97.02|
|50|2.00|1.41|75.00|87.50|93.75||70|1.43|0.78|70.00|91.00|91.00|
|51|1.96|1.37|51.00|88.24|94.24||71|1.41|0.76|71.00|91.59|91.59|
|52|1.92|1.33|52.00|88.94|94.69||72|1.39|0.73|72.00|92.16|92.16|
|53|1.89|1.29|53.00|89.62|95.12||73|1.37|0.71|73.00|92.71|92.71|
|54|1.85|1.26|54.00|90.27|95.52||74|1.35|0.69|74.00|93.24|93.24|
|55|1.82|1.22|55.00|90.89|95.90||75|1.33|0.67|75.00|93.75|93.75|
|56|1.79|1.18|56.00|80.64|96.25||76|1.32|0.64|76.00|76.00|94.24|
|57|1.75|1.15|57.00|81.51|96.58||77|1.30|0.62|77.00|77.00|94.71|
|58|1.72|1.12|58.00|82.36|92.59||78|1.28|0.60|78.00|78.00|95.16|
|59|1.69|1.09|59.00|83.19|93.11||79|1.27|0.58|79.00|79.00|95.59|
|60|1.67|1.05|60.00|84.00|93.60||80|1.25|0.56|80.00|80.00|96.00|
~

*** 81～100% [#p81]
|~p|~E[X]|~σ|~f(0)|~f(1)|~f(2)|~ |~p|~E[X]|~σ|~f(0)|~f(1)|~f(2)|
|RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:||RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:|RIGHT:|c
|81|1.23|0.54|81.00|81.00|96.39||91|1.10|0.33|91.00|91.00|91.00|
|82|1.22|0.52|82.00|82.00|96.76||92|1.09|0.31|92.00|92.00|92.00|
|83|1.20|0.50|83.00|83.00|97.11||93|1.08|0.28|93.00|93.00|93.00|
|84|1.19|0.48|84.00|84.00|97.44||94|1.06|0.26|94.00|94.00|94.00|
|85|1.18|0.46|85.00|85.00|97.75||95|1.05|0.24|95.00|95.00|95.00|
|86|1.16|0.44|86.00|86.00|98.04||96|1.04|0.21|96.00|96.00|96.00|
|87|1.15|0.41|87.00|87.00|87.00||97|1.03|0.18|97.00|97.00|97.00|
|88|1.14|0.39|88.00|88.00|88.00||98|1.02|0.14|98.00|98.00|98.00|
|89|1.12|0.37|89.00|89.00|89.00||99|1.01|0.10|99.00|99.00|99.00|
|90|1.11|0.35|90.00|90.00|90.00||100|1.00|0.00|100.00|100.00|100.00|
~


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