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For general positive integer <math>r</math>, {{harvnb|Matsui|Ano|2016}} discussed the tight lower bound of win probability.
When <math> r=3,4,5 </math>, tight lower bounds of win probabilities are equal to <math> e^{-1}+ e^{-\frac{3}{2}}+e^{-\frac{47}{24}} </math>, <math> e^{-1}+e^{-\frac{3}{2}}+e^{-\frac{47}{24}}+e^{-\frac{2761}{1152}} </math> and <math> e^{-1}+e^{-\frac{3}{2}}+e^{-\frac{47}{24}}+e^{-\frac{2761}{1152}}+e^{-\frac{4162637}{1474560}}, </math> respectively.
For further numerical cases
== See also ==
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