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MonteCarloPi[samplesize_Integer] := N[4Mean[If[# > 1, 0, 1] & /@ Norm /@ RandomReal[1, {samplesize, 2}]]]
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{#, MonteCarloPi[#]} & /@ (10^Range[1, 7]) // Grid
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monteCarloPi = 4. Mean[UnitStep[1 - Total[RandomReal[1, {2, #}]^2]]] &;
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monteCarloPi /@ (10^Range@6)
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MonkeyDartsPi[numberOfThrows_] := (
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xyCoordinates = RandomReal[{0, 1}, {numberOfThrows, 2}];
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InsideCircle = Length[Select[Total[xyCoordinates^2, {2}],#<=1&]] ;
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4*N[InsideCircle / Length[xyCoordinates],1+Log10[numberOfThrows]])
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Grid[Table[{n, MonkeyDartsPi[n]}, {n, 10^Range[7]} ], Alignment -> Left]
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