n = 10000;
Do[{
i = 0;
Do[{
cut1 = RandomReal[];
If[cut1 < 0.5, a = cut1, a = 1 - cut1];
b = RandomReal[1 - a];
c = 1 - a - b;
If[a + b > c && b + c > a && c + a > b, i++];
}, {n}]
Print[N[i/n]]
}, {10}]
n = 200000;
Do[{
i = 0;
Do[{
cut1 = RandomReal[];
a = Min[cut1, 1 - cut1];
b = RandomReal[1 - a];
c = 1 - a - b;
If[a + b > c && b + c > a && c + a > b, i++];
}, {n}]
Print[N[i/n]]
}, {10}]