Clear[slump,start,data,xt,tid];

data=Table[N[Mean[Table[{tid=0,xt={slump=Random[UniformDistribution[{0,1}]],If[slump<1/2,start=0],If[1/2≤slump<3/4,start=1],If[3/4≤slump<7/8,start=2],If[7/8≤slump<15/16,start=3],If[15/16≤slump<31/32,start=4],If[31/32≤slump<63/64,start=5],If[63/64≤slump<127/128,start=6],If[127/128≤slump<255/256,start=7],If[255/256≤slump<511/512,start=8],If[511/512≤slump<1023/1024,start=9],If[1023/1024≤slump,start=10],start}[[13]],While[tid<10 && xt<19/2,If[xt<1/2,tid=tid+Random[ExponentialDistribution[1]];xt=1,tid=tid+Random[ExponentialDistribution[3]]];slump=Random[UniformDistribution[{0,1}]];If[slump≤1/3,xt=xt+1,xt=xt-1]],If[xt>19/2,1,0]}[[4]],{i,1,10000}]]],{j,1,200}];

N[Mean[data]]

Sqrt[0.00826*(1-0.00826)/20000000]

0.00826

data