Here is my current recommendation for a real-world trading fraction:
min[ 0.9/max[ .0001 , 2*max[ -Ri ]_i=1toN ] , ½*( new_Kelly_formula ) ]
new_Kelly_formula = max[ 0, s1 ]*( s2*s2 - s1*s3 )/(s2*s2*s2 + s1*s1*s4 - 2*s1*s2*s3) ,
where
S1 = sum[ Ri ]_i=1oN ,
S2 = sum[ Ri*Ri ]_i=1toN ...