I wouldn't quite go that far. The fact that markets can remain irrational longer than participants can remain solvent means that participants with deeper pockets have an inherent advantage, even if they have less information. How quickly a random walk will take you to zero depends on how far above the baseline you start.
If I inherit a billion dollars tomorrow, I will have zero additional information and be no more sophisticated than I am today. But I will have deeper pockets than any retail investor and will be able to withstand market irrationality longer than them.