Right. But say at the quadrillionth decimal place you find a sequence of a million zeros, then a million ones, then a sequence of ones and zeros that forms a recognizable picture when plotted as a bitmap. Even though you'd expect that sequence to appear *somewhere* in pi, the odds against it occuring so early by "chance" would be astronomical.
Not really. It's only 1 chance in 10**111 that the first digits of Pi are 3. 1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651. A sequence of 111 zeros would have the same probability (as would a sequence of 111 ones.)