In any case, there's a fun way to easily estimate the chance mentally. You just have to know that a 1 in x chance repeated x times is approximately 63% success ( 1 - 1/e )
160 tries is about 2 and a half of x (so to speak, because x is 64) so you have roughly .3 x .3 x .7 (round first two down then last one up). To get ~6% chance which we can see is really close.
So you're claiming that not getting e4 (160 times) is a 1/64 chance because there are 64 squares?