After picking some scheme to generate messages that predict n bits of their hash in some form, the chance of finding at least one message that correctly predict

After picking some scheme to generate messages that predict n bits of their hash in some form, the chance of finding at least one message that correctly predicts its hash is 1 - (1 - 1/x)^x where x is 2^n. This approaches 1 - 1/e = 63.2 % for large n. So by trying a few different schemes, for example slightly varying the prefix »The SHA256 for this sentence begins with:«, it becomes quickly very likely to succeed. In the limit of large n, for example only 5 different schemes will yield at least one correct message with 99 %. With 5 patterns, 24 bits and SHA-1. The SHA-1 hash of this text starts with 051E35. The hash of this text starts with A943BD. The SHA-1 hash of this text starts with B6640C. The SHA-1 hash of this message starts with C3B03D. The SHA-1 hash of this message starts with D93717. Or the same as before but as patterns just padding the 6 hex digits with zero zero to eight dots. 0AF3DE.. 2AF7DF....... 3E0E50. 8EE84C..... 919025... A57198.... B20775..... DA525A........ ED20F4..