How to force sed to search not from the beginning of a line with '*' quantifier?

Question

linux

Given:
# echo 'abcd' | sed -e 's/a*//'
bcd (as expected)
# echo 'abcd' | sed -e 's/b*//'
abcd (why?!!)
How to rewrite the expression to get acd in the second case?

Answer 1

~$ echo 'abcd' | sed -e 's/b*//
g'acd

Answer 2

% echo 'abcd' | sed -E 's/b+//'
acd
% echo 'abcd' | tr -db
acd