«The origin of the term bankers' rounding remains more obscure. If this rounding method was ever a standard in banking, the evidence has proved extremely difficult to find. To the contrary, section 2 of the European Commission report The Introduction of the Euro and the Rounding of Currency Amounts suggests that there had previously been no standard approach to rounding in banking; and it specifies that "half-way" amounts should be rounded up.»
https://en.wikipedia.org/wiki/Rounding#History
The whole page about rounding is mind blowing. And then the comments about different programming languages and number representations in computers and so much more.