A key part of “modern” (centuries old but still new in the scheme of things) is “double entry book keeping”.
That basically means that every change in a balance (e.g. you having more money) is accompanied by an equal and opposite change (i.e. another player having less money).
The advantage here is its easy to audit – the bank just checks all the transactions pair off and sum in each account to the same amount. If anyone fakes a transaction it’s relatively likely the person missing money lets the bank know as they want it back.
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