Moscow is far from being a pickpocketing capital like Barcelona or Naples and generally feels safer than many other major European cities. But there are several points to consider.
Good news first:
In the metro we pay a fixed price at the moment you enter it. Its price doesn’t depend on how far you go or how long you will be underground. Price of one ride is 55 RUB (1 USD is about 65 RUB).
There are also cards for unlimited trips valid for a number of days:
1 day - 230 RUB
3 days - 438 RUB