Stopped Clock Paradox

Paradox
Of two clocks, one is better than the other if it shows the absolutely correct time more often than the other.

Consider:
 * Clock $A$, which loses $1$ minute every day
 * Clock $B$, which is stopped.

Clock $A$ is $1$ minute slow after day $1$, and $2$ minutes slow after day $2$, and so on.

There are $720$ minutes in $12$ hours.

Hence it will be $720$ days, or nearly $2$ years, before it shows the right time again.

On the other hand, clock $B$ shows the correct time every $12$ hours.

Hence clock $B$, a stopped clock, is better than clock $A$, which loses but a minute a day.

Resolution
First thing to note is that a clock that loses $1$ minute a day is a poor clock, and on an practical level not all that much better than a clock that does not run at all.

But let us modify our absolutely correct to correct within $30$ seconds, which is reasonable for an old dial clock.

One can assume that an adequate clock will lose or gain no more than $30$ seconds over the course of a number of months.

If I had a clock which was worse than that, I would throw it out and get a better one.