To Marxists a state is organised violence of one class to suppress another...
That's an oversimplification of a complex issue which was resolved in different ways in different Marxist currents.
For instance, I don't think that any kind of Marxism should confuse specific apparatuses of repression for the whole of the apparatuses which function as the organization of capitalist rule. And that's what you did.
One other point in Marxist theorizing about the capitalist state concernes the famous distinction between the base (economic activity) and the superstructure (ideological forms which are more or less derived from the mode of production).
Thus, one Marxism may postulate that the capitalist state is not part of the capitalist system, that it is external to it in its function of maintaining favourable conditions for capital accumulation.
Another Marxism would argue that the capitalist state also intervenes into the relations of production, that it constitutes these relations in their specificity.
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“The possibility of securing for every member of society, by means of socialized production, an existence not only fully sufficient materially, and becoming day by day more full, but an existence guaranteeing to all the free development and exercise of their physical and mental faculties – this possibility is now for the first time here, but it is here.” Friedrich Engels
"The proletariat is its struggle; and its struggles have to this day not led it beyond class society, but deeper into it." Friends of the Classless Society
"Your life is survived by your deeds" - Steve von Till