I want to post the model i have in my mind currently (after reading your answers) and see if you agree or disagree with it.
A gas in a box (idealized closed system) has N possible states. Each of those N states has a certain entropy value. Given the gas is in one of those N states with a certain entropy value, there are X states with a lower entropy value, we could calculate the total probability of the gas reaching one of those X states.
There are also Y states with a higher entropy value, we could also calculate the total probability of the gas reaching one of those states.
total states N = X+Y (+1?)
Each of the X and Y states in particular have their own probability value depending on which state the gas is in currently. (not sure here if there are states with 0 probability depending on the current state of the gas - input appreciated)
The gas could jump to either a state of the X states or of the Y states, hence reach a state of higher or lower entropy at any given time. However, it is more likely to reach one of the Y lesser entropy states if the combined probabilities (of all Y states) are higher for such a state (and vice versa).
The point where reaching one of the X states is just as likely as reaching one of the Y states, hence, falling into a state of higher or lower entropy is equal, is what some seem to call the equilibrium state(i would rather call equilibrium point). This is NOT the maximum entropy state of a gas.
In fact, reaching a maximum entropy state for a gas seems highly unlikely just as it is highly unlikely for a gas to reach a minimum entropy state. Not impossible for both options, given enough time.
A gas inside a box will always tend to move towards the equilibrium point because of above considerations.
Once at the equilibrium point, where the next state of the gas being one of higher entropy is just as likely as being one of lower entropy, the 2nd law of thermodynamics has no meaning at all, not even in the form of "A closed system is more likely to increase in entropy".
edit: Furthermore, once at the equilibrium point, nothing stops the gas from reaching a state of minimum entropy, given enough time. It's just not very likely to happen in short time(not impossible). Given enough time however, it's a given it will happen at some point.
Feel free to toast me now, and hopefully tell me where i am wrong so i can adjust my worldview if required.