The reasoning in my statistical physics book is as follows:
$\cdot$ The basic postulate of Statistical Mechanics is that for a system with a fixed energy, particle number and volume, each microstate is equally likely to occur.
$\cdot$ For a certain physical quantity A, the entropy (and multiplicity) will have a maximum at A* of A.
$\cdot$ Starting at A different from A*, the system will explore other available states and automatically end up in configurations with the value A*, because a large majority of microstates has a value for A very near A* due to the high multiplicity at A*.
$\cdot$ Conclusion is that a system starting in A will always end up in a state where S has its maximum (at A*)/the entropy always increases if we leave a system alone.
I do not understand that, when the system explores all available states and when every microstate is equally likely to occur, that the entropy necessarily increases all the time. Isn't there a small chance that the system will end up in a state with significantly lower entropy and that it immediately gets in to a high entropy state again after?