If that were true, then it would be just as likely that all the molecules go to the next room as stay evenly distributed. Not quite, I counter. Because in fact there are many more ways for the molecules to be evenly distributed than there are for them to be all in one room, if we count all the microstates that make up these two macrostates . We can get it into the tidy state, but it takes energy on our behalf, because we are choosing just one of the many possible arrangements of objects . The tidy state is ordered , and the messy state is disordered .
Nature tends towards states with highest entropy because they are the most likely.
Liquid water has a higher entropy than ice, because it is disordered. When water turns to ice, it gives off energy in the form of latent heat, because ice is a lower-energy state than water. To the surrounding system, the air molecules etc. And when they gain energy, they increase their disorder, because they gain new ways of zipping around. Whether or not it does depends on the temperature.