In a tug of war game on rough ground who will win? The one who applies greater force on the rope or the one who applies greater force on ground?
The force on rope is equal for both of them at any time.
For winning the game the force on ground is responsible.
Force on the ground can never be greater than force on the rope
Each players individually exerts some force on the rope and on the ground, but that doesn't means that the same amount of work is done on the rope and on the ground, or that one players exerts the same total force as his opponent. The winner overcomes his adversary only if/when because he exerts an overall greater force distributed both on the rope and on the ground.
No one must necessarily slip: imagine that your feet rest in a little hole or on a starting block. Ground is just a point of support. The loser will be thrown off balance when he cannot withstand the torque.
A lot of confusion has been brought through the comments adding to what already stated in the accepted answer, which has been soon refuted by Jàn Lalinsky:
Let's se if we can clarify all aspects starting from this crucial one. Suppose a dumbbell of 20 Kg is laying on the floor: g is constant, the reaction of the floor is constant ergo the force on the dumbbell on each direction is equal at any time. Now suppose you lift it with your arm[s]:
g is still constant but your reaction is not constant and the bumbbell will have oscillations whose amplitude depends on your strength. The dumbbell will never be perfectly still, even if the contrary force is constant.
As to the rope the situation is even worse as the opposing force is never equal. Let's consider only two players: the rope will never be still because when one player jerks it, the reaction of the opponent will always be delayed by, say, at least 2/10th of a second and after the jerk he must recover 'hang' from the effort for a fraction of a second or more, so, the reaction of the opponent will restore the position of the centerline or move it further toward the other side.
That as to the first fallacy: the force on rope is never equal for both of them at any time and the rope is never perfectly still.
Now the force on the ground: Each player must always stand at an angle (with the ground) less than 90°, best less than 45°, as in this picture: (http://en.wikipedia.org/wiki/Tug_of_war#mediaviewer/File:Touwtrekken.jpg), with at least one leg fully stretched. (I couldn't find a picture with one player. Consider only the first player: the other players can, in turn, bend knees and relax until the get the 'hang' command:
in order to:
It seems obvious that when leg(s) are stretched a player can exert no direct force directly on the ground, as he cannot stretch his leg(s) any further: look at the first player in the picture, how can he exert force on the ground if not by pulling the rope? If he bends his knees, he can exert some force *some*times. On the other hand, if he kept his knees always bent he would be easily carried away. In conclusion, the force on the ground cannot be greater than the force on the rope and cannot be the determining factor to the victory, and moreover no work is ever done on the ground. As prievously stated, ground is only a point of support and he exerts his force mainly on the rope, bending shoulders backwards and forearms closer to the chest.
That as to the second fallacy: the force on the ground cannot be responsible for victory, the victory goes to the player that exerts a greater overall force (on rope/ground) for a longer time. If their strength is equal the one who gets tired first loses.