Whatever weapon you fence, if you are looking for a great drill to improve your distance, try the glove game. In this drill no weapon is needed. You need a partner and each of you needs a glove to hold. The fencers start on the en garde lines and take turns trying to hit their opponents with their gloves. The attacker may only use a maximum of two advances and a lunge while the defender may use whatever footwork they want. While two advances and a lunge is the maximum, the fencers do not need to use all of their steps during each attack. After each hit, the fencers reset to the en garde lines and whoever started first goes second this time.
In this drill because of the relatively small amount of space that the fencers can cover while attacking, the defender must stay close and be prepared to change directions quickly when an attack ends. The benefits of this drill will be that the defender will learn to stop on a dime and take over immediately and the attacker will develop a sense of when their quick, surprising attacks will be able to hit their opponent. This will help them figure out their distance for when to start an attack; an essential skill in any of the three weapons. This drill is particularly fun because once you get comfortable with the basics of it, you and your opponent will basically be bouting.
The most common mistake made by the defender is giving up too much distance on defense. Unlike in an actual bout, the point of this drill is to keep the distance tight so you can take over as soon as possible when your opponent misses. If you frequently pull the attack short by running away and giving up your chance to make a riposte you are missing the point of the drill.
As for the attacker, I will often see the attacker only using their full amount of steps for attacking, even if it puts them in a bad position. Unlike in a real bout situation an attack in the glove game has a definitive end. This is so that both you and your opponent can figure out the distance more accurately. I have seen situations where beginners play this game and the defender figures out the distance before the attacker does and waits right on the edge of distance for the attacker to make a full double advance lunge that has no chance of hitting and then just get immediately popped afterwards for their mistake! This game requires thought as much as good balance and footwork so don’t be scared to play around a little!
Try it out at your next practice but since everyone has different timing, this game should be played against more than one opponent for optimal results.
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Jonathan Yergler
The Fencing Athlete 
My issue with the glove game at a higher level is that if you allow attackers not to use their full allotment of footwork, then it is impossible for the defender to know when their role has switched to attacker until after the attacker has already switched to defense mode and is opening distance. This then encouraging chasing the other person while they are moving away, which is generally counterproductive in epee.
That is even more of a reason to stay close to your opponent: to be ready to take over in case they decide to switch to defense before they have used all of their steps. If anything I would say that gives the higher level of the game even more depth that can continue to help you improve even after mastering the obvious lessons that the drill teaches.
I completely agree with the conventional weapons. But epee really functions differently. The glove game models the turn taking of priority pretty well, but it doesn’t model the way distance and timing work at higher levels in epee.
So in that respect no, it does not exactly resemble a high level epee situation. But in all three weapons you need to have sharp footwork so you an stay close to your opponent whether they make a real attack or a broken one. The glove game will enhance your ability to do that.