As the cartoon opens, Wile E. Coyote runs up to Bugs Bunny's hole and constructs a door. He hits the door and Bugs opens it. The Coyote advises Bugs of he being a rabbit and himself a genius, and he will eat Bugs and he is faster and smarter than him. Bugs, unimpressed, says "I'm sorry mac, the lady of the house ain't here. And besides, we mailed you people a check last week." The Coyote leaves, asking himself, "Why do they always want to do it the hard way?"
At his cave hideout, the Coyote's first plan then follows: he makes one thermal tamp and takes a cook book and ingredients for preparing "Rabbit soup" in the rabbit's hole. Bugs (in another hole) looks at his work and asks him what he is preparing. The Coyote says the hole has a rabbit inside, but it does not. He looks into the hole and Bugs pushes him and traps him in the hole. He then picks up a bat, goes back down the second hole, and clobbers the Coyote at the other hole, prompting the Coyote to remark, "Well, back to the old drawing board."
Afterwards, the Coyote prepares a second plan: the use of a chute for entering a cannonball in Bugs's hole. After the ball arrives in the hole via the chute from a cannon, Bugs uses a second chute for returning the ball to the Coyote. The Coyote then returns to his cave.
Some time later, Bugs goes to the Coyote's cave to sign what appears to be a will (Bugs claiming he's giving up, but needs a witness for his will). He proffers the will for the Coyote to sign and one "pen" (actually a lit stick of TNT) with which to sign it. Coyote knows its a TNT stick and puts out the fuse. While gloating, it is revealed there is a fuse at the other end of the TNT stick, which explodes just as Coyote realises it.
The Coyote builds one explosive lady rabbit and activates her, but nothing happens. Shortly thereafter, the Coyote encounters one coyote lady (also an explosive) and Bugs detonates that robot. The Coyote (now charred from Bugs's exploding coyote) looks at the robot rabbit he failed to ignite and tries to push her out the window, but she explodes.
The Coyote then makes an exploding bird-hunting disc (usually used for Road Runners, Mice and Rabbits) with a "hunter options" mechanism. The disc flies to Bugs's hole and encounters a chicken (Bugs disguised), who then writes "Coyote" in on the "hunter options" mechanism, twisting the dial to the new target. The disc returns to Coyote's home, blowing up not only Coyote's home- but the whole mountain.
The Coyote makes one last plan: He puts an explosive liquid substance in a line of carrots in a rack inside his alternate home, a ramshackle shack (This plan being seemingly desperate, as in logic, Bugs would not be in any edible pieces after the explosion). Bugs, using a tractor, carries the shack to the desert's railroad track (later seen again in Stop, Look and Hasten). Meanwhile, Coyote is admiring his new self-given title "Super Genius" (Which he comments "I like how that rolls off the tongue- Wile.E.Coyote: Suuuper Geeenius"). All the while, a train rushes toward the shack. Coyote realises this and - in vain - puts the window blind down. The train hits the shack, and the impact causes a great explosion (what with the shack being filled with many explosive items), launching Coyote high into the air onto a branch.
Coyote (still dazed and covered in ash from the previous scene) returns to Bugs's hole, rebuilds his door, knocks on it and says "Allow me to introduce myself. My name is Mud." and abruptly passes out. Bugs then looks into the camera and says to us, "...And remember, MUD spelled backwards is DUM!" (dumb)
- Wile E. Coyote: Allow me to introduce myself. My name is Wile E. Coyote, genius. I am not selling anything nor am I working my way through college, so let's get down to basics: you are a rabbit and I am going to eat you for supper. Now don't try to get away, I am more muscular, more cunning, faster and larger than you are and I am a genius, while you could hardly pass the entrance examinations to kindergarten, so I'm going to give you the customary two minutes to say your prayers.
Bugs Bunny: Sorry, Mac, the lady of the house ain't home and besides, we mailed you people a check last week.
- Bugs Bunny: (singing) I'm looking over a three-leaf clover that I overlooked be-three...
- Bugs Bunny: I have come to give myself up, on account of I cannot compete no more against such genius.
Wile E. Coyote: A wise decision, my friend. You have saved yourself from a fate worse than the frying pan.
Bugs Bunny: I have only one last request. I have made my last will and testament, but I need a witness to make it official. Would you sign it with this fountain pen? (hands Wile E. the will and a lit dynamite stick for a pen)
Wile E. Coyote: Why certainly, my boy! Delighted to be of service! Very amateurish attempt upon my person.
(Wile E. extinguishes fuse, throws stick up in the air repeatedly - not noticing the lit fuse on the other end)
Wile E. Coyote: Being a genius certainly has its advantages. (notices the lit fuse, dynamite explodes)
- Wile E. Coyote: Brilliance. That's all I can say. Sheer, unadulterated brilliance!
- Bugs Bunny: Fight fire with fire, I always say.
- Wile E. Coyote: (while preparing his explosive carrots) Wile E. Coyote, Supergenius. (he hears the sound of a train whistle in the distance, but he ignores it) I like the way it rolls out. Wile E. Coyote, Supergenius!
(The train whistle is heard louder than before. Wile E. turns and sees a train heading directly at his shed. He pulls down a window shade right before the train hits his shed, blowing it up. The Coyote is then seen holding onto a branch high above the tracks, charred dark grey and speaking groggily.)
Wile E. Coyote: Wile E. Coyote... Supergenius!
- Wile E. Coyote: Allow me to introduce myself, my name is Mud.
Bugs Bunny: And remember, Mud spelled backwards is Dum!
- This was the second cartoon to feature Wile E. Coyote (following 1949's Fast and Furry-ous), and the first in which he is identified by his full name. It is also the first in which the Coyote speaks; his voice, like Bugs's, was provided by Mel Blanc.
- VHS - Road Runner vs. Wile E. Coyote: The Classic Chase
- DVD - Looney Tunes Golden Collection: Volume 4, Disc 1