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Playing dead involves your dog lying down. Before he can learn this trick, he should be comfortable with the command to lie down. Preferably, this area should also be quiet so that your dog does not become easily distracted. If your dog does not already know this command, teach him by holding a treat high in the air with your hand. As he is looking up at the treat, push on his back end until he sits; firmly say the word 'sit' as you are doing this. Once he is seated, reward him with the treat by bringing the treat to him instead of allowing him to jump up to get the treat. Firmly tell him 'No' if he jumps up. Practice this several times a day for few days until he can sit without you pushing on his back end. Each practice session should last about 10-15 minutes. Continue to give him treats as positive reinforcement each time that he sits. Hold a treat in front of his nose, but do not allow him to eat it. Instead, slowly move the treat down to the ground while still holding it in front of his nose. Say the verbal cue 'down' as you are moving the treat to the ground so that your dog associates the verbal cue with the action of lying down. Your dog should be lying down by the time you move the treat down to the ground. If he gets back up, continue practicing until he lies down each time you move the treat down to the ground. Reward with him a treat when he lies down without quickly getting back up. Hold your hand in front of your dog's nose as if you had the treat, but do not have a treat in your hand. Use the same hand motion as if you had the treat to get your dog to lie down. Once again, reward him with a treat when he reliably lies down without quickly getting back up. You will need to practice this command with your dog several times a day for at least a few days. Each practice session should last about 10-15 minutes. If you want to challenge your dog, you can gradually decrease the visual cue until he learns how to respond to only your verbal cue to lie down.
Teach your dog the 'down' command before teaching him how to play dead. Choose a comfortable area to train your dog. Command your dog to sit. Stand directly in front of your dog while he is seated. Guide your dog to lie down without a treat. Continue practicing until your dog learns how to lie down at your command.