Some dogs can't resist a good belly rub and/or scratch, and the reasons are both behavioral and neurological. While showing off his tummy is a conscious act that speaks to his relationship with you, your dog also undergoes a neurological reaction when you start stroking his fur. The combination of the two can make tummy rubbing a wholly satisfying experience for your pet -- if he lets you do it in the first place.
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When your dog displays his tummy for a rubdown, he is performing an act that displays his absolute trust in you, as rolling over to show you his belly leaves him completely physically vulnerable. Of course, it's pretty obvious that rubbing his belly just plain feels good to him, much like other types of petting, but it also shows his confidence that you won't take advantage of his vulnerability.
Science also plays a role in why your dog likes tummy rubbing, and his appreciation for the rub is linked to the reasons he enjoys all types of petting. Dogs have a particular brain neuron that responds exclusively to the stimulation of hair follicles, which means that when you rub his tummy, the stroking of his tiny belly hairs is actually providing a specific type of stimulation in your dog's brain. This neurological stimulation is only possible through stroking, which makes petting like belly rubs uniquely satisfying.
While your dog may love tummy rubs, don't confuse his uncontrollable leg-kicking with the throes of ecstasy. The leg-kicking associated with tummy rubs is often considered a sign of your dog's enjoyment, but in reality, this is an involuntary reaction, much like kicking your own leg when a doctor tests your reflexes with a mallet to the knee. If your dog always kicks his leg and doesn't appear to enjoy tummy rubbing, try stroking an area of the belly that doesn't induce kicking, and he may like it more.
Rubs Him the Wrong Way?
Not all dogs enjoy tummy rubbing, and while this may be related to the potentially-irritating involuntary kicking reaction, it may also be behavioral. Rolling over to display the tummy and engage in rubbing requires absolute trust on your dog's part, and if he is unwilling to concede -- or unable to trust humans -- he is unlikely to do so. Don't force a dog to engage in tummy rubbing -- if you roll your dog over and rub his belly, it can be an upsetting experience that further shakes his trust. Also, too vigorous rubbing may be overstimulating to some dogs to the point of discomfort. So start off with gentle stroking, and carefully pay attention to his reactions to see if he is enjoying it (that is, happily remaining on his back and allowing the rubbing to commence) while you work your way toward rubbing/scratching more vigorously.