The Bullmastiff is a tough dog, able to withstand incredible punishment, and, as you can see, I am a great fan of the breed, but one on one, if the cougar decided to stay and fight, the cougar would probably win 97 out of 100 times, just because a cat has 5 pointy ends, and a dog only has one. I believe a Bullmasitff could inflict major damage on a cougar, but in the end, the decision would go towards the big cat. Another thing to point out, is the Bullmastiff wasn't bred to be a fighting dog, it was bred to be a guard dog, and protect his/her master's property and family (originally to protect night watchmen) and they do it better than any other breed of dog. They can sweep a man off his feet and keep him pinned down without using their muzzle. They are very quick, and very powerful. And as was pointed out, a cougar will usually not stand and fight, because they have a high level of self preservation, where Bullmastiffs are notorious for fighting to the death to protect their family. As such, I really don't believe a cougar would attack with a large dog such as the Bullmastiff around. And I do know this, I have no fear of any animal - man or beast, when I have my Bullmastiff with me or when she is with my children. Their presence commands and demands respect, or fear, your choice.