Even though fat contains 9 calories per gram, compared to 4 calories per gram for protein, and 4 calories per gram for carbohydrate – increasing your fat intake can help you lose weight on a low carbohydrate diet, as long as you don’t take your calories to stupid. In general, the more of the right kind of fat you eat, the less hungry you will be, and the fewer carbohydrate cravings you will have. Substituting fat calories for protein calories decreases blood glucose. (I used to be a biochemist. I’ll spare you the lecture.) Low carbohydrate diets work best not as high protein diets but as high fat diets. 75% of your calories ideally should come from fat, not from protein. The best fat to eat is omega3 (salmon) fat, or mono (olive oil) fat, or saturated fat from ruminants (animals that chew their cud, beef or lamb or veal).