There is 3,500 calories in a pound of fat. So, if you eat less per day than your body burns in a day, you'd lose, e.g., 350 fewer calories per day equals minus one-pound of fat per 10-days.

A complicating factor is that, if through a reduction in daily calories, you lose weight faster than you put it on, your body may switch to a "surviival" mode and that changes everything, e.g., in that mode you can live on less and the body will try to convert and store everything that you eat as fat.

I think that the reason high protien and fat combined with low carbs allows some people to eat more without gaining weight is that the body is faked out: it is programmed to "think" that if you're getting that much "quality" in your diet, you obviously have no problem hunting and your environment is very abundant so, no worrries about storing up for the winter.