Cartos are equal to about 5 or 6 cigarettes because of the amount of liquid they hold: 1ml. You can make it seem like more by not inhaling much, taking light puffs, not using it for the 12 minutes or so it would take to get the same amount of nicotine in a cigarette, and so on.
it depends if you are cutting down at the same time as you are switching to an ecig. If you are just switching then you will want the equivalent delivery of your full cigarette's worth, and that is about a quarter-pack of cigs per carto.
If you are also cutting back then you might use the ecig very lightly, and in that case a carto could go further. It would be the same as smoking half the cigarette, not inhaling much, and the like.
To get the same hit from a mini as a cigarette, you need to inhale about 6 seconds (maybe more), use it for more than twice as long as a cigarette lasts, etc. That way, the ecig session is equivalent to a cigarette. But you don't have to do that - you can use it very lightly. In that case a carto might last you all day - but don't call it the 'equivalent of a pack of cigs' because it isn't. It only contains 1ml of liquid, about 22 drops, and experienced users will tell you that a cigarette is about 4 drops. And don't forget that you cannot use all the liquid in the carto, as some stays in the filler.