I see what you're saying. If you're taking a 5 second hit with a 3ohm over a 3 second hit with a 1.8ohm, I honestly don't know what the ratio of battery life is to one another. Given that you hit them in the same amount of time, the battery should last longer while using a 3ohm.
Well, here's what I *believe* I know - please suggest corrections and I can make them (today I think anyway)...
In terms of the total capacity of a batteries charge (expressed on the battery as "mAh" or milliAmpHours), to determine how much of that total you are using each activation, you could determine the milliAmpHours:
Code:
3.7 @ 1.8 ohms = 2000mA * 3sec = 6000mAs (1 milliAmpHour = 3600 milliAmpSeconds)
3.7 @ 3 ohms = 1250ma * 5sec = 6250mAs
6000mAs is about 1.7mAh. So, with a longer activation, you are making up for the lost wattage per activation: stretching out the hit certainly balances things out for the most part (at least given these examples). At this rate a 900mAh battery should last for about 500 of EITHER of these activations for those durations...theoretically, and approximately...
The actual mAs usage per activation will be a function of battery drain over the span of activations as well as even each individual activation. That approximation is built in to these equations: "3.7v" or "3.6v" batteries typically top out a full charge voltage of 4.2v. Over their usable charge however, 3.6-7v serves as a general guide of the average voltage supplied to your circuit.
So, in terms of the power you generate (to provide an approximation of the hit 'strength') for each duration, you have:
Code:
3.7 @ 1.8 ohms = 7.6W * 3sec = 6.3 mWh (milliWattHour)
3.7 @ 3 ohms = 4.6W * 5sec = 6.3 mWh
Of course, there are always more variables (viscosity of the fluid, the rate of capilary action through the wick/bridge, the total coil surface area, etc, etc) that effect what portion of those mWh's are transferred to your vape cloud. Chemical characteristics and such also make for a battery's "preference" for low or high drain applications.
To me, this seems pretty accurate in fact. I prefer a lower-resistance atty and I do notice a loss of battery endurance. The reason seems to be because a 5 second hit on a 3ohm doesn't do the trick for me; I'll take 5 seconds on a 1.8 thank you very much. The above numbers are just estimates of course, but that "maximum hit" (mWh) that I want (say on the order of 10mWh?) I can get from 1.8 ohms much easier - stressing neither the capacity of my mouth nor my patience.
Random tip in either case: discharge your batteries to about 50% depleted. I'm sure you've depleted them (or at least activated the protective circuitry) a few times so you know about where that is. If you go about 1/2 of that time and charge them then, your battery should last longer overall (speaking about what I've read on Li-Ion batteries anyway).
Long story short (which you should always say when you just realized it's been too long aready), the ratio of consumption is directly proportionate with the ratio of the resistance differences.
Code:
3 : 1.8 [1.66667 to 1]
7.60556w * 5sec : 4.56333w * 5sec [1.66667 to 1]
enjoy
The Provari is next in my line of sight. It...will...be...MINE! 
