You are assuming empty cell would have 0 V, 50% charged cell would have 4,2 * 50% = 2,1 V and fully charged cell would have 4,2V. It is not so, voltage does not drop linearly with discharge. Besides that, Li-Ion batteries must not ever be completely discharged as they would explode or at least be irreversibly damaged - charging would not be possible anymore. That's why all of them have some electronics which monitors the voltage and cuts off discharging when the charge level drops below set limit. Higher that limit and longer (more cycles) the batteries would last.
Same with charging and overcharging. If they are charged too high they can explode or get irreversibly damaged. That same electronics prevents overcharging also.
Here is a typical chart of voltage (white line) of a battery during discharge:
http://www.zeva.com.au/tech/LiFePO4/...rge-2.6ohm.jpg
It is a LiFePo battery so max is 3,4V and not 4,2 but general curve shape is still informative and valid. On the left side you can see that at first voltage quickly drops and than stays almost constant until only about 20% of charge is left where it again starts to drop faster. Over about 70% of charge interval the voltage hardly changed at all - for this LiFePo battery it changed for about 0.1V only - from 3.2V down to 3.1 V. Charge state went from about 95% down to about 25% but voltage only dropped for about 3%.
Li-Ion batteries don't like being charged to the max and they dislike being completely discharged even more. This "disliking" shows through drop in capacity after a few such cycles. You go through 1000 100% discharges and the battery will only hold say 30% - 50% of its initial charge as when it was still new. But if you treat it kindly (do not charge it to the max and never empty it) and you may find that after 1000 such incomplete discharge cycles the battery could still keep over 80% of its initial charge as when it was still new.
Now, with tweaking these parameters - hove high to charge it (up to 90%, 91%, 95%, ...) and how low to let it discharge (down to 30%, 25%, 20%) - you can increase its lifetime without compromising the capacity too much. For example you decrease max range with one charge for about 20% (only allow for 80%DOD) but more than double or triple the available cycle count before the battery dies on you. In this way you increased the total distance given battery will last i.e. you maximized the miles/$ for given battery.
Linear Mode
