If we go by simple logic and the rule of mathematics, a power bank 10000mah should be able to charge a device of battery capacity 2000mah alteast 5 times. And this would have been true if other constraints were not in place. When we talk of electronic gadgets, the actual performance and the stated performance would always vary because of internal and external factors like heat loss, power loss, battery health and some other factors.
If you buy power bank 10000mah for a device, you are not really going to be able to use all of the 10000mah battery into use, there would be looses that would lessen the real capacity of the power bank.
The first factor that affects the battery capacity is the conversion rate. Conversation rate is the loss of power, could be in form of heat loss too, that occurs when you charge a device with a power bank. The reason here is fairly simple, if you stuff in a big bite of food in your mouth, there will always be some food that will spill. Similarly, when we talk of charging a device with a power bank, there is loss of power because of the difference in the output voltage of the power bank and the input voltage of the device that you charge with it. The output voltage of the power bank varies between 3.7 volts and 4.3 volts, this fluctuation occurs as the battery of the power bank begins to deplete. Now, the input voltage of most of the devices is 5V. In order to compensate for the less voltage, the output voltage of the power bank is converted to be equivalent to 5V. This conversion results in heat loss. You can calculate the conversion rate in a simple way, Charge the power bank and use it to power a device with 2% battery, record the performance of the power bank and calculate the conversion rate.
The second factor that affects the battery capacity of power bank is the battery health. With time, as you use Smartphone/gadget/device, the battery health gets affected. All those times when you did not charge your phone with an original charger or when you were negligent towards ever charging your phone to a 100% or when you always used USB ports of desktop/laptop to charge it will come and bite you back. These things and several other factors can affect the battery health of the Smartphone you own. When we talk of real capacity of a power bank 10000mah, the battery health is considered to be perfect but this is not really the case when we check that in real time. For calculating battery health of Smartphone, there is no fix method, but if you think that the phone is working fine, the average efficiency can be used i.e. 80% or 0.8
These two important factors affect the real capacity of the power bank and thus the actual battery capacity is low then the real battery capacity. To calculate the actual number of times that you charge a device with your power bank 10000mah, use the following formula:
Real battery capacity of power bank * conversion rate * battery health/ battery capacity of gadget= no of charge time