I bought from ebay
http://r.ebay.com/Xdqjmw where it says Amp Hours: 6-8 hours. Using Qantas calculation ("Note: Watt hours (Wh) are determined by multiplying the voltage (V) by the amp hours (Ah). ie. 12V x 5Ah = 60Wh") this makes it 160Wh so within the limit (just). As explained earlier (with link provided) the 50000mAh is meaningless (and Qantas knows this hence the use of Wh). I had never seen the MaxOak website that puts it at 185Wh
The reality is that Qantas were happy to take it but this particular airport was not. Every other airport is happy to take it (I have flown with it ~50 times). Qantas argument was that the airport was liable not them.
Of course, now I know that it is 185Wh I will not try to fly with it again. However, following Qantas guidelines (to determine Wh by multiplying voltage and Amp Hours) it was reasonable of me to assume it was OK and therefore unreasonable of Qantas not to compensate me for its loss (imho - but I realise I'm not getting much support for this view here

).
It doesn't matter what someone on ebay says that it is - the ebay seller listed the mAH and the voltage at a level that would still lead to a Wh that exceeds Qantas's limit - voltage 5V and aH of 50 = 250 -- not sure how it is reasonable to think that it is ok
at 3.7v and 50 Ah , it is 185Wh as listed by the manufacturer - the 50000 is not meaningless , but is exactly what the manufacturer says it is - 50,000 mAh = 50 Ah
50,000 ÷ 1,000 ≠ 5 , which is what would be required for the item to be 5Ah
Any Qantas agent that said that Qantas was ok with it was incorrect since it is listed under dangerous goods
Qantas owed no compensation for refusal to carry goods listed in its dangerous goods list