The Iraqi army we trained is totally useless – training doesn’t impart motivation. Not our kind of training, anyhow. So how should the Iraqi government deal with the Islamic State?
The obvious answer is mercenaries, many of which already know Iraq pretty well. The Iraqi government has sufficient oil revenues to pay the sort of force I’m thinking of; at least they would if they could just moderate the corruption for a while. You’d want to hire the better sort of merc as far as you could – ex-US and British. Avoid bottom-feeders like Colombians.
Although ISIS is far more effective than the Iraqi Army, they’re far less competent than any Western army. They have plenty of enthusiasm, but so did the Dervishes at Omdurman. It’s not enough.
Of course the Iraqi government hates Blackwater types (who doesn’t?) , and might well stab them in the back after they take care of the the enemy. Still, I think that they could take care of themselves.
Ten Thousand should be enough for the job.