So if we pulled out of the Middle East, what would the probabilities be?

[AnalystInParadise]

62. No not really at all what would happen

1. The Kurds have far more soldiers, far more tanks, and far more artillery than ISIS. The Peshmerga was not mobilized when ISIS left Mosul to advance towards Irbil. Now the Kurds are mobilized and ISIS has pulled back. So no, the Kurds would not be conquered. 31,000 total ISIS fighters versus 300,000 Kurdish fighters with the Kurdish Tank Brigade also mobilized is a losing proposition for ISIS.

2. Nothing we do (short of keeping 50,000 Americans in Iraq) will make the Shia-led government more inclusive to the Sunni's. Moderate Sunni's will cling to the Shia government because the alternative is worse. The Sunni moderates are largely secular and can work with the Shia, they can't do the same with ISIS.

3. The Saudi government and the Gulf state GOVERNMENTS are terrified of ISIS and what it represents to their own system of control. Individuals in those countries however willingly send money to ISIS. The governments do not fund them. ISIS receives funding through the Hawala system. It stuns me that no one EVER talks about this system. When I was in Iraq, we routinely seized Hawala brokers in Iraq who were giving money to Al Qaeda. Money from Europe, North America, all over the place. Hawala is the problem. http://en.wikipedia.org/wiki/Hawala

4. Iran is already sending troops to Iraq. They will continue to do so, and those troops will march freely in the streets whether we do anything or not. http://www.bbc.com/news/world-middle-east-29186506

5. The Gulf states have next to no Armed Forces. Even the Saudis are largely a garrison army. The Gulf State would get destroyed. And by Gulf States we are really talking about the Saudis. Because even if the Gulf States sent HALF their armies into fight, leaving the other half to keep the peace back home, then the Gulf States would send less than 65,000 total soldiers into the fight. Even if the Iranians only committed 25% of their total combat strength, they would still outnumber the Gulf States. AND the Gulf States military forces would have to fight through SHIA controlled areas. Yeah that is so not happening.
Qatar military: 8,500 Man Army Iranian Army: 350,000 Army
UAE military: 21,000 man Army
Kuwait military: 11,000 man Army
Bahrain military: 9,000 man Army
Saudi Military: 75,000 man army

6. Why would Syria be in more trouble?

7. Oil would be just fine as the Gulf States would not get involved in Iraq, unless they are suicidal which they are not. Step 7 of your fantasy is predicated on the Gulf States ignoring all logic and common sense and sending their military's to certain defeat. As always the Arabs would make necessary deals to survive as they always have.