Sorry, but you are wrong on that one. Iraqi and Persian oil fields were not major sources of oil. Most of Western Allied oil came from North America, and Russian oil from the Caucasus.
Bottom line, conquering Caucasus/Mid-East wouldn't have solved Axis oil issues. Likely effect would've been burning as much or even more oil to get there than could've been extracted before those fields would be lost again. It might've crippled USSR though until US Lend Lease would shift to more oil deliveries.
I know that most of oil came from North Africa. In fact, most of WORLD's oil came from NA in 1930s and 1940s. However, besides NA, there were several places on Earth where oil was extracted in large quantities. Indochina, Caucasus, Venezuela, Mexico, Romania, Iraq and Persia.
I use Statistical Yearbook of the League of Nations as a source when it comes to mineral and industrial production -
http://digital.library.northwestern.edu ... 0276ah.pdf
Crude Petroleum 1938 in metric tons (000's omitted):
164 153 United States
10 359 Iran
4272 Iraq
7 398 Netherlands Indies
28 071 Venezuela
6 603 Romania
28 859 whole USSR
For comparison - 552 (!!!) Germany
Everything pales in comparison to American oil extraction, but the Americans never had any oil problems. USSR had enough fuel for their giant forces during WWII, too, and their output was much, much lower. More oil was extracted in Iran alone than in Indochina or Romania and oil from both these countries had much strategic influence. The Japanese functioned pretty much on Indonesian oil until their merchant marine was decimated in 1944. Germany never reached Iraq, Persia or Baku and while it had oil problems, it was still conducting armoured offensives (even with heavy armour) and u-boot raids in 1943 or even 1944 (Battle of the Bulge) on their small stockpiles.
Also, the extraction of oil can be increased if necessary. For example, looking at this table -
http://ww2total.com/WW2/History/Product ... erials.htm - you can see that both German crude and synthetic oil production increased almost two times in the 1939-1941 period. In fact, their domestic production in 1941 was greater than their imports in 1939 and in 1943 their production was greater than ever! German stockpiles of all kinds of petroleum were greater in 1943 than in 1941 with a similar rate of consumption. All this WITHOUT capturing vital oil fields in Iraq, Persia or Baku. Note the difference between the Soviet oil production in 1941 (when they really needed it) and 1943-44, too (33 vs 18).
The game doesn't include refineries for either side and logistics is abstracted (the Americans don't have to transport supplies and fuel by convoys, so the Allies have some advantages, too), so I think that we should exclude these aspects from the equation.