Saudi Arabia and Russia are the world's most influential oil producers right now, along with the U.S., but the kingdom appears to be going its own way, announcing half a million barrel output cut from December.

With a lot at stake for the oil producers, however, the relationship should remain close, according to oil market expert Daniel Yergin.

"I think it's intended to be a long-term relationship and it started off about oil prices but you see it taking on other dimensions, for instance, Saudi investment in Russian LNG (liquefied natural gas) and Russian investment in Saudi Arabia and I think this is a strategic relationship because it's useful to both countries," IHS Markit vice chairman Dan Yergin told CNBC on Monday.

While Saudi Arabia and Russia are close, particularly given their pact in late 2016, along with other OPEC and non-OPEC producers to curb output by 1.8 million barrels per day in order to support prices, oil markets have changed since that deal - and largely thanks to that deal.

Oil prices have recovered almost too well with the U.S. criticizing OPEC (of which Saudi Arabia is the de facto leader) for higher prices and markets have been fluctuating on concerns over both a potential decline in supply (due to U.S. sanctions on Iran) and a potential oversupply – due to an increase in production from Saudi Arabia, Russia and the U.S. in recent weeks --- that led prices to fall around 20 percent since early October.

On that note, Saudi Arabia pumped 10.7 million barrels per day in October, Russia pumped 11.4 million barrels per day and the U.S. also an estimated 11.4 million bpd.

Yergin told CNBC's these "big three" producers were changing the face of the global oil market. "It's the big three, it's Saudi Arabia, Russia and the U.S., this is a different configuration in the oil market than the traditional OPEC-non-OPEC (one) and so thinking is having to adjust so there's that new relationship … and the world is having to adjust."

Also speaking to CNBC Monday, BP Group Chief Executive Bob Dudley said that the "OPEC-plus agreement (between OPEC and non-OPEC producers including Russia) and coalition is a lot stronger than people speculate. I think Russia doesn't have the ability to turn on and off big fields (which) can happen in the Middle East ... But I fully expect there to be coordination to try to keep the oil price within a certain fairway," he said.