My wife is a Russian refugee from the Soviet Union, and I know how Russians think.
My guess is that Putin will make an offer to have Syria give up their chemical weapons, in exchange for the White House ending their financial and military support of the terrorists who are prosecuting the war in Syria.
This will put Obama in an untenable position, and he will probably have a nervous breakdown.
Russians are not crippled by the PC emotional baggage which most Americans have been subject to since they were toddlers. They also are great chess players. They look many moves ahead, and anticipate what their opponent is going to do.