Did President Trump really mean it when he told Palestinian President Mahmoud Abbas that there is a "very good chance" of a Middle East peace deal? Here is the man who along the lines of Alice in Wonderland is prone to tweet six improbable things before breakfast. And on the face of it what he told Abbas is surprising. This is the president who announced that he would move the US embassy in Israel from Tel Aviv to Jerusalem. This is the president whose son-in-law and close aide Jared Kushner is a prominent US Zionist and backer of Israeli causes. This is also the president who in February had what looked like a love-in with Benjamin Netanyahu when the Israeli premier was one of the first foreign statesmen to visit the Trump White House. At that meeting Trump appeared to be ambivalent saying that he was looking at a two-state or a one-state solution and added: "I like the one that both parties like". Given the abject failure since the Oslo Accords in 1993 and 1995 and the Saudi-led 2002 peace initiative to reach any agreement on the future of Palestine, this would seem extraordinarily disingenuous. Trump gave the impression of having breezed in to one of the most crucially important political standoffs of the last 25 years having read none of the briefing papers but relying rather on his gut instinct. And yet could there be something behind this apparently naïve new White House initiative? It is not simply that Trump can claim to be starting over with a blank sheet of paper. It may also be that he will use a different pen and even a different color ink than those of his predecessors. For the self-styled master of the "Art of the Deal", negotiating a just settlement for the Palestinians would be a singular achievement. Barack Obama and Netanyahu fell out early. Obama took office as the Israelis were concluding their ruthless bombardment of the Gaza Ghetto that killed 1,400 Palestinians. Though the stirring rhetoric of his Cairo speech ultimately proved utterly empty, it infuriated the Israeli premier and set the stage for a steady decline in relations between the two men. Nevertheless, Obama never had the courage to force Israel back to the negotiating table by trimming or withholding US military and economic aid. Trump has started off differently. He does not even appear to have taken up the establishment view embraced by Obama's predecessors, which is to stick to the Israeli-written script that they cannot talk to terrorists who refuse to accept the very existence of Israel. George W Bush, who had destroyed Iraq in the cause of democracy, then refused to acknowledge the democratic victory of Hamas in the 2006 Palestinian elections. For Washington, Palestinian democracy was only acceptable if the right side won. Netanyahu appears confident that he has Trump's support. But there have been other occasions when a politician elected on one platform has exploited that victory to pursue entirely different objectives. For instance, Spain's socialist leader Felipe Gonzalez used his mandate to force through radical welfare and labor reforms and take his country into the EU in defiance of his party's original policy. Trump is already established as a political maverick from whom the unexpected can be expected. Palestinians may yet discover that they have an evenhanded dealmaker to work with.