London - Britain's incoming prime minister Boris Johnson has bet big on a risky Brexit strategy that he hopes will take the UK out of the EU on favourable terms.
His 27 European counterparts argue with growing anguish that they have gone over every conceivable option in the three years since Britons voted to leave the bloc.
They say the deal both sides agreed they could live with was what outgoing Prime Minister Theresa May signed last year -- and what her parliament has repeatedly voted down.
He says that a healthy dose of optimism and a dash of "constructive ambiguity" can get Britain out of the European Union on better terms by the twice-delayed October 31 deadline.
Genius or joker? Who is Boris Johnson
- Plan A -
Johnson would ideally like to come up with a new treaty replacing May's widely-hated deal.
Yet even he admits this might be a stretch.
The summer break and leadership transitions in London and Brussels leave a matter of weeks in September and October for formal talks.
The existing agreement involved 17 months of haggling and produced 585 pages of legal text.
The EU 27 have been repeating for months that they will now only listen to ideas about a separate and largely aspirational document outlining future ties.
What now for Brexit?
- Plan B -
Johnson's alternative starts with parliament ratifying "the best bits" of May's deal.
These included such non-contentious issues as EU citizens' rights and extensions of various security and diplomatic cooperation pacts.
What it explicitly excludes is the dreaded "backstop" -- a hugely disputed fix for avoiding a hard border between EU member Ireland and Britain's Northern Ireland.
Johnson also wants to adopt a policy of "constructive ambiguity" over whether Britain will start paying off its estimated £39 billion ($49 billion, 43 billion euro) withdrawal bill.
The cash pile would be used as leverage to get Brussels to sign off on a "standstill" agreement that rolls over existing trade rules until a new treaty is signed.
Johnson envisions gradually unrolling a mix of "technology-based solutions" and waiver agreements that keep the Irish frontier free-flowing over this interim span.
He argues that everything can be settled "well before" Britain's next scheduled election in May 2022.
How Britain voted on Brexit
- Plan C -
It is a high-stakes gamble that might demand more goodwill from EU leaders than they can muster at this stage in the bruising process.
Brussels would like to avoid setting a precedent for other eurosceptics across the bloc by conceding to an EU uber-critic like Johnson.
And this is where Johnson's headline-grabbing threat of a no-deal Brexit comes in.
A chaotic split threatens to unleash much heavier damage on Britain than it does on the considerably larger and more diversified EU economy.
But most EU leaders would rather not get blamed for simply letting Britain fall off a cliff.
And Irish officials view a hard border as an existential threat to an agreement that ended decades of sectarian bloodshed in the North.
A no-deal divorce would also point to a spectacular diplomatic failure that might alienate Britain and make future relations far more fraught.
Fallout of a no-deal Brexit
- Will it work? -
Scepticism about whether Johnson's plan can work is widespread.
Johnson's bravado is running up against the realities of obscure global trade mechanisms such as the General Agreement on Tariffs and Trade (GATT).
Its Article 24 could allow tariff-free trade in goods between Britain and the EU for up to a decade while a permanent trade agreement is being worked out.
But it can only be used by the mutual agreement of both sides -- a point that Johnson admitted on July 12 he did not know.
He has since said that it would still be in the EU's best interests to cooperate.
And if his strategy fails and Britain splits away after 46 years without a plan?
"We are resigned to it," Johnson said last week.
Boris Johnson vows to 'get Brexit done' on October 31
By Dmitry Zaks