The recent World Chess Championship set a new record, but it was not one likely to give the game more mass appeal. There were 12 slow matches, conducted in a soundproof glass box, between the reigning champion and his challenger – and every one ended in a draw. The contest was finally resolved only by quickening the pace with a deciding run of games in which the players had to think and move much more rapidly.

Something similar is going to happen with the four-dimensional version of chess known as Brexit. Grinding deadlock will be ultimately resolved by a fast-moving tiebreaker phase.

The past 30 months have unfolded at a painfully slow pace as Theresa May has tried and failed to find a match-winning formula without ever quite being defeated by her various opponents. She began with the hard Brexit opening called “red lines”, a strategy conceived in the soundproof box inhabited by the prime minister and her aides during the period when she was impervious to any advice from diplomatic grandmasters. This strategy blew up when it collided with the realities of striking a deal without wrecking the economy. Then there was her early election gambit, initially hailed as a stroke of genius by many of her colleagues, which left her with no parliamentary majority. She subsequently adjusted to a “bespoke” – also known as a spatchcocked – version of Brexit, which has been denounced by both those who want to maintain a close relationship with the EU and those who desire a starker rupture.

Once parliament votes down the deal, the slow games will be over and we will move into quickfire decision-making

I have yet to find anyone at Westminster who thinks that she can win the parliamentary vote on 11 December. Even the dogs on the street know she is heading for defeat. The recent prognostications of the Treasury and the Bank of England have been of no help to her at all. The Moggites, never anything but utterly predictable, have jeeringly dismissed the forecasts that a no-deal Brexit would have a ruinous impact. Those who want to reverse Brexit have noted that every version of it, including Mrs May’s, is worse for jobs, trade and investment than remaining within the EU. The plucky ministers prepared to defend the boss have the unenviable task of trying to argue for a deal that the government’s own forecasters say will leave Britain poorer.

The number of Tory MPs who are declared opponents of Mrs May’s deal is 100 and rising. Even if we halve that, to allow for rebels flaking under pressure from the whips, it is still impossible to see how she can prevail without the assistance of a substantial number of opposition MPs, help that won’t be forthcoming. There are Labour MPs who would prefer her deal, awful as many of them think it is, to any of the alternatives, but to support her would be to risk denunciation by their party leadership and deselection by their local activists. Any Labour MP who might have once thought of voting with the government has even less incentive to throw a lifeline to a Tory prime minister if Mrs May is going under anyway.

Once parliament votes down the deal, the slow games will be over and we will move into quickfire decision-making. This is when all the contestants will have to play speed chess. Here are the possible endgames.

There is a cosmetic tweaking of the terms of Mrs May’s deal, if the EU is prepared to play ball with that, which is designed to make it more palatable to her party and this is followed by a second, successful, attempt to secure parliamentary approval. In so much as Number 10 has an idea that merits being called a strategy, this seems to be it. There is only one snag with this plan: there is a vanishingly small number of people at Westminster who think that enough MPs can be persuaded to change their minds between a first vote and a second.

The next endgame sees Britain crashing towards a no deal, the parliamentary equivalent of a chess player deciding to upend the board and break all the pieces. There is no majority in parliament for this calamitous outcome, but it could happen by horrendous accident if MPs can’t agree on anything else, because no deal is the default position of the withdrawal legislation.

Some are still fastening their hopes to the concept of fashioning a parliamentary consensus for a different form of Brexit, which usually involves the word “Norway”. This is not impossible, but there isn’t coherent agreement on an alternative nor clarity about who would negotiate it and how it could be made to happen in the short time left.

A big chunk of the Conservative party will oppose another referendum, so one can only happen with Labour support

Another referendum, which Mrs May has always set her face against, could end up being her least worst option. Is that her secret plan B? That would help to make sense of otherwise inexplicable decisions, such as running around the country trying to sell her deal to the public when the voters that currently matter to the prime minister are all sitting in parliament. Maybe, some of her colleagues speculate, she is warming up for a referendum campaign. I’ve said before that parliamentary stalemate is the likeliest route to the question being thrown back to the people. It is true that Mrs May has used strong language – words such as “betrayal” – to describe another referendum. Then again, she was never going to have an early election right up until the moment she called one.

Here, Labour’s position will be critical. A big chunk of the Conservative party will oppose another referendum, so one can only happen with Labour support. As we report today, the most recent meeting of the shadow cabinet had a discussion about Brexit – quite a rarity for that body. Several of its members have also started to twig that events will unfold at pace and speedy decisions will be required once Mrs May has been defeated in parliament. In the words of one of their number, Labour will have to be ready to “move quickly through the gears”.

Having long hoped that Brexit might somehow trigger an early election and having repeatedly called for the same, Jeremy Corbyn will have to table a motion of no confidence in the government. He will do so even though most of the people around him think this will be futile. John McDonnell, the shadow chancellor and always a man to watch at times such as these, has recently conceded that triggering a general election is “very difficult”. He went on to say that, if there isn’t an election, Labour will “inevitably” call for another referendum.

By my reckoning, a majority of the shadow cabinet either want Labour to come out in full-throated support of another referendum or think that they will have to end up backing one because there will be no other viable positions for the party. This majority includes Tom Watson, the party’s deputy leader, and Keir Starmer, the party’s chief spokesman on Brexit. It probably also includes Emily Thornberry, the shadow foreign secretary, though colleagues say that she is being calculatedly cautious about saying so explicitly.

Minds have been concentrated by Mrs May’s suggestion of a TV debate between herself and Mr Corbyn. This has forced Labour people to confront the truth that their Brexit fudges are crumbling before everyone’s eyes. No one thinks Labour could negotiate all the benefits of being within the EU for Britain while no longer being a member. Labour spokespeople struggle to defend that posture through short interviews. Ninety minutes of sustained scrutiny of Mr Corbyn about Brexit on primetime TV comes with substantial perils for Labour, especially if its leader is left exposed on whether the people should have the final say.

There is still significant resistance to another referendum among some in the shadow cabinet and elements of the Labour leader’s inner circle. Their preferred – if never declared – outcome has been for Brexit to happen and the Tories to be held culpable for it. So those who think that Labour will have to embrace another national vote came away from that shadow cabinet meeting encouraged because Mr Corbyn didn’t try to close down the discussion.

Declaring for another referendum would cost Labour support among some of its traditional voters who want out of the EU. But there will also be a price to pay – and probably a much steeper one – for betraying the wishes of Labour members and supporters who are desperate for the British people to be given an opportunity to reverse Brexit. We are coming to the end of the long period when Labour managed to just about get away with suggesting to both Leavers and Remainers that it was on their side. That position will soon be entirely unsustainable.

They say that to govern is to choose. At this critical juncture in Britain’s history, it will also be the case that to oppose is to choose.

• Andrew Rawnsley is an Observer columnist