There are four candidates for Conservative leader plying the conference with themed hats and tote bags – but only two are sucking all of the oxygen. It is no accident of scheduling that Robert Jenrick and Kemi Badenoch were the ones on the BBC’s Sunday with Laura Kuenssberg, much to the chagrin of their rivals.

Reason would then dictate they would be the final two selected by Tory MPs to face the party members’ vote. If that transpires, the outcome would be very unpredictable. Jenrick has undergone a dramatic makeover and won the backing of the most MPs but he is virtually unknown to the wider public. Badenoch is the straight-talking renegade who is more of the members’ darling but who terrifies many of her parliamentary colleagues.

But whispers are loud in Birmingham that it may not be the final outcome – that a surprise candidate may yet join Jenrick in the final two. The former immigration minister is confident he has the numbers among MPs at the next two rounds of voting – so confident that some of his team were in the conference bar by the late afternoon.

However, there is no such confidence he would beat Badenoch – and so rumours swirl of how MPs may conspire to keep her out of the final two. The path to doing so is tricky. Jenrick’s team has forcefully denied it would lend votes to other candidates to exclude Badenoch. That may well be true because Jenrick does not have anywhere near enough to play with.

The numbers in this much reduced parliamentary party are very tight – it is nothing like the Boris Johnson contest when he soared ahead. Neither of the other two contenders, James Cleverly or Tom Tugendhat, want to be part of any games – they are neck and neck on votes.

Cleverly outperformed expectations in the final round and made a compelling stump speech at different conference receptions. Tugendhat’s team says he is the one who has gained the most ground among MPs and so has the momentum.

David Cameron’s winning performance at the party conference in 2005 looms large in Conservative mythology – the speech of a lifetime could transform any of the candidates’ fortunes. But so too could any major gaffe.

Jenrick has the most politically aggressive backers. And the strategy by his outriders has been to emphasise to undecided MPs that Badenoch is the biggest risk.

The row over Badenoch’s comments on maternity pay on Sunday were the best opportunity for them to prove the point. Her rivals see it as her Andrea Leadsom moment – a reference to when that leadership candidate was forced to drop out of the contest for some ill-advised comments on motherhood in 2016.

Not only did Badenoch have to twice clarify what she meant, but she went on the offensive and insisted she had been misinterpreted by the media and bad faith actors. “We don’t need to play games, she does her own damage,” one supporter said.

Both sides need to be careful. The party higher-ups have let it be known they will issue “yellow cards” for any bad behaviour or attempted stitch-ups by candidates. So far none have been issued though there have certainly been some bitter private briefing wars.

And there is another concern playing on the minds of many more experienced MPs and party veterans, even those who do not support Badenoch. They believe it is a highly dangerous game for MPs to be seen to stitch up the contest – it is not long ago that they saw the fury of the membership at multiple previous contests, Michael Gove’s attempted coup against Boris Johnson, the removal of Liz Truss and the installation of Rishi Sunak.

The membership is extremely precarious, not just the voluntary party but councillors and other local elected officials who have been decimated over the last few years. The party needs to make progress at next year’s local elections. And for MPs to engineer a stitch-up yet again could be a fatal error – and drive even more into the arms of Nigel Farage’s Reform UK.