They must beat Somerset at Headingley Carnegie and hope their rivals implode in dramatic style.
Yorkshire have played one game more than their nearest competitors and sit out the final round of fixtures next week.
If second-bottom Yorkshire survive, it would go down as one of the most remarkable escapes in Championship history.
Yorkshire’s plight is highlighted as follows:
They will definitely be relegated if they fail to beat Somerset.
If they beat Somerset, they would still be relegated this week if they fail to claim at least 15 points more than third-bottom Worcestershire manage in their game against fourth-bottom Sussex at New Road.
As such, even were Yorkshire to beat Somerset with a maximum return of 24 points, they would go down if Worcestershire drew with Sussex and took at least 10 points in the process.
Either way, Yorkshire would be relegated if Worcestershire managed 10 points from their remaining two games, with Worcestershire concluding their campaign against Durham at Chester-le-Street in the final round of fixtures starting on Monday.
If Yorkshire somehow manage to finish above Worcestershire, they would still go down if Sussex managed seven points from their last two games and if bottom club Hampshire took 29 points from their final two fixtures.
Following their trip to New Road this week, Sussex finish their season against Nottinghamshire at Trent Bridge.
Hampshire take on Lancashire at Liverpool this week followed by Warwickshire at the Rose Bowl next week.
Yorkshire, indeed, could well finish bottom, with only five points separating them from Hampshire.
Yorkshire’s plight is exacerbated by the fact they have won fewer Championship games (two) than anyone in the Division.
If teams finish level on points in the Championship, most wins is the first tie-breaker. After that, it comes down to fewest defeats, the team achieving most points in contests between teams level on points, most wickets taken and, finally, most runs scored.
Spectators are reminded that play starts at 10.30am in all Championship matches played in September.