Manchester City, Liverpool and Arsenal face play-off prospect for Champions League By Mark MitchenerBBC SportFootballSharethis pageManchester City, Liverpool and Arsenal could face a 39th game to determine qualification for EuropeManchester City, Liverpool and Arsenal all face a possible play-off to determine qualification fornext season's Champions League.The three clubs, occupying third to fifth place in the Premier League, are separated by three points going into Sunday's final round of games.But their goal difference, and goals scored, are similar enough to raise the prospect of two teams finishing joint third or fourth with identicalrecords - necessitating a one-off play-off match.However, bookmakers are clearly not convinced. Of three possible scenarios where a play-off would be required, the one with shortestodds is around 595-1.The top three teams qualify directly for the Champions League group stage, with the fourth-placed side entering at the preceding play-off round, while the fifth-placed side will enter the Europa League.How do they stand at the moment?Goals forGoals againstGoal differencePointsFinal gameMan City7539+3675Watford (a)Liverpool7542+3373Middlesbrough (h)Arsenal7443+3172Everton (h)Premier League rules state: "If at the end of the season either the league champions or the clubsto be relegated or the question of qualification for other competitions cannot be determined because two or more clubs are equal on points, goal difference and goals scored, the clubs concerned shall play off one or more deciding league matches on neutral grounds, the format, venue and timing of which shall be determined by the board."Last season, there was a chance that Liverpool and West Hamcould have finished with identicalrecordswith a Europa League place at stake.So, how could it all happen?Manchester City v Liverpool: A play-off for third placeThis would require a high-scoring draw for City at Watford, while Liverpool give relegated Middlesbrough a thumping at Anfield.For instance, a 3-3 draw for City and a 3-0 win for Liverpool would produce this scenario, with the teams tied for third place (and that Champions League group stage place):Goals forGoals againstGoal differencePointsLiverpool7842+3676Man City7842+3676The sides would also be locked together with identical records if City drew 4-4 and Liverpool won 4-1, and so on.However, Arsenal cannot affect this scenario - even by winning, they could finish no higher thanfifth.What do the bookies say?Betfair is currently offering odds of595-1for City to draw 3-3 and Liverpool to win 3-0.Manchester City v Arsenal: Doomsday scenario for City?By contrast, a heavy defeat for City raises the spectre of finishing level on points with Arsenal.If City were to lose 4-0 at Vicarage Road, and Arsenal to sneak home 1-0 against Everton, the sides would finish like this:Goals forGoals againstGoal differencePointsArsenal7543+3275Man City7543+3275The same permutation would be reached if City lost 5-1 and Arsenal won 2-1 - you get the picture.What makes this scenario even more complicated is that it could produce a third/fourth place play-off if Liverpool fail to beat Middlesbrough - or a fourth/fifth place play-off if the Reds win at Anfield.What do the bookies say?William Hill is currently offering odds of1707.5-1for City to lose 4-0 and Arsenal to win 1-0.Arsenal v Liverpool: Champions League on the lineThe final scenario would leave Liverpool and Arsenal fighting for fourth place on the most perilous of knife-edges since they battled for thetitle on the final day of the 1988-89 season.If Arsenal draw 1-1 with Everton and Liverpool lose 2-0 to Middlesbrough, this is how they would finish tied for fourth:Goals forGoals againstGoal differencePointsArsenal7544+3173Liverpool7544+3173Other combinations of results which would leave the sides level would be a 2-2 Arsenal draw coupled with a 3-1 Liverpool defeat, or a 3-3 Arsenal draw if goal-shy Boro win 4-2 at Anfield, and so on.The good news for Manchester City fans is that under this third scenario, they would finish third, whatever their result at Watford, and clinch that cherished Champions League group stage place.What do the bookies say?Ladbrokes is currently offering odds of1282.5-1for Arsenal to draw 1-1 and Liverpool to lose 2-0.