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Former Maidstone striker Jake Robinson denied his old club victory at the Gallagher.
Robinson’s second-half penalty just about beat Ravan Constable after Ibrahim Olutade had marked his first start of the season with an early goal for the Stones.
Maidstone pushed hard for a winner - Charlie Seaman with a glorious chance - but Ricay might have snatched victory themselves at the death.
The point was enough to move Hakan Hayrettin's side up a place to sixth in National League South.
Olutade was one of two changes to the starting XI from Tuesday night’s goalless draw at Ebbsfleet.
Both were injury-enforced with Olutade in for Scott Rendell while Joan Luque was restored to the line-up after George Porter failed a fitness test.
The visitors’ XI included four Stones old boys in keeper Dion-Curtis Henry, Lawrie Wilson, Jai Reason and Robinson, plus Lewis Knight was on the bench.
Henry didn’t have the best of times on loan at Maidstone from Palace during their National League relegation season.
And he had a moment to forget on his return, too, as Maidstone opened the scoring in the seventh minute.
The hosts had already fired an early warning with Olutade testing Henry in a fast start after Seaman nutmegged Ronnie Henry, the Ricay skipper who worked under Hayrettin at Luton.
While keeper Henry was equal to that, he gifted Maidstone their goal by spilling Seaman’s low shot straight into the path of Olutade, who pounced from a few yards out.
The Stones looked well in control, going close to a second through Luque from the edge of the area, while Henry made a confidence-boosting save from Justin Amaluzor after the winger beat Joe Felix for pace.
Billericay threatened midway through the half after Robinson beat the offside trap but his shot hit the side-netting.
That was a rare bright moment for the visitors who arrived at the Gallagher with two wins from seven league games.
Maidstone went in search of a second after the break, captain George Elokobi sending a header just wide from Amaluzor’s inswinging corner.
Just past the hour mark, Amaluzor put the ball past Henry but Olutade couldn’t quite keep it in play and the chance was gone.
Billericay levelled from the penalty spot in the 68th minute after Elokobi’s challenge on Robinson just inside the box.
Constable looked to have Robinson’s dinked penalty covered but it somehow squeezed through his grasp and into back of the net.
Gavin Hoyte’s strike was blocked as Maidstone looked for a quick response and a huge chance went begging when Seaman fired over from Sam Corne’s cross with the goal at his mercy.
United maintained the pressure and moments later Amaluzor rolled the ball inches past the far post.
The hosts might have lost it with a minute to go after Constable spilled another strike from Robinson but Ricay couldn’t capitalise on the rebound.
Maidstone: Constable, Hoyte, Ellul, Elokobi, Chesmain, Corne, Krasniqi, Amaluzor, Luque (Temelci 76mins), Seaman, Olutade (Akanbi 87mins). Subs not used: Lewington, Brown, Odusanya.
Referee: Alex Blake.