O'Neill's play-off specialists Republic of Ireland stand between Denmark and place in 2018 World Cup

Danes have Eriksen and Bendtner, but winning second leg at Dublin against hard-as-nails home team will be more difficult than expected

Ireland's optimism comes from the way they have excelled at brinkmanship under Martin O’Neill. Andrew Couldridge / Reuters

The Republic of Ireland have been here before. No European team have as much experience in play-offs.

They have qualified for the last two European Championships courtesy of two-legged knockout ties. They reached the 2002 World Cup after a play-off. They progressed to the 1994 tournament after a game against Northern Ireland that, while not actually a play-off, had the feel of one.

Many a happy Irish memory stems from play-offs. In the interests of balance, it is worth noting that they would have booked places in a further three World Cups and two European Championships but for play-off setbacks.

Yet they approach Tuesday night's clash with Denmark in Dublin in bullish mood.

Highlights from first leg

“I only see one outcome,” midfielder David Meyler told Sky Sports. “I think Ireland are going to the World Cup. I don't think anyone will stand in our way.”

That optimism comes from the way Ireland have excelled at brinkmanship under Martin O’Neill. They tend to take qualification from groups down to the wire. They have normally been outsiders, both because of the standings and because they have been pitted against more talented teams.

In the past 26 months, the Republic have beaten Euro 2012 finalists (Italy), 2014 World Cup winners (Germany) and Euro 2016 semi-finalists (Wales), in group games that had the feel of eliminators; they were do-or-die contests.

“It was beat Italy or go home. In a way, that is a good thing: it really clears your mind,” O’Neill told Michael Walker in Green Shoots.

Goalkeeper Darren Randolph echoed those sentiments after the first leg when he said: “It’s win or bust now.”

O’Neill’s Ireland have shown an ability to prosper on such occasions. It is all the more incongruous as arguably no current team with a lower general standard of play has claimed three such teams as Italy, Germany and Wales.

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Centre-back Shane Duffy described Saturday’s stalemate in Denmark as “scruffy, a little bit ugly".

That was being generous.

Ireland, Duffy included, defended doggedly. Denmark midfielder Thomas Delaney described the task of opening them up as: “A bit like opening a can of baked beans with your bare hands: it takes time.”

But O’Neill said: “We would obviously want to be better with the ball in Dublin.”

It ranked as another understatement. Ireland were abject in possession; they often are. They tend to prevail courtesy of defensive fortitude, incessant effort and an ability to conjure a magical moment in an otherwise uninspired display.

They are noted for their spirit and relentlessness.

“Denmark are a very good team [with] very good players, but they don't have the character and the heart and the desire that we have,” Meyler insisted.

Denmark have become a more direct team since the end of Morten Olsen’s reign. The one world-class player on either side, Christian Eriksen, was muted. The Tottenham Hotspur playmaker believes a win for Denmark on Tuesday night would be bigger than Spurs beating Real Madrid.

A score draw would also do, something that Nicklas Bendtner said gives the Scandinavians a “slight advantage".

Ireland do not have their own Eriksen. Or even their own Bendtner, considering the Danish substitute has 29 international goals.

Instead, they have Shane Long, the scorer of the wonderful winner against Germany and often O’Neill’s preferred forward, has gone 29 games for club and country without a goal.

He could nevertheless be recalled. So could Wes Hoolahan, the slow technician who is rarely trusted away from home. Meyler is available again after suspension, although another defensive midfielder would be less welcome than an injection of creativity.

Yet the lesson from O’Neill’s reign is that, when the stakes are highest, Ireland will usually find a way to prevail.