The United Nations has classed Denmark as the happiest country in the world for three of the past five years, with Gallup research reckoning that the average Dane experiences 80 positive emotions per day. The factors assessed include affluence, stability, health, education and personal fulfilment. Football success does not come into it, apparently.

On Saturday evening, all the same, most of the 38,000 people at Copenhagen’s Parken Stadium will giddily urge the home team to take a decisive step towards next year’s World Cup, while Martin O’Neill and the Republic of Ireland will strive to bring a little misery to Denmark.

The Irish are Europe’s most gnarled play-off participants. This will be the eighth such duel they have contested, more than any other country in the continent. They have lost more than they have won but are on a roll, having prevailed in their last two play-offs, most recently by beating Bosnia-Herzegovina to reach Euro 2016 while Denmark were losing a make-or-break tie against Sweden.

The pair of performances against Bosnia were among the best produced under O’Neill and helped form the conviction that his team have a knack for rising to big challenges, albeit sometimes after failing to take the initiative in smaller ones.

In this campaign they have been particularly valiant away, with their finest displays yielding 1-0 victories in Austria and Wales. “We’ve got to use those experiences to good effect,” says O’Neill. “The players have matured. There’s a good belief in the camp that maybe didn’t exist a couple of seasons ago, an inner self-belief – not one that is flaunted – that we can go out and be competitive against anyone.”

No one could accuse Ireland of flaunting their self-belief, at least not if that means controlling possession and attacking with gusto. They have, however, played with indomitable spirit and a good deal of solidity and hoped they might prove clinical enough to scrounge an away goal from one of their few chances.

The Denmark manager, Age Hareide, does not envisage them taking a radically different approach on Saturday. “They are easy to read and difficult to beat” he says. “They don’t change much game to game, they play the same style, but they stick together and work well.”

Hareide knows all about O’Neill – they lived together when they were team-mates during a spell at Manchester City in the early 1980s and have remained in touch since – but there was a glint of pique in the Irishman’s eyes when told of his former tenant’s comment. O’Neill insists he will seek at least one away goal to take into Tuesday’s second leg in Dublin.

“If you watch a lot of Denmark there a similar pattern in most of their games … so we know what to expect from them,” adds O’Neill. “The away goal is obviously important and it’s something we’re capable of getting. We’re just going to go for that. We need to get on the front foot, as we were against Wales [in October]. We were on the back foot for the first 15 minutes [against Wales] and had to defend strongly to get a foothold, then the game levelled out and we came more into it and got the goal. We remained unbeaten away from home [throughout the group stage]. That’s a testament to the sort of character in the team. We are close to the World Cup and it’s there for the taking.”

The clearest indicator of O’Neill’s determination to take the game to the Danes would be to give a rare away start to Ireland’s most creative player, Wes Hoolahan, perhaps behind a front pair of Shane Long and Daryl Murphy. But that would be uncharacteristically bold. It is far more likely Ireland’s attempt to pilfer an away goal will take the familiar format and they will play with one striker while Glenn Whelan returns to central midfield in place of the suspended David Meyler. That would suggest an aspiration to parry Danish attacks and land a counterpunch.

Those attacks will revolve around Christian Eriksen, the Tottenham playmaker who is even more influential for country than for club. He has done his utmost to get his country to Russia, scoring eight of the 20 goals they mustered in the group stage and creating many of the others as Denmark finished second to Poland.

Will O’Neill try to man-mark him out of the game? “I don’t mind if they do that as there is more space for other players with their quality and they could take advantage, but it’s Ireland’s decision and it doesn’t really matter,” said Eriksen. The Spurs player added, however, that Denmark can only beat Ireland by first “breaking their spirit”. To which Robbie Brady, scorer of Ireland’s awaygoal in the play-off against Bosnia two years ago, replied: “They can try.”