What happens there against Leicester Tigers on Saturday evening will determine whether Ulster go into the last eight at the top of the pile or a long way down the pecking order as one of the two best runners-up.
How strange that the one challenger with five wins out of five is guaranteed nothing more definite at this stage than a place somewhere in the quarter-finals. That Toulouse, Toulon, Clermont and Munster have already qualified as pool winners despite losing along way makes Ulster's uncertainty all the stranger.
That they are in such a position is a tribute to the Tigers' dogged tracking of the Pool 5 leaders from the opening round in Belfast last October when Owen Williams' late penalty allowed the losing Tigers to snatch the most precious of bonus points.
There is a danger from an Ulster perspective of their campaign being diverted down a more difficult road, as happened last season.
Should the province's potent mixture of home-grown Irish internationals and their imported Southern Hemisphere brigade headed by Johann Muller fail to make it six-out-of-six, they will have to take their chance away from Ravenhill.
Their inability to take full advantage of a competitive but below-strength Montpellier in Belfast last week has heightened the tension over Saturday's finale.
Ulster missing the try bonus point and Leicester coming from behind to secure theirs in Treviso means that a home win, no matter how small the margin, would send the English Tigers through as pool winners - unless Ulster achieve the improbability of two bonus points and Leicester none.
A home win would push Ulster down to No.7 and put them at possible risk of having to return to the East Midlands in April for a quarter-final.
They have had enough of those of late at English venues, losing to Saracens before almost 40,000 at Twickenham last year and to Northampton Saints at Milton Keynes two years before that.
Ulster's hierarchy will view the Leicester trip as the perfect opportunity to show the whole of Europe that their squad has matured into potential champions since losing to Leinster in the 2012 final. They are clearly better than when they last appeared at Welford Road and unrecognisable from their first effort there, ten years ago.
Six days after Leicester's England World Cup-winning contingent had been subjected to a pointless pasting at Ravenhill, Ulster went to the East Midlands with high hopes only to be engulfed by a crushing response from a Tigers team offended at justifiable descriptions of them as a fading force.
What they did in turning a 33-0 thumping one week into a 49-7 landslide the next, had never been done before or since on such a scale. Martin Johnson even managed to finish it off by stampeding 25 yards for the final try.
The 75-point swing made Northampton's recovery against Leinster almost minuscule by comparison, although in the end both Ulster and Leicester succeeded only in knocking each other out by clearing the way for Stade Francais to win the pool.
This time Leicester will gladly settle for something far more modest not that Ulster will be daunted at the prospect of taking the Tigers' lair by storm. Harlequins did so in November and both Northampton and Bath very nearly did so in forcing draws.
Leicester are never more dangerous than when European prestige is on the line. Like Ulster, they, too, are playing for a home quarter-final having also qualified.
And just to add extra spice to the occasion, the Tigers are in the process of restoring some of their long-term casualties - Anthony Allen, Steve Mafi, Graham Kitchener, Ed Slater and the Samoan prop who scored their try at Ravenhill, Logovi'i Mulipola.
Leinster and Munster, the two other RaboDirect PRO12 heavyweights who have won Europe's glittering prize five times between them, finish the pool competition at home - Leinster against Ospreys, Munster against Edinburgh.
Neither will be taking anything for granted, least of all Leinster given their Welsh opponents' liking for the RDS where they have won not one PRO12 Grand Final but two.
Unlike Munster, Leinster have still to qualify but even if they take all five points on Friday night, a top-four finish guaranteeing a home quarter looks beyond their reach.
Munster would have been on course for a home tie had it not been for their losing start at Murrayfield.
Edinburgh at Thomond Park on Sunday lunchtime offers Paul O'Connell and company the chance to settle a score against opponents back in the hunt for an Amlin Cup place after wins over Gloucester and Perpignan.
By Sunday, Munster will have a clearer picture of whether they have any realistic chance of a home tie.
If the big French trio keep winning (Toulouse in Italy against Zebre, Toulon in Glasgow and Clermont at home to Racing), they will almost certainly clinch three of the home ties with Ulster or Leicester taking the other.
Ulster at Welford Road in the Heineken Cup:
November 18, 2011:
Leicester 20, Ulster 9.
Leicester: G Murphy; H Agulla, M Smith, A Forsyth, A Tuilagi; T Flood, S Harrison; M Ayerza, G Chuter, D Cole; L Deacon, G Parling; T Croft, J Salvi, T Waldrom.
Try-Smith. Penalties-Flood 5.
Ulster: S Danielli; A Trimble, D Cave, N Spence, C Gilroy; I Humphreys, P Marshall; T Court, R Best, D Fitzpatrick; J Muller, capt., D Tuohy; S Ferris, C Henry, P Wannenburg.
Penalties-Humphreys 3.
January 17, 2004:
Leicester 49, Ulster 7.
Leicester: S Vesty; N Baxter, L Lloyd, G Gelderbloom, A Healey; J van der Westhuyzen, H Ellis; G Rowntree, D West, D Morris; M Johnson, B Kay; W Johnson, N Back, caspt, H Tuilagi.
Tries- Lloyd 2, Back, van der Westhuyzen, M Johnson. Conversions-S Vesty 3. Penalties-S Vesty 6.
Ulster: P Wallace; J Topping, S Stewart, P Steinmetz, T Howe; D Humphreys, N Doak; R Kempson, M Sexton, S Best; M Mustchin, R Frost; A Ward, N Best, R Wilson.
Try-Topping. Conversion-Humphreys.
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