In his first outing on the European stage, for Glasgow Warriors against Northampton Saints last year, the mighty South African claimed a try after just 24 minutes and ended the game, which the Saints won 24-15, with the consolation of a man-of-the-match award.
That display is recalled with fondness by Warriors' supporters mostly because they had precious few other memories to savour after last season's Heineken Cup campaign. Yes, it ended on an upbeat note, with Peter Horne's brilliant solo try allowing Glasgow to take revenge over the Northampton side with a 27-10 win at Scotstoun, but their stated ambition to become a force in Europe was rather undermined by that fact that it was their only win in six pool games.
In truth, Glasgow played much better than that record might suggest, but there is no arguing with the arithmetic. Hence the heightened sense of determination around the club as the next tranche of games in this season's competition comes into view. Astonishingly, all four teams in Glasgow's group have won one game, lost one game and collected one bonus point so far. But over the next two weeks that parity is likely to be shattered.
Glasgow opened with that amazing match in Toulon, when they trailed 34-0 to the reigning champions after 40 minutes but fought back to collect a try bonus point before going down 51-28. On the same weekend, Exeter thrashed Cardiff Blues, but all tables were turned a week later as Cardiff beat Toulon 19-15 and Glasgow edged past Exeter 20-16. If Warriors can back that up with a victory in Cardiff on Friday then their prospects of a last-eight place will soar.
"It's a massive game for us," said Strauss. "Getting the win against Exeter put us in a good position. Cardiff are a team we are familiar with because we play them in the Rabo quite often and have played them already this season. We now have them back-to-back and if we can pull these two off it will put us in such a good position to achieve our goal of making the Heineken cup play-offs."
Glasgow began this season's RaboDirect PRO12 campaign with a 22-15 win against the Blues at Scotstoun in early September. The Welsh side subsequently suffered the embarrassment of a humiliating home loss to Zebre - still the Italian side's only competitive victory - and are now languishing in ninth place in that competition, But Strauss is under no illusions about the potential of a side that can now call on the firepower of the Lions captain Sam Warburton, Lions man-of-the-series Leigh Halfpenny and Lions Test wing Alex Cuthbert.
"Coming from South Africa, I think I can compare it to the Currie Cup and Super Rugby," said Strauss of the difference between PRO12 and Heineken rugby. "Even though you might be playing against the same guys, everyone ups it at that level. You play a team like Cardiff in the Rabo and they are one team, but when you play them in the Heineken they just step it up so much.
"It is a massive competition. For people in the southern hemisphere, it is the only European rugby they see, so the teams that do well in it are the teams they identify with. It is massive, really important for us."
The famously hirsute Strauss has ditched his celebrated beard for the moment, but the strength of his ambition is undiminished. The promise of regular European rugby was one of the things that drew him to Glasgow in the first place and he sees success on that stage as critical in taking the club's reputation to a higher level.
"It is one of our big goals, especially this season," he explained. "As a team, we felt we didn't do ourselves justice in the Heineken Cup last season. We fell short in most games. But after beating Exeter here and with Cardiff then beating Toulon, it is such an even group. We are in a good position. Glasgow have never made the quarter-finals of the Heineken, so it is very important for us because we're building a culture here and we wanted to be a successful culture."
The third and fourth rounds bring the added intrigue of back-to-back games against the same opponents, an experience Glasgow will then repeat later this month when they play their two 1872 Cup Inter-City games against Edinburgh. It would almost certainly have suited the Warriors better to play the first of their two matches against the Blues at Scotstoun, but Strauss reckons that two tough clashes are in store, regardless of their order.
"There are pros and cons to everything," he shrugged. "Playing them twice, you know what's coming next week. You know what to do and what changes to make, but it is the same thing for them. They get a feel for you in the first game and they can make changes, maybe do things that didn't go so well. The second game is going to be even tougher."