I’ve seen several angry posts about Shun involving the last episode and his riding duels so I’d like to issue a collective “please calm down” and point out that his entire reasoning for participating in underground dueling was actually addressed in the episode’s dialogue.
1) Shun was separated from the other Lancers during dimensional travel. This also seems to be what happened when he and Yuto went to Standard – judging by how surprised Yuto was to see Shun. He’s used to this maybe not going as planned. He’s used to focusing on the objective at hand in order to achieve his goal – finding Ruri, who is confirmed to be in Academia at this point – regardless of where his comrades are. He knows they’ll turn up if they’re okay at this point. Shun does not like to rely on people he doesn’t completely trust (the other Lancers), presumably because that hasn’t gone well in the past. They don’t need to be present for him to put the plan into action. The fact that he’s still carrying through with Reiji’s plan despite the absence of his comrades says a lot, actually.
2) Reiji’s entire plan is to recruit strong allies so that they can take on Academia. Shun has been told off by not only Reiji, but Serena as well, and he knows he can’t just march into Academia by himself and expect it to go well. His impulsiveness has been checked, and he’s simply following the plan. It would be stupid for him to up and leave at this point, because as frustratingly difficult and slow as it is, Reiji’s plan has a chance of working. As much as Shun wants to see Ruri again, he knows better.
3) The Friendship Cup is going to attract a lot of strong duelists. Shun found this out presumably through Gallagher, and is working on securing his entry into the tournament. He’s not doing riding duels for the hell of it – his duel against Dennis may or may not be his tenth consecutive win, which will secure his entry into the tournament. If he can enter it, he will be closer to their entire objective of meeting with strong duelists and recruiting them to their cause. He wants to ask Jack Atlas to work for their cause. This is actually a really great idea, as Dennis pointed out early in the episode.
4) This is actually probably the least impulsive choice Shun has made of his own volition in the entire series. He’s not attacking people for the hell of it or blowing his cover (outside of relying on Xyz summoning – which he knows will be questioned anyway if the others are engaged in a duel at all, because they’re all using different methods). And, if he does lose against Dennis – then Dennis has a chance at entering the Friendship Cup, and the plan still goes through either way. The only thing that makes this duel a bad idea in retrospect is that Shun is really starting to grow suspicious of Dennis, so he may regret it in the end if Dennis is the victor and something goes wrong in the grand scheme of things.