For context, the exact quote is:
When Waterloo is war-gamed, France usually wins: the Napoleon player attacks early, masks Hougoumont with a maximum of one division, has the rest of Reille’s corps support d’Erlon’s historical attack, which uses a columnar formation and is accompanied by two divisions of Lobau’s corps with the Reserve Cavalry corps in close support. Ney’s cavalry charge is supported by infantry and artillery, which pulverize Wellington’s squares long before the Prussians arrive.
There is no citation associated with it, though the acknowledgment section does thank "Dr William J. Lademan, Director of the Wargaming Division at the Marine Corps Warfighting Laboratory."
As a general question, how do war games of Napoleonic battles "work"? I'm having trouble imagining how it would be done in a way that is actually historically valid or useful.
Of the Napoleonic battles, Waterloo is probably the most well covered in terms of Wargaming, and I wouldnt be surprised if its one of the most well covered topics of any era. Napoleon, for all his faults, in inspirational and leads us to be aspirational. Some of his gambits should never have worked, while others (like Waterloo) were tantalizingly close, merely one mistake away from victory. Further, Waterloo is so tantalizing because of Napoleon's myriad of "mistakes" (one could argue if they really were, or if they were justified, a subject well beyond this post). It leads the reader to say "well if he had just done this, just attacked a little quicker, just pushed a little harder, he would have won". And because of how decisive Waterloo turned out to be, that one day, that one defeat completely changed Napoleon's life, French history, and all of Europe. So I think the question of "what-if" at Waterloo is, in many ways, a timeless question.
As for Roberts' quote, I would imagine he didnt bother to cite any war games because of the nebulous, and rather tangential, nature of what hes saying. I think he, like I am now, is trying to capture that feeling of the great, tragic, and avoidable defeat. Rather than convey some great truth (any wargame worth it salt will give the Allied player some chance of victory), Roberts is trying to convey emotion and drama.
As for wargames of Waterloo itself, Im sure you could find dozens of "After Action Reports" of Waterloo itself, as well as the entire Ligny-Quatre Bras- Waterloo campaign. I could recommend two videos from a youtuber I enjoy, Calandale. He recently played through Napoleon's Last Battles, an older game about the battle which produced a pretty close result, though better than the French did historically. He also played Le Retour de l'Empereur, in which he completely blew the Allies out. Just a note, Calandale generally seems to prefer to play the full campaign version of a game, so in both cases he plays out all three (or four, depending on how the game goes) battles. In both cases he ends on the Waterloo map, but how he gets there is sometimes very different. Though, that is also one of the many "what-ifs" regarding the battle.
More generally, Ive really been thinking about the place of Wargaming in historical scholarship. The traditional thinking towards Wargaming is that its a fun hobby and a wonderful distraction, but not useful for the fact-based historian. It doesnt matter that I can win Waterloo. It only matters that Napoleon lost. And to some extent I agree with that. Wargames cant ever truly capture a battle because they are, by necessity, abstractions. However, after reading Seth Owen's book Fatal Choices about the decision making surrounding the Battle of Coronel, I think that there might be something of value to using wargames to explore difficult decisions. While they wont, obviously, produce historically accurate results (unless your war game involves rebuilding a squadron of British battle cruisers and pitting them against their German counterparts), these games can help put you into the mind of the commander and see things through his eyes. A good wargame forces you to make tough decisions, and helps you understand why battles evolve the way they do. I think that they might have some use in solving some of these big historical questions. Im just not sure how they can be useful and what, specifically, they can contribute to the conversation. Perhaps one day when I figure that out, Ill write some kind of article about it.
I know that last part doesnt deal directly with your question, but I thought my musings were relevant to the conversation at hand. Id love to hear what you, and others (especially other flaired users!) think about Wargaming's relationship to historical scholarship.
Quick Edit: After rewatching a bit of each of the linked videos, I think the Le Retour vid is a bit better if you want more of a discussion of the historical situation and some of the alternate scenarios. Its also, I think, a more interesting game to watch.