When Tony winner Leslie Odom Jr. played Aaron Burr in Broadway’s “Hamilton,” he seethed. Joshua Henry, who originally played the part in Chicago and will reprise the role in the upcoming tour, charmed. Now Wayne Brady, the versatile star of TV and stage playing Hamilton’s killer for a limited run in the Windy City, coolly calculates.

In Lin-Manuel Miranda’s megahit musical “Hamilton,” Aaron Burr is the narrator of Alexander Hamilton’s story as well as his antagonist. While Hamilton’s core attributes and beliefs don’t really change during the show, Burr’s do, with two key numbers defining the arc. In “Wait for It,” he explains that unlike Hamilton and his desperate efforts to make history, he’ll lie in wait, confident that history will come to him. Then in the show-stopping “The Room Where It Happens,” Burr rejects his previous patience and actively seeks to grasp power.

As the founding father of this founding father, Odom Jr.’s Burr smoldered. We saw the embers of his envy early, and the slow burn burst into full-on fury in “Room Where It Happens.” As a performer, Odom Jr. emanated seriousness and even a certain reserved sadness, and his Burr eventually came across with genuine pathos. His Burr was a man of substance, if not strong ideals. We felt the depth to which the character sank, and no other actor has yet interpreted the music with as much sophistication and resonance as Odom Jr.

Henry, who radiates star power like a young Sidney Poitier, is a happier presence than Odom Jr. When he first advised Hamilton (played in Chicago by the excellent and very serious-minded Miguel Cervantes) to “Talk less, smile more,” Henry’s grin was broad and genuine, whereas with Odom it had seemed something Burr had to make an effort to paste on. When Henry’s Burr boasted about his appeal to the ladies, we believed it, and the actor’s charisma seemed a key component of a character who could come so close to being president without having a strong political point of view.

With Henry, “Room Where It Happens” wasn’t driven so much by jealousy as by the overwhelming compulsion to experience the high of exclusive, historic deal-making. He was tantalized by his own potential for power. As when Odom Jr. performed it, the song exploded, but now with a different, more positive spin; Henry reserved Burr’s anger for later in the show, when Hamilton decides to endorse Jefferson for president over him.

The talented Brady comes off as both a darker version of Burr and a lighter one. It’s darker because his Burr has an air of mischief-making and a touch of smarm — his flirtation with Angelica really earns him the response, “Burr, you disgust me.” But it’s also lighter in that Brady’s Burr is more shallow and emotionally impervious. Insults raise an eyebrow — Brady’s specialty — but then slide off as if he’s coated in Teflon. To this cool and calculating Burr, politics is an amusing game, not be taken personally. His take on “The Room Where It Happens” is mellower than either of his predecessors, albeit no less of a showstopper: This Burr is just making a strategic decision. Even when events continue to conspire against him, Brady’s Burr never seems to get truly angry.

In some ways, Brady’s performance is more detailed than the others, filled with reactions — those lifting eyebrows! — and comfortable in the confidence, and occasional smugness, of the privileged establishment. What future Burrs should study, though, is the unabashed joy Brady’s Burr takes in his role as a master of ceremonies (not surprising for an actor who has an ongoing gig as the host of “Let’s Make a Deal”). In announcing the entrances of key characters, Odom Jr. and Henry were more like Roman sentinels proclaiming someone’s biographical credits. Brady invests the introductions with an enthusiasm that falls somewhere between Ed Sullivan and a carnival barker.

In the original Broadway production, the focus was placed unquestionably on Hamilton from the start — in part because the actor who played the part, Miranda, was the show’s creator-star. Odom Jr.’s Burr was a background figure who gradually attracted more and more of your attention, until he took it over entirely with “The Room Where It Happens.”

Because Brady’s stint is the closest thing to star casting that “Hamilton” has yet had, the production-design choices that once served to ensure that Burr doesn’t disappear too much into the background (such as a coat that’s a different color from everyone else’s in the opening number) only serve to further magnify attention on the already well-known actor. Brady also happens to be significantly taller than nearly all his fellow cast members. The effect makes Burr come off like a star who never quite makes top billing, who waits too long for the right role, whose career is distinguished but disappointing, ending in scandal. It works.