One theory I have is that Leader can still "remember" things that have left a lasting imprint on him. From our perspective these seem to mostly be things he learned from Baku. Namely:
- The most thrilling gambles are when you leave someone with nothing but their life, and they come back to fight you again. I think him not instantly killing Baku in the first Leader game is suspicious. I don't think he had lost his memory between the re-learning after the Fukurou gamble and Surpassing the Leader, but it obviously fundamentally changed him and made him Souichi again instead of Hal.
- You must gather people who are genuinely loyal to you; the loyalty Kakerou provides is only for the one who keeps winning, and will shift. Baku learned this on his first go-around with Kakerou and forged stronger bonds with his allies the second time around, which is one reason why Kyara had to stop being a referee. In Oofuna and Nobuko, Hal seems to have a couple allies around him now that are genuinely loyal to him, not just out of obligation to their Kakerou duties.
These might be the only lessons we know he learned for real based on his time with Baku. We don't really know what Kakerou is imprinting on him, and how much of it is real or fake. But that's just my hunch.