Naw, both would end far too quickly and the simple knife in the dark is both a waste of money and brings zero fulfillment.
Motivation and anger more like.
Honor is for the weak, besides in those ancient times most legitimate business was very cutthroat too, as it was the time before better business bureau's and anti-thrust agencies.
Kraterous' game seems to be more fancy clothes and decadent parties, not whatever his family's business is. Many nobles were historically vulnerable by their disdain for business, as you've already written into the game many had educated stewards to take care of those boring, mundane matters for them and many of Rome's most successful businessmen were those second-class citizen freedmen (and their direct descendants). Probably because while they were nominally Roman citizens they were denied a place in its politics, but they could contract with the Patricians on equal terms, so the business world was wide open to them.
Well it helps to have a plan to keep oneself motivated to persevere.
You'd think an mc who survives the Arena would be used to the risk.
Happened to many (former) nobles of those provinces Rome conquered (and to the noble mc). For the most part they adapted.
There's also possibly this trope at play and while my mc certainly remember his old nemesis, for him having the mc disposed of might have just been Tuesday, particularly given the vast and nearly unbridgeable social gap between them in antiquity.
It would not set him free however. In fact my mc may partly cover against this by leaving a will to his heir that says to transfer that slave to the most miserable, dangerous position we've got. So if he thought the second-best position a slave in antiquity, as a relatively well-treated house slave, much like the mc on the Cato path, could have was misery, wait until he sees the galleys, chained to an oar.
Side note, I'm honestly surprised the slave trader in the beginning didn't have a galley and made his stronger male stock row it during that voyage. While not all merchants used them those who valued speed, and that included most slave traders, did if they could afford it.
Lastly that assumes he can be more devious than my mc, from a position as the house's most closely watched slave at that. Remember my mc would keep him around for strictly personal reasons, not profit or efficiency.
True, but an empty life of decadence where he never gets to attempt true revenge, which is what a lack of any education would seem to condemn us to post-manumission, should we make it that far, is not something that would be at all appealing to my mc. He's not someone to put all his trust in another educated slave or freedman to manage any money he's made and basically tell him how to run a business and household.
Well, notably for gay men like me, dynasties in the ancient world worked by passing on the family name, rather than the bloodline as it became under Christianity and would allow adopting an heir if one does not have biological children of one's own. Of course if they both make it to freedom, then with her permission my mc could try for children with his best friend, even if he does not love her romantically in that way. They would hardly be the first husband and wife in those particular circumstances.
Still his revenge would be deeply personal and he'd be unlikely to involve any sons he may have to deeply in, as this would be one area where they should stay out of his affairs, except perhaps for that slight role in any last will and testament as to the disposition of Kraterous, should he own the guy by then.
Of course, it has all the benefits of making communication a bit easier even there. Just not as much as it would for a house or educated slave, though still more than on the plantation or in the mines of course.
Understanding it would always come in handy, whether my mc would deign to speak it himself, unless it is with people who already know he speaks it now, is another.
I see your point, if you wanted to you could, just like with manumission, afford to sacrifice a bit of historical accuracy there. My mc would not be okay with it, but then he'd hardly be in a position to do anything about it. Though you'd probably be better off avoiding the subject and sacrificing a bit of historical accuracy there as it would likely go against some of CoG's policies to depict such non-consensual things.
What you might allow instead is for the mc to strictly optionally sleep with wealthy Romans in exchange for gifts or favours with no penalty except for (slightly) less chance for a thumbs-up if we lose and of course a bit less money.
Like another poster already mentioned for the Greek noble specifically Latin would not be optional during the time period and for the Greek merchant background it could be optional, like it is for the nobles of the other backgrounds. But they would at least have far more opportunity and encouragement to learn it than non-Greeks.
Considering he seems to be the rare patrician businessman who truly cares about business the conclusion seems self-evident here. I'm honestly amazed we could choose what to learn from his steward at all as it may have been more logical and potentially profitable for him to instruct the guy to teach us to speak Latin first, no matter what.
Still while the slave masters and lanista's of the Arena would probably be pleased that we can understand them without a translator they may be less keen on conversation and would probably not be bothered by a slave who mostly chooses to answer in "yes and no" short and terse answers, with emphasis on the "yes, master" of course.
As for the most part they'd want combat, not conversation, out of us.
Community college is more pleasant and diverse age-wise, but less prestigious then University. Still after the bullying experiences I received at university during my bachelor phase I had no desire to return there for a masters degree. The fact is I would have also been a bit older then most students by then as I did a stint as a political aide for a couple of years in-between the two. Law school in this country is the 2.5 years that come after university, so a form of post-graduate education, even if it is a good deal more practice oriented then most such things, particularly the Phd. Note that it is also academically possible to get a Phd in legal studies and that is a very different path from law school, though some do enter the other after having completed the other one. I have neither the money, time nor desire for a Phd in legal studies though. If I never have to write an academic paper or thesis again it would be too soon, imho.