How does Kvothe's deal with Riem (the bursar) work?

Question

At the end of The Wise Man's Fear, after Kvothe returns to the University, he strikes a deal with Riem (the University's bursar). The deal works in the following way: in exchange for Kvothe flunking his Admissions (which causes the Masters to increase his tuition), Riem charges Maer Alveron's coffers with the increased tuition and pays Kvothe half of tuition above 10 talents.

So, in other words:

Before the deal is struck:

1. Kvothe's tuition is set to X during Admissions,
2. Somebody (Kvothe himself) pays Kvothe's tuition X to Riem.

After the deal is struck:

1. Kvothe's tuition is set to X during Admissions,
2. Somebody (the Maer) pays Kvothe's tuition X to Riem,
3. Riem pays some-of-X back to Kvothe.

I feel I am missing something vital, because the deal doesn't make a lick of sense to me. To be more precise: I can't get what Riem gets out of the deal, how Kvothe paying a larger-than-average tuition plays into this¹, and how deficits caused by the deal can remain undetected (by, say, the Masters).

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¹ It seems to be implied that Riem does indeed withdraw the amount of tuition - instead of, say, twice the amount of tuition - out of Maer's coffers (all emphasis mine):

As a result, I was assigned a tuition of twenty-four talents. [...]

Afterward I returned to the bursar's office. I officially presented Alveron's letter of credit to Riem and unofficially collected my agreed-upon cut: half of everything over ten talents. I put the seven talents in my pocket [...]

^{Chapter One Hundred Forty-Two: Home, The Wise Man's Fear, Patrick Rothfuss}

(24 - 10) / 2 = 7

Then Hemme read my tuition: fifty talents. [...]

Riem's eyes brightened at the sight of my tuition slip. [...]

Once I had the door closed, I tore open the heavy envelope and poured its contents into my hand: two gleaming gold marks worth ten talents each.

^{Chapter One Hundred Fifty: Folly, The Wise Man's Fear, Patrick Rothfuss}

(50 - 10) / 2 = 20

Answer 1

Kvothe has a blank check from the Maer. Literally. He is allowed any amount for his tuition.

Under normal circumstances, Kvothe has never had a tuition more than ten talents (typically it's more like 8). Not being able to afford a higher tuition, he made sure his skill and talent was seen in every admissions interview to keep that tuition as low as possible.

The bursar naturally likes to be taking in more money. The school needs money to run, so Kvothe having a higher tuition helps the school run, but the bursar doesn't run the interviews.

So the deal operates as follows - Kvothe, who is normally clever enough to ace his admission interviews and keep his tuition low, throws his interviews, driving up his tuition. The bursar gets to collect more money from the Maer's blank-check letter of credit, which makes him happy. Kvothe gets a slice of this so he doesn't have to live in poverty anymore, which makes him happy. Everyone comes out ahead - except the Maer, who is being overcharged but likely won't notice the grift, and Kvothe doesn't respect the Maer after being shafted by his wife, and is much more open about that disrespect now that he's half a world away from him. The bursar keeps the accounting books, so unless (when?) Kvothe screws things up badly, the masters likely will never know about it either.

The text mentions the bursar as a "practical man", so this is likely not the first off-books arrangement he's made to keep money flowing into the school.

Answer 2

I think you're missing the simple practicality of the deal for the Bursar.

Ignoring all the hinting and winking, Kvothe basically goes to the bursar and says, "I've got this nifty letter from the Maer which says he'll pay whatever tuition I am charged."

But we know how well I do on the admission's exams; we both know it will end up being ten talents or less. HOWEVER, if I agree to "throw" the entrance exam then the tuition will be a lot higher and the university will make a lot more money from the Maer.

But it's got to be worth my while... So, if you agree to give me a kick-back on the tuition, I'll make sure you're able to bill the Maer for a lot more money than you'll get otherwise, and it will be a win-win for all. Well, except for the Maer but he won't even notice...

Answer 3

This is caused by a deal Kvothe made with Riem. Since there is no standard tuition for the school he made a deal. While ten talents may look like a decent amount on paper, and unless there is an auditor checking the amounts that the Bursar collected for each student, their deal could easily be missed as Kvothe's tuition fees are basically written down on a receipt that he takers the Bursar to pay.

Kvothe basically has a blank check from Maer and made a deal with Riem, I pay ten talents to the school and we split anything over.

I left my baggage in Simmon’s room and paid a visit to the bursar in the basement of Hollows. Riem was a balding, pinch-faced man who had disliked me ever since the masters had assigned me a negative tuition in my first term. He wasn’t in the habit of giving money out, and the entire experience had rubbed him the wrong way. I showed him my open letter of credit to Alveron’s coffers. As I’ve said, it was an impressive document. Signed by the Maer’s own hand. Wax seals. Fine vellum. Excellent penmanship. I drew the bursar’s attention to the fact that the Maer’s letter would allow the University to draw any amount needed to cover my tuition. Any amount. The bursar read it over and agreed that that seemed to be the case. It’s too bad my tuition was always so low, I mused aloud. Never more than ten talents. It was a bit of a missed opportunity for the University. The Maer was richer than the King of Vint, after all. And he would pay any tuition. . . . Riem was a savvy man, and he understood what I was hinting at immediately. There followed a brief bout of negotiation, after which we shook hands and I saw him smile for the first time.

(Note I will update with the exact page number later and citation, I pulled this from a PDF)

Answer 4

As your calculations show, it simply doesn't work. This gets pointed out by readers from time to time, for example, in the TOR reread.

As written, the Maer is paying the University exactly the assigned amount of tuition, and Kvothe and Riem are defrauding the University. Kvothe could have struck this sort of "deal" with Riem earlier - it's beneficial with or without the letter. Furthermore, Riem gets nothing out of the "deal", as he has apparently always been at liberty to steal tuition funds.

What Kvothe should have done is have Riem overcharge the Maer and split the difference between the amount charged and his assigned tuition. The amount of tuition in this case, of course, wouldn't matter, so Kvothe could't be paid "for insolence and ignorance" in a twist of dramatic irony. There's no mystery here: Rothfuss tried being ironically clever and failed.