I finally had time to type this up after this thread was pointed out to me.
Here's the most accurate estimate of the value of Puissant X vs. Affinity w/ X, where X is an ability, that I have yet seen. Many may not agree with several of the specific estimates made, but you can easily tweak any of the numbers I've given to reflect differences in your sagas. Regardless, this will still be a better estimate than is usually made. (Note, I am also not assuming the "munchkin" approach as it was named by the OP. However, I am not assuming that every single source quality will be of the same parity (even or odd), as the OP did, which unfairly favors Puissant X.)
First, we need to understand when the two situations are equally beneficial. It could be argued that when the rank of X with Affinity w/ X is two greater than the rank of X with Puissant X, the affinity is better because of things like teaching and training limits from the teaching standpoint. However, it could also be argued the other way based on those same things from the learning standpoint. In all other cases, they are equivalent at this point, so let's just say they are equally beneficial at this point.
Now we need to understand just how much experience Affinity w/ X is really worth. I've mostly only seen people saying 1.5 times the experience without it. However, that is an absolutely worst-case scenario. If there is ever a point at which an odd number of experience is earned, then Affinity w/ X has provided more than. Any time a single experience would have been gained, two are instead, meaning Affinity w/ X has provided a 100% bonus. With three experience, give are gained instead, meaning the bonus is 67%. Etc. So, just how much is it really worth. This is a non-trivial but crucial estimate. To handle this estimate, it is advisable to break all abilities into three categories: Magic Theory, others that can be studied from books, and all the remaining abilities. In each case we'll have to determine how many times experience will be earned to reach any given rank and figure that half of those times will provide an odd number of experience, so using a 1.5 multiplier will miscount the number of experience earned by 0.5 experience. Thus the number of experience earned with the affinity will be:
E'=1.5E+0.25N,
where E' is the experience with the affinity, E is the experience without it, and N is the number of seasons in which experience has been gained in the ability.
Determining N is the tricky part and it can only be an estimate unless we look at an actual character's past. We need to determine how much experience is gained in any season in which advancement is made in the relevant ability. To do that we must look at how much experience is gained via any given method and try to determine a meaningful average. Let's start with the basics. Exposure will provide 1 or 2 experience, for an average of 1.5 experience. Adventure will provide 1 to 5 experience, for an average of 3 experience. Practice will provide 1 to 8 experience, but it will rarely be split so 3 to 8 is a better range, and 4 or 5 is most likely, so an average of 4.5 is reasonable. Training and teaching are highly variable based on the teachers and whether you're alone or not (for teaching). An estimate of a quality of 9 for training and 12 for teaching on average is not unreasonable, though I've seen teaching reach into the upper 20's fairly easily. As discussed elsewhere, lower quality books (for ease we'll put summas and tractatus together) are less likely to circulate much, making a quality of 11 quite a reasonable average. We should also try to take things like Apt Student and Book Learner. In my experience Book Learner is the most common and the others not so much so, so I'll add 1.5 to the quality of the books. In addition to this, correspondence is done for those areas in which books are written, so I'll add another 0.5 to the qualities for those things. That leaves:
Non-book abilities
Exposure: 1.5
Adventure: 3
Practice: 4.5
Training: 10
Magic Theory and other book abilities
Exposure: 2
Adventure: 3.5
Practice: 5
Teaching: 12.5
Books: 13
Now we need to try to gauge the relative frequency of these things. For non-book abilities training is harder to come by, and the rest are probably fairly balanced. If we estimate training as half as common as any of the others, then we get 4 experience on average in a season of advancement of a non-book ability.
For non-Magic Theory book abilities just taking an even split of all five methods may be decent, yielding about 7 experience on average in a season of advancement of a book ability.
For Magic Theory experience is usually only gained via exposure, teaching, and books. As magi commonly spend about two seasons a year in the lab (according to Covenants) and maybe one season every three years studying Magic Theory, then we get something around 3.5 experience on average in a season of advancement in Magic Theory. (Note, the rules heavily favor lab work, and I figure a lab rat is the type who would most frequently take Puissant Magic Theory or Affinity w/ Magic Theory.)
Where do we put these estimates? Here is how we calculate N:
N=(E-S)/R,
where N is the number of seasons in which experience has been gained in the ability, E is the experience (without an affinity), S is the original number of experience put into an ability, and R is the rate determined above.
So, what is S? Again, this can only be an estimate unless we examine a specific character's past. I would hazard to say most characters with Puissant X or Affinity w/ X will want X to start relatively high because they want to focus in it. I would say putting 50 starting experience into such an ability is quite reasonable, though certainly more or fewer will happen. Fewer would favor Affinity w/ X more than this argument does. More would favor Puissant X more than this does.
So, combining all of this yields:
E'=1.5E+0.25(E-50)/R
E'=(6R+1)E/4R-25/2R
Non-book abilities: E'=25E/16-25/8
Book abilities: E'=43E/28-25/14
Magic Theory: E'=22E/14-25/7
Now we have to relate all that to the cost to reach the different ranks. We want the rank with E' to be two higher than the rank with E. The necessary formula is:
E=5+10+15+..+5n=5n(n+1)/2,
where n is the number of ranks. So for the affinity:
E'=5(n+2)(n+3)/2.
That leads us to:
Non-book abilities: 5(n+2)(n+3)/2=125n(n+1)/32-25/8
Book abilities: 5(n+2)(n+3)/2=215n(n+1)/56-25/14
Magic Theory: 5(n+2)(n+3)/2=110n(n+1)/28-25/7
Divide all formulas by 5 and multiply them by their greatest denominator:
Non-book abilities: 16(n+2)(n+3)=25n(n+1)-20
Book abilities: 28(n+2)(n+3)=43n(n+1)-20
Magic Theory: 14(n+2)(n+3)=22n(n+1)-20
Write these in standard form:
Non-book abilities: 9n^2-55n-116=0
Book abilities: 15n^2-97n-188=0
Magic Theory: 8n^2-48n-104=0
Solve these:
Non-book abilities: n=7.8
Book abilities: n=8.0
Magic Theory: n=7.7
What this tells us is that as a basic guideline you reach effective rank 9 (7+2) with Puissant X earlier than you reach rank 9 with Affinity w/ X, but you reach rank 10 with Affinity w/ X faster than you reach effective rank 10 (8+2) with Puissant X.
Next is the question of the limit of experience earned in any ability. Reaching an 8 is pretty tough and won't happen that much. And even if you do have 8 ranks and Puissant X, you're only missing out in a couple spots due to the large number of experience required to go from one rank to another. Plus, you'll probably spend most of your character's career just trying to reach that point, so you'll be using lower values most of the time. So I agree you should stick with Puissant X unless it's a very long-running saga and the character will be active a lot later in the saga. The one case where this is not so true is with Magic Theory. With the estimates here, a magus will get there in about 15 years. (If players don't realize just how much the rules favor lab work over casting scores, this could take longer, but it certainly shouldn't for a lab rat. Certainly, it will be taking well under 15 years for any of my lab rat characters since I've seen the item creation rules a lot.) So if you're in a relatively short-lived saga, stick with Puissant Magic Theory. However, if you're in a longer-lived saga (let's say 20+ years), especially if you're lab-focused (15+ years), go with Affiinity w/ Magic Theory for later gains. Certainly the older archmagi will have done much better by taking Affinity w/ Magic Theory over Puissant Magic Theory. Better yet, take both!
Chris
