tl;dr– Experience (EXP) isn't countable, so it's a "How much?" thing. By contrast, experience-points (XP) are countable, so they're a "How many?" thing.
How much of a concept, or how many in a quantification?
Characters acquire experience (EXP), which can sometimes be quantified in terms of experience points (XP).
Analogies:
Concept |
Example quantifiers |
Experience |
Experience-points, levels, bars(Note) |
Money |
Dollars, Euros, Pounds, months of one's salary |
Distance |
Kilometers, miles, meters, feet, football fields |
Time |
Seconds, minutes, days, years |
Note: Some games show experience in a figure composed of multiple bars, so players might refer to "bars" of experience, where each bar might be like 5% of a level.
We ask "How much?" of a concept, or "How many?" in a quantification.
Questions that don't require quantified responses might still get a quantified response.
Alice: How much longer?
Bob: 5 seconds.
Alice didn't ask for a quantification, but Bob provided one. It works, even if Alice didn't necessarily need to an exact number of seconds.
Alternatively, Bob could've responded like this:
Alice: How much longer?
Bob: Pretty soon.
Regarding the example in the question:
Alex: 'Great, how ___(many/much) XP have you got?'
Either way could work.
Using "much" would ask a more general question. For example, the answer could be "Almost enough to level!".
Using "many" would imply a more specific request for a number of experience-points.
Note: Ambiguity between "XP" and "EXP".
"XP" and "EXP" mean different things to different folks.
Personally, I tend to think of "EXP" as being the first few letters from "EXPerience", while "XP" comes from "eXperience Points".
However, some folks use them as synonyms, sometimes preferring "XP" because it's shorter. They may not even recognize a distinction between the concept of "experience" and a quantization of it with "experience points".
For folks who don't consider the difference, they may not be using the normal grammar rules discussed above, but rather just always default to asking "How much?" on a more idiomatic basis.