Math question + XP dilemma

In your example, there is the following sequence of operations

X / N = Q , then
X - Q = Y , then
Y / N = R

Q is X-Y, which means X / N = X - Y
solving that for Y: Y = X - X/N
then R = (X - X/N) / N or X/N - X/N^2

Just a quick check to see if we're in line with your example
N = 4 and X = 20 gives R = 20/4 - 20/16 = 5 - 1.2 = 3.8 (3 with a remainder)
if N = 6 and X =20 you'd get R = 20/6 - 20/36 = 3.33 - 0.55 which would be 2 (eliminating the remainder)

By your brute force method:
20 / 6 = 3
20 - 3 = 17
17 / 6 = 2

so it checks out.

As you can see it's not simple arithmetic as it scales with the square of the number of players...thus you cannot reduce it simply as you feared you might have done.

If I were you, though, I'd create a table with total XP on one axis and number of players on the other and at the high end of the XP chain reduce it to arithmetic series, such as each 10 XP above a threshold 1 player gets 10, 2 players each get five, 3 players each get 3, 4,5, or 6 players each get 2, 7 or more players each get 1...something like that.

Thanks for the opportunity to actually use math I learned a thousand years ago but never use in a job that they told me I needed to be smart in math in to get!

I'm not entirely sure what kind of game you're creating...RPG? Board Game? Card Game?

Regardless, having XP in a game should, in my opinion, should really scale according to the scope of the game. If it's a video game, XP is easy because you can automate the XP per kill and scaling doesn't require an immense amount of work or physical elements. Yes, you have to account for scale and such, but that comes out in gameplay.

If you're doing something like a board or card game, I'd keep it extremely simple. 1XP per player per fight regardless of how many players or enemies are in the encounter. Yeah, it can be cheese for the player that doesn't "do" anything, but calculations are simple.

If you're doing something like an RPG, consider something slightly more complicated or try something different. I'm working on a card game that gives loot in lieu of XP and loot (in my case) can be in the form of bullets (for their weapons), equipment, or weapons. That way everybody gets something that can benefit them and random enough for them to keep them on their toes.

Regardless, you're going to need to keep it simple unless the whole theme of the game is XP, which I'm pretty sure isn't the sole focus of the game.

But I understand your question. How do you divide up XP for multiple minion or multiple player encounters? Again, I'd stick with something extremely simple, even if it seems off. You want the player to not be bogged down by the mechanics of the XP math and be more focused on the task at hand.

Anyways, that's my take.

This is what bothers me. Why the special treatment on XP distribution?
Why not simply divide XP amongst the players in a normal way?

The only reason that I can think of is that the combat mechanics show altering results in the game if things grow to fast or to slow.

Are you willing to share the combat mechanics with us?

If you put it that way. Maybe something along the lines of (XP/N)-N and rounding down.

20 XP gives
1N: 19 per player
2N: 8 per player
3N: 3 per player
4N: 1 per player

But then again. Rounding down becomes more devastating with more players. So substracting isn't even needed.

Simplicity it is.

Total XP = XP1 + XP2 x Number of missing players (max is 3)

So a creature gives XP, then you give XP for missing team effort.

And then divide this XP by the number of players.

Example:

XP1=20
XP2=5

1 player gets 35
2 players get 15 each
3 players get 8 each
4 players get 5 each

You can play with the second XP value for certain creatures. For example, a creatur that hits multiple opponents will nog be giving much XP2. But a lot of XP1. Meaning that this creature will be relatively weaker against 1 player, and thus give less XP.

The other end gives extra XP to 1 player if the creature needs a lot to be killed.

Give everyone all the xp. Then, there is a lookup table for the number of players that has the xp costs for leveling. It might look something like this:

players 1 |2 |3 |4 |
level 1 0 |0 |0 |0
level 2 20 |45 |60 |90 |

It has the same effect of making it take longer for a bigger group to get their upgrades as adjusting the xp, but without a formula the player has to worry about. They can look at their xp stack and have a good idea of how close they are getting. They can level in the middle of a mission if you want that. It also leaves you the flexibility to do things like give the last player to get a hit in some bonus xp, if you want that. You can adjust the scaling rather than relying on a strict forumla (maybe 4 players are really overpowered and need to be nerfed a bit more than 3 would for instance).

Saluk's idea sounds great for keeping everything reasonably balanced and easy to grasp though, unlike the attempts to automatically scale each xp gain.

Re: solo game - I don't know that having the game be a bit easier for a solo player is necessarily a bad thing. I find that harder games are less fun solo because I don't have the social pressure or encouragement to make it through and am more likely to walk away. I think many coop games are in fact easier solo in general, so whether it's good or bad, at least it's the norm.

My table idea for leveling could be used for the upgrade cards as well. The levels were just a suggestion. Replace "level" with "card power level".

The infinite possibilities get me every time, no matter what creative process I am engaged in!

Just to throw more fuel on the fire, here are a few other places that you could scale:

1) encounters - with more players, they are fighting more or more powerful creatures. Many attacks in sentinels for instance do (H-x) damage, where H is the number of heros. So with more players, more damage is being dealt.

2) hero abilities - the fireball for a solo player can target 4 enemies, but with 4 players it can only target 1. You may need to do this anyway in addition to your other scaling depending on what kinds of powers you include.

It's also worth noting that in these kinds of games (the Pathfinder Adventure game is one I play regularly), I typically will play with 2 heroes if I am solo, 2 or 4 in a 2 player game, and 3 at 3 players. I think this is pretty common. So it might be worth thinking about if it would be easier to just balance the 2 and the 4 player game. 3 player can be either a little easier than with 2, or a little harder than with 4.