# XP Math Question

### Rules Questions Pathfinder Adventure Path, Lost Omens, Rulebook Subscriber

I just noticed that there is a small hole in the experience point math for building encounters. It occurs when you have a trio of creatures whose base CR is even.

Consider the following examples, groups of CR1 and CR2 creatures:

CR 1
1x = 400 (CR1) OK
2x = 800 (CR3) OK
3x = 1200 (CR4) OK
4x = 1600 (CR5) OK

CR 2
1x = 600 (CR2) OK
2x = 1200 (CR4) OK
3x = 1800 (CR?) WRONG
4x = 2400 (CR6) OK

This issue extrapolates out for all even CRs.

So my question is, if I have such a threesome of CR2 creatures, do I use the 1800 XP value, resulting in an off-table XP sum, or do I just treat them as a CR5 encounter (1600 XP)? I'm leaning towards the latter. Well, 3 x 600 SHOULD be 1800, no? So I'm not sure what the problem is... Pathfinder Adventure Path, Lost Omens, Rulebook Subscriber
Bruno Kristensen wrote:
Well, 3 x 600 SHOULD be 1800, no? So I'm not sure what the problem is...

1,800 isn't an experience sum on the table. It's slightly above CR5.

Bruno Kristensen wrote:
Well, 3 x 600 SHOULD be 1800, no? So I'm not sure what the problem is...

The issue is that 1800xp is 200 more than rated for a CR5 encounter.

I would use the 1800 number, and just consider the encounter CR5+.

delabarre wrote:
1,800 isn't an experience sum on the table. It's slightly above CR5.

That's correct. It's a logarithmic scale based on powers of two; doubling the encounter raises the CR by 2, but trippling the encounter does not raise the CR by three.

This is not an error; it's just the way the system works. Three monsters of CR X are worth a little more XP than a CR X+3 encounter.

Mirror, Mirror wrote:
Bruno Kristensen wrote:
Well, 3 x 600 SHOULD be 1800, no? So I'm not sure what the problem is...

The issue is that 1800xp is 200 more than rated for a CR5 encounter.

I would use the 1800 number, and just consider the encounter CR5+.

Yes, my understanding is that you just add them all up. For instance, a CR 8 + CR 2 encounter is worth 1,200 + 150 = 1,350 xp, even though it's still a CR 8 encounter in total. Pathfinder Adventure Path, Lost Omens, Rulebook Subscriber

Sounds like the consensus is to use the 1800 value, compute the experience awards by hand (600, 450, or 300), and then use "CR5" for anything else, such as determining random treasure.

delabarre wrote:
Sounds like the consensus is to use the 1800 value, compute the experience awards by hand (600, 450, or 300), and then use "CR5" for anything else, such as determining random treasure.

No, I'd use 3x CR 2 xp awards, and 3x CR 2 treasure awards (i.e. 3 x 800 gp instead of 2,300 gp).

(Note: As a GM, I don't generally use xp at all, and I make up my own treasure rather than using the guidelines in the book. But if I did were using the book's suggestions, that's what I'd do.) Pathfinder Adventure Path, Lost Omens, Rulebook Subscriber
AvalonXQ wrote:
It's a logarithmic scale based on powers of two; doubling the encounter raises the CR by 2, but trippling the encounter does not raise the CR by three.

Table 12-3 disagrees with you. Pathfinder Adventure Path, Lost Omens, Rulebook Subscriber
hogarth wrote:

No, I'd use 3x CR 2 xp awards, and 3x CR 2 treasure awards (i.e. 3 x 800 gp instead of 2,300 gp).

(Note: As a GM, I don't generally use xp at all, and I make up my own treasure rather than using the guidelines in the book. But if I did were using the book's suggestions, that's what I'd do.)

I'm actually using the treasure tables in the WOTC Magic Item Compendium until the GameMastery Guide arrives next month.

That being said, I disagree with the idea of treating groups of creatures differently (treasure-wise) than single creatures. Theoretically, the risk is the same (hence the CR) so the rewards should be the same as well.

Table 12-3 is an approximation. Like I said, the system is a log2 function; multiples other than powers of two will not yield exact values. Six CR 6 encounters don't add up exactly to any CR, but they're not too far off from CR 11, which makes the table a useful estimate if not perfect.

3x CR 2 creatures equals 1800xp (600x3=1800). As for what CR that totals is only relevant as a sort of gauge to how difficult of an encounter it's going to be for your PCs. Since it's above the given XP allowance for 5, but less than 6, you can either call it "better than cr5, not quite 6", or just use the XP budget for 6 and call it a day.

AvalonXQ wrote:
delabarre wrote:
1,800 isn't an experience sum on the table. It's slightly above CR5.

That's correct. It's a logarithmic scale based on powers of two; doubling the encounter raises the CR by 2, but trippling the encounter does not raise the CR by three.

This is not an error; it's just the way the system works. Three monsters of CR X are worth a little more XP than a CR X+3 encounter.

+1. Avalon is correct.

It works that way for any CR.

3 CR2's are a CR5 not a CR'6 as an example

Ninja'd by Slatz before I even finished posting.

One way to present the XP math is to apply the equation

XP = 2^(CR/2)*300

Which is exactly correct only for even CRs. For odd ones, estimate that sqrt(2) ~ 4/3, and act with that assumption. Which means, for odd CR 2*n + 1, the equation becomes...

XP = 2^((2n+1)/2)*300 = 2^(2n/2)*2^(1/2)*300 = 2^n*(4/3)*300 = 2^n*400

For even CR 2*n, of course, the equation is just 2^n*300.

This equation works beautifully, although they could have created a slightly more accurate progression by just applying the logarithm directly and rounding to the nearest hundred. The problem there is that it would no longer be universally true that the "double = +2" rule would no longer apply. This "4/3" approximation, while less accurate in tracking the logarithmics at higher levels, preserves that simple rubric.

The basic CR relationship is simple: to rise from an odd to an even, multiply by 3/2, and to rise from an even to an odd, multiply by 4/3. Or, to calculate the relationship from scratch, divide the CR in half, double 300 that many times, then multiply by 4/3 if you have a half left over.

delabarre wrote:
That being said, I disagree with the idea of treating groups of creatures differently (treasure-wise) than single creatures. Theoretically, the risk is the same (hence the CR) so the rewards should be the same as well.

I don't think the risk is necessarily the same, since CR numbers greater than 1 are rounded to the nearest integer.

For instance, I think we would all agree that a CR 8 + CR 4 encounter is at least a little more difficult than a CR 8 encounter. According to the table, it should be about as difficult as an encounter with 5 CR 4 creatures, so it would fall somewhere between a CR 8 and a CR 9 encounter. So why not give XP and treasure accordingly instead of choosing either CR 8 or CR 9? For a CR 8 + CR 4 encounter, the total XP would be 6,000 xp and the total treasure would be 6,700 gp.

----

Actually, as an aside the "Treasure Values per Encounter" table is a bit odd. Even though you get the same XP for 2 CR 8 encounters vs. a CR 10 encounter, you get more treasure from 2 CR 8 encounters. Pathfinder Adventure Path, Lost Omens, Rulebook Subscriber
hogarth wrote:
Actually, as an aside the "Treasure Values per Encounter" table is a bit odd. Even though you get the same XP for 2 CR 8 encounters vs. a CR 10 encounter, you get more treasure from 2 CR 8 encounters.

Even odder (pun intended): A party of PCs would get the same XP fighting two CR8 creatures separately, or a single EL10 encounter composed of 2 CR8 creatures in tandem. However, the total treasure haul would be greater in the first case, even though the second case presents the greater risk.

If your most powerful abilities are limited-use, fighting two enemies in sequence can sometimes be more dangerous than fighting them in tandem. Pathfinder Adventure Path, Lost Omens, Rulebook Subscriber
AvalonXQ wrote:
If your most powerful abilities are limited-use, fighting two enemies in sequence can sometimes be more dangerous than fighting them in tandem.

Your PCs don't camp for the night between each encounter?

I kid, I kid.. ;-)

It is not exact, because they made it simple.

As you already know 2 creatures of CR X equal 1 creature of CR X+2, and that's the only solid rule. Every other rule about CRs and xps comes from there, and is usually simplified, that's why you may have problems with uneven numbers of creatures (3*CRX=CRX+2 + CRX= ??)

Rules tell you to go with xp, but rules also give you the option to use CRs if it makes things easier for you.

Or, you know, level up when GM says so.

Evil Lincoln wrote:
Or, you know, level up when GM says so.

Now that's just crazy talk. ;-) 