Varsovian:
I'd like to try running it
Ah, that's a different conversation then.
The CR system in Pathfinder is a rough guideline that isn't going to work really well for a solo game (it barely works for a regular game). One of the first keys to understanding it is to understand that the biggest limiter in Pathfinder is action economy. That is, PF characters can often do a lot of "stuff", but they can only do one or maybe two things at a time.
In combat, this is why a single monster against a large party works so horribly - the PCs just have a bunch more actions than the monster. You'd be having a similar problem if you tried to use the normal CR system against a single PC - the PC's one-two actions wouldn't stack up against those of two or three opponents.
You can still use the CR system to figure out approximate challenges, but you're going to be using much, much lower numbers than the PC's level.
For example, if a PC were to fight his clone, that clone's CR is equal to the PC's level -1 (if the PC were using NPC classes like warrior, etc, it would be level -2). A clone battle is a 50/50 fight, which would put it at least at APL+3 (Epic) in terms of battle difficulty. Using these numbers, we can extrapolate an "average" encounter for a single PC would be level-4 (with easy at level-5, challenging at level-3, and hard at level-2).
To check the numbers, let's do some math (note, CRs below 1 go fractional - 1/8, 1/6, 1/4, 1/3, 1/2)...
PC Level | Easy | Average | Challenging | Hard | Epic |
---|
1 | 1/8 | 1/6 | 1/4 | 1/3 | 1/2 |
3 | 1/4 | 1/3 | 1/2 | 1 | 2 |
5 | 1/2 | 1 | 2 | 3 | 4 |
7 | 2 | 3 | 4 | 5 | 6 |
So, let's take a few monsters out of the Bestiary for perspective:
A bat with the celestial of fiendish template is CR 1/8 and an "easy" encounter for a level 1 PC.
A housecat or rat with the celestial or fiendish template is CR 1/4 and a "challenging" encounter for a level 1, but an "easy" encounter for a level 3.
A level 1 PC is CR 1/2 and an "epic" challenge" for a level 1, a "challenging" fight for a level 3, but an "easy" fight for a level 5.
A Velociraptor, swarm of bats, or some of the smaller big cats are CR 2, which makes them an epic encounter for a level 3, a challenging encounter for a level 5, and an easy encounter for a level 7.
Finally, the smallest of dragons or an owlbear are CR 4, which makes them an epic fight for a level 5 or a challenging fight for a level 7.
Those... actually, those all look about right. The game design tends to assume most of your fights fall into "average" or "challenging", with a smaller number of fights at the other difficulties.
My major caveat to this is that when you add multiple foes, you have to be really careful, because you dramatically up the difficulty (the book's chart is +2 to the CR for the second monster, then +1 for each additional). A level 7 against 3 level 1 PCs might look like an Average encounter on the chart, but it's probably going to result in a dead level 7.