Boring self-aggrandizing game geekery ahead:

Gamer's Guild has a joke houserule about automatically winning Catan if you build 3 cities around the desert. I verified this was a joke by doing so tonight, though as it happens I won anyway. It all made sense, though.

Desert in the inner tier of tiles. First to build, picked 5-10-9 stone-stone-wheat. Last to build... there were better places pip-wise than the 4-3 wood-brick I chose, but none that would give me those cards, and being able to build a road out the gate is nice. The obvious candidates to build next were 5/ocean/3:1 port, 8 wheat around the desert, 5 sheep around the desert. I went for the wheat, then sheep (my only sheep), picking up more wood and clay, and the port last. Perfectly natural settlements around the desert. First city was the stone-wheat triple, duh! But second? The 5 just turns 3 stones into 4 stones, doesn't give anything else, and risks getting suppressed as an attractive nuisance. Desert cities at least doubled two tiles each, thus not being squelchable by the robber. Thus, cities around the desert. Finally won with a breakout road, and a last settlement -- rolled a 7, but I had a year of plenty in my hand, and might have had enough cards to win anyway, didn't check; would have needed 11 cards total, losing 5 to keep wood wheat sheep and 3 stone to turn into brick. Alternately, the next dev card was a VP, though of course I didn't know that.

It was a close game, two others were one VP card or settlement away from victory, and the last guy still had 8 VPs. Started slow since inland deserts often do that, plus we rolled a ridiculous number of 7s -- discarded all the ones in the first two turns, which was a lot. Later the game picked up, though often was choked for brick or wood at various times, though it really oscillated -- I'd go from having 4 wheat and clay each to having no clay and needing it.

anima got a solid lock on largest army without any natural stone, just by buying it with clay or other stuff. P. never had 3:1 till the end, but still did pretty well trading in sheep, sheep, sheep, and sheep.

Some not very deep thoughts:

To build a city from scratch, without exploiting branching roads, takes
* 3 brick (2 roads, settlement)
* 3 wood (ditto)
* 3 wheat (settlement, 2 for city)
* 3 stone (3 for city)
* 1 sheep (settlement)

I believe this helps explain why sheep are in such surplus. I knew this roughly, but not how even the numbers were. If you use branching roads, brick and wood go down to 2, which is still more than sheep.

There's 3 stone tiles to 4 wheat, so you'd think stone would be more valuable, and maybe it is if you count carefully enough, but wheat usually feels more reliably valuable... probably because the demand is more constant -- more spread over time, and more useful in small quantities, vs. "do I accumulate stone and risk going over the 7 card limit?"


Also, I've wondered how many resources it takes to win. This varies a lot, depending on how you get your points. Almost the cheapeast possible way to win is:
* Buy a road building card, and connect your two starting segments; build another road for Longest Road. 5 cards, 2 points.
* Buy 3 soldiers and get largest army. That'd be 9 cards, except you get to steal cards, so 6 resources, for 2 points.
* Buy 4 Victory Point cards, 12 cards.
So, 23 cards, 8 points. This of course takes extreme luck. Nearly as bad is 5 VP cards, 2 cities, one settlement: 15+10+6 = 31.

More honest-feeling is lots of cities. If you use branching and minimal roads, that's 4 cities, 2 settlements, or 4*(2+4+5) = 44 resources.
A Monopoly on stone is a good way to cut that down if you're luck, turn 3 cards into the 12 stone you need, for 32 cards.

The upper bound is fun in a twisted way:
* compete for longest road *and lose*: 26 resources spend on roads, 0 points.
* compete for largest army and lose: 7 soldier cards, 14 resources, or 21 if you don't steal from other players.
* Buy road-building cards after you've run out of road segments, 6 resources.
* Buy Monopolies and fail to get anything for them: 6 resources.
* Use Year of Plenty to turn 3 resources into 2: net loss 2 resources. (Or don't bother using them, 6 resources.)
* Finally win via settlements and cities. Normally building settlements would be more expensive, but here you've already built roads, so cities become more expensive for you. 4*9=36 resources.
So: 26+14+6+6+2+36=90 resources. Or 101 with the worse assumptions. And this doesn't count resources lost to theft or rolled 7s.

So, ridiculously easy: 3 cards/VP; sensible, 5.5 cards/VP (44/8); ridiculously hard: 11+ cards/VP