Mathematicians of Catan

[mindstalk]

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

Comments

[tempter.livejournal.com]

Interesting. I'll have to look at this more when I have some free time.

I didn't realize all the other numbers were in such parity for the city building. When I started playing, I mostly ignored development cards, which meant that sheep were effectively useless beyond the initial settlements. Seafarers did a good job by allowing construction of boats using sheep; I don't think it's usually efficient, and doesn't fully fix the imbalance, but at least there's something to do with them beyond trade them for stone or wheat.

[mindstalk.livejournal.com]

I've never ignored dev cards, but I don't necessarily seek them out; they're if I have the cards for it, or if I have stone but can't buy a city, then I'll seek wool to make the stone useful. Well, somewhat seek dev cards: soldiers are useful for getting the robber off your 8!

I've been told Seafarers was the original concept; don't know if that's true. Never played it, apart from the Pioneers Linux clone, which I couldn't figure out in that mode, plus the constrained terrain seemed less fun.

I think Rich's Catan set had an extra sheep port, so I sort of "grew up" assuming sheep were meant to be the undervalued, highly traded, commodity.