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Mathematicians of Catan

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

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( 2 comments — Leave a comment )
tempter
May. 15th, 2009 08:44 pm (UTC)
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
May. 15th, 2009 09:10 pm (UTC)
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.
( 2 comments — Leave a comment )

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