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If you use the standard rules, where the number tokens are laid out on the board in a pattern (small letters are below the pips), which seating position has the greatest odds of receiving the most goods?

  • Assume all players are trying to receive the most goods, with no consideration of good type.

  • Assume you are using the normal rules for the first two rounds, I.E. The first player places a settlement, followed by the second player clockwise until all players have placed a settlement. Then the last player places a settlement, and the second settlement placement continues counterclockwise.

    • Assume a 4 player game.

    • Assume the predetermined board setup for beginners which is supposed to be well balanced (extra points if you solve this for a random resource placement).

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Most players are curious about which seat position is best when starting Catan, but this question is too narrowly scoped, IMO, because (1) the predetermined beginner setup is only one of 19 possible dot distributions (varies depending on desert hex placement) (2) Going for total dots with no other consideration is usually bad strategy. Extreme example: I'd rather have 4/4/3 brick/wood/wheat than 13 dots of sheep. But it's usually much more complex than that in a real game as you have to consider ports, trading power, the likely setup of other players, etc. –  Joe Golton Feb 3 '12 at 21:44
    
The answer to this question is easier to answer than, "what seat position is best." My intention was to build off this question. –  user1873 Feb 4 '12 at 2:40
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2 Answers

up vote 7 down vote accepted

Key assumption: Every player places both of their initial settlements according to what will get them the most resources (so we don't have people going for port combos, weird 12/2 superstitions, etc.)


I just downloaded the rules and have the Beginner's Setup in front of me. If you don't, then this won't make any sense!

We all agree that it suffices to add the number of dots and use this to determine if one spot is better than another.

  • First takes 10/5/8 (Brick/Ore/Sheep) = 12 dots

  • Second takes 6/9/3 (Wood/Sheep/Ore) = 11 dots. This can be interchanged with P3's move

  • Third takes 8/10/4 (Wheat/Sheep/Wood) = 11 dots. Again, P2 could have done this.
  • Fourth takes 9/5/10 = 11 dots
  • Fourth takes 6/5/11 = 11 dots
  • Third takes 6/4/3 or 6/4/11 = 10 dots.
  • Second takes...

Here I will stop, since I have to go to class. But one thing is clear: Player one has a one dot advantage after the first placement, and Player 4 has twenty-two dots after his second placement. And it looks like The second player, on his second placement, will have AT MOST an eight-dot location. Since the first player would then have an eight-dot location (at best), his total is maximum 20 dots, where third has 21 and fourth has 22.

In conclusion, player 4 emerges with most resources

(edited, as I was having trouble keeping track of which spaces were available)

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I've been telling the people I play with this for ages. The last person has the best options. Plus since they are placing two at the same time they can get all 5 resources (maybe)... –  Coomie Feb 7 '12 at 6:06
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it is also easier to go for the longest road when you start in fourth or third. keep that in mind.

To me, it all depends on the board : like if there is one supreme location and players takes it... but that's kind of rare. There are usually 4 honestly good places and then it gets worse, so the advantage of being first is not that good to me.

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Welcome to B&CG! –  Pat Ludwig Oct 25 '12 at 16:09
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