You cannot have three adjacent hexes with the same number of dots. You can’t have two adjacent hexes with the same (dice roll) number on them. īefore answering the question I must point out that some combinations are impossible. Then the chance that this settlement will pay off is. , or as I will write from here onward, 5-3-2). Now suppose your settlement is on a 6/4/11 intersection (which corresponds to dots For example, there are 3 ways to roll a 10 (4 & 6, 5 & 5, or 6 & 4) and there are 36 possible rolls, thus the chance of rolling a 10 is 3/ 36. The reason this is true is that if a chip has n dots, then the chance of rolling the number on that chip is precisely n/36. The intersection with the largest dot-sum is the most valuable. I was surprised to discover that the simple answer is the correct answer: add up the dots on the adjacent hexes. I’m ignoring the other strategies: settling on ports, spreading out your settlements, getting a broad range of resources, etc. My question is: how do we look at a board and determine the most valuable intersections? By valuable I mean greatest likelihood of yielding a resource card when the dice is rolled. The dots give you an easy way to determine which are the valuable hexes. The round chips not only have numbers, they also have dots on them. You may put your settlement along the coastline or the desert, but the downside is that it would be adjacent to only 1 or 2 resource hexes. Thus it is good to put your settlement next to a 6 or an 8, 5 and 9 are good too, however the hexes with 2’s and 12’s are not worth much. For now I’ll ignore what happens when a 7 is rolled. If the player has upgraded a settlement to a city and it is adjacent to the hex, he or she gets 2 resource cards. Once each player has two settlements, play begins.ĭuring each person’s turn a pair of dice are rolled and anyone with a settlement adjacent to a hex with that number on it gets a resource card of that type. The players take turns placing settlements on the corners where three hexagons meet. Each chip has a number 2 through 12 (except 7) on it. The mathematical analysis is extremely simple, but is kind of fun and maybe a little useful to know.Īt the start of the game the hexagonal game pieces are put in place randomly (as shown in the picture above, which you can click on to enlarge) and the round chips are distributed according the the rules. I just found my notes that I wrote, so I thought I’d share them here. Where should I place the robber to do the most damage?.What are the most valuable intersections? This information is most important to know at the beginning of the game when placing the first two settlements.This post will probably be interesting only to those people who know the rules to the game (sorry), but I will give a brief explanation of the relavant rules so that anyone can follow the discussion.Ī couple of years ago I asked myself the following two questions about Settlers of Catan. I’ve been on a big Settlers kick lately, because I’ve downloaded a version for my iPod Touch. It is a great game because it is a combination of luck and strategy and it is different each time you play. One of my favorite board games is Settlers of Catan.
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