Resource Pips: Reading the Totals Under the Board

What a pip is, and what the chips add up

A pip is one dot on a number token — one of the 36 equally likely results of rolling two dice. The coloured chips under the board add the pips of every token on each resource’s hexes. The total is that resource’s expected income over 36 rolls for the whole board.

A 3–4 player board has 18 number tokens worth 58 pips; the 5–6 player board has 28 tokens worth 88. The desert carries no token and adds nothing. Because each size has a fixed mix of terrain, every resource also has a fixed fair share:

On 58 pips one pip is 1.72 percentage points; on 88 pips it is 1.14. The Balanced resources switch uses that scale: it rejects a candidate when any resource is more than 7 percentage points from its fair share — about 4 pips on a 3–4 player board and about 6 on a 5–6 player board.

How to read a chip total

1. Add the pips on that resource’s tokens. Wood on the first board below has tokens 8, 11, 10 and 10: five + two + three + three = 13 pips.
2. Compare with the fair share, not with the biggest number. Ore’s 10 looks small next to wood’s 13, but ore’s fair total is 9.7, so 10 is on schedule.
3. Look at which tokens carry the total. A resource whose pips sit on one 6 is a single point of failure; a resource spread over three tokens pays more often. The chip cannot show that; the board can.

The tool prints the chips after the score line, colour-matched to the terrain. The desert never gets one, and the five chips always add to 58 or 88 — a quick check when you read a physical board too.

Three generated boards: abundance and scarcity

All three use the default rules, code 1101 in the share link: no adjacent 6 & 8 on, no same numbers touching on, no 2 & 12 touching off, balanced resources on.

Everything near its fair share (score 92)

Every resource is within about one pip of its fair total: wood and sheep 13 against 12.9, wheat 12, brick and ore 10 against 9.7. Ore’s 10 does not mean ore is scarce — it is exactly on schedule, and all five resources sit within about 1.5 percentage points of their share. With a board like this, pick starts on pips and resource mix; no resource is rationed.

Brick starved, wood flooded (score 89)

Brick is the shortage: 6 pips, 10.3% of the board against a 16.7% fair share. Its three tokens are 2, 4 and 11, so its best hex pays 3 of 36 rolls — there is no brick 5, 6, 8 or 9. Wood is the surplus at 16 pips, carried by two 8s and a 6, with a single 12 adding one more. Roads and settlements both need brick, and the drawing puts a 2:1 brick harbor on the brick coast, so the few brick hexes are leverage for whoever settles them while everyone else pays the bank rate or trades wood away.

The score is still 89. The formula penalises the largest skew — 6.3 points here — and this board sits just inside the 7-point rule. A high score means structurally fair, not every resource plentiful.

5–6 players: 88 pips and an ore surplus (score 76)

On 28 tokens the board holds 88 pips, so one pip is only 1.14 percentage points and the same gap is a smaller share than on a 58-pip board. Wood is short: 15 pips against a fair 18.9. Ore is long: 20 pips against 15.7, the largest skew at 4.9 percentage points. Ore’s tokens are 8, 4, 5, 10 and 8 — two 8s carry its 20 pips, level with sheep for the highest total on the board. If you build cities, ore is what you trade away; if you need wood, expect to pay for it.

The score of 76 comes mostly from four same-resource pairs (−16 points) and that 4.9-percentage-point skew (−7.3 points), plus a one-pip start spread (−0.6); the scoring method shows the arithmetic.

What one total hides

• Distribution. On the first board brick and ore both total 10. Brick gets there from tokens 5, 12 and 8 (4 + 1 + 5); ore from 3, 5 and 9 (2 + 4 + 4). Equal totals, different reliability: ore pays on three numbers, brick leans on a nearly dead 12.
• Access. The totals are board-wide. They do not say which intersections reach those hexes; the numbered start markers rank pips, not access to one resource.
• Harbors. No chip and no scoring term reads the ports. A 2:1 harbor on a resource you control changes its effective value, and that is invisible in the totals.
• The robber. The totals assume every token is active. A robber on a 6 removes its 5 pips until it moves.

The odds behind the dots are on the dice probability chart, the rule list that shapes these boards is on balanced board rules, and the 0–100 score is explained in the scoring method.

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