Legacy: Rulebook
Legacy is a strategy game for any number of players. In the online version you play alone, but it is a good way to learn the rules. Also, check out this example game after reading the rules to see the game in action.
Game Parts
 Uniquely numbered cards from 1 to 90
 Three journey cards (marked with a star)
 A pencil and a fullsized sheet of paper for each player
Overview
Every player builds a legacy consisting of a garden, an empire and an opus. When a numbered card is drawn, each player adds that number to one element of her legacy. You can take a peek at this example game to see what a completed legacy looks like. To win, be the player with the highest scoring legacy at the end of the game.
Order of Play
 Begin by shuffling the cards to form a 93card, facedown deck. Draw a card; all players use the same card.
 If the card...
 ...is the first or second journey card (a star), then set it to the side and draw another card. All players should be able to see how many journey cards have been drawn.
 ...is a numbered card, then each player should write that number into an element of her legacy. When you are adding the first number to one of your elements, label it with "opus," "empire," or "garden" so it is clear to other players.
 When the third journey card is drawn, the game ends immediately. The player with the highest scoring legacy at the end of the game wins!
Legacy Elements
A player's legacy is made up of one garden, one empire, and one opus; each element has a different structure and a different scoring system. You may leave any of the elements empty and place all your numbers elsewhere. The score of a legacy is the sum of its three element scores.
Opus
A player’s opus is a zigzagging line of numbers that always starts in the “high” position and then alternates to the right between “low” and “high” positions. The opus looks like a score of musical notes.
Any number may be the next number in the opus, but numbers always alternate between "low" and "high" and are always added at the rightmost end of the opus. The example opus below started with 28 in the "high" position, and then 11, 45, and 83 were added by alternating between "low" and "high."
An example opus that started with 28. 
There is always only one place to add new numbers to the opus. 
What matters in the opus is the 1’s digit of the numbers you play in it. You want numbers that have a high 1’s digit in the “high” position (e.g. 39, 28, 9) and numbers with a low 1’s digit in the “low” position (e.g. 10, 51, 2).
An opus scores the sum of the 1's digits in "high" position minus the sum of the 1's digits in "low" position.
The example opus below scores (8+5+7)  (1+3) = 20  4 = 16.
This example opus scores 16. 
(81) + (53) + (7) = 7+2+7 = 16.
Garden
A player’s garden looks like a tree; any number may be the bottom number, which is called the trunk. Every branch of the tree must have a smaller number branching from a larger one, just like the branches of a real tree get thinner the further they are from the trunk.
Add a new number to the garden only if it is smaller than a number already in the garden you want to branch from. The following garden started with trunk 56, then smaller numbers 18 and and 39 were added branching above 56. Circle a number when it has the maximum of two numbers branching above it, like 56 and 39 in this example.
An example garden that started with root 56. 
Suppose the next card drawn is 17 and you decide to use it in your garden. Here are all the possible positions to add 17 to the example garden:
A new number in the garden has to branch above a larger number. 
A garden scores (5 × L) + H, where L is the number of leaves and H is the maximum height of any leaf.
A leaf is any number that has no numbers branching above it.
The height of a leaf is the length of a path from the root to that leaf.
The garden below scores (5×3) + 4 = 19.
This example garden scores 19. 
There are 3 leaves (17, 22, and 14 have no numbers branching above) and the maximum height is 4, because the path to leaf 14 is four numbers (56393614).
Empire
A player's empire is a connected grid of numbers. The objective of the empire is to connect numbers and form a rectangular perimeter, like building a wall.
When you add a number to your empire, every number after the first is placed adjacent (either horizontally or vertically) to a number already in the empire. Adjacent numbers must alternate between even and odd values. Here is an example empire:
An example empire; adjacent numbers have to alternate between even and odd. 
17 is odd, so it can be added adjacent to any even numbers. 
Choose any one rectangle; the empire scores (M × N) + C1+C2+C3+C4, where M and N are the dimensions of the rectangle, and each Ci is the 10's digit of a corner of that rectangle.
When a number serves as more than one corner, its contribution is only counted once.
You may choose any complete rectangle in your empire, because sometimes a slightly smaller rectangle will score higher if it has better corners.
You may choose any complete rectangle in your empire, because sometimes a slightly smaller rectangle will score higher if it has better corners.
Here are several example empires and their scores:
This empire scores 23. 
Numbers 19 have 10's digit equal to 0. So the four corners 17, 80, 6 and 21 have corner contributions C1=1, C2=8, C3=0, and C4=2.
Therefore the score of this empire is (4 × 3) + 1+8+0+2 = 12 + 11 = 23.
This empire scores 13. 
So the score of this empire is (4 × 1)+1+8 = 13.
This empire scores 8. 
Finally, this empire is 1by1 and scores (1 × 1) + 7 = 8.
Check out a complete example game here.
What does "largest rectangle" mean for the empire? Is it the rectangle with the largest area (L x W)? Largest perimeter (L+W)? Something else?
ReplyDeleteWhat if there is more than one largest rectangle for the empire? Do you choose the one with the vertexes whose values total the highest? For example, my empire has a 90 with a 11 to the right of it and a 7 below it. There's a 1x2 rectangle with 90 and 7 as its corners, and a 2x1 rectangle with 90 and 11 as its corners. Do I get to choose the latter, as it's worth 1x2+9+1=12? (Note that a 1x3 rectangle with the 90 in the middle is worth a mere 1x3+0+1=4.)
You are exactly right, you can choose the rectangle that maximizes your empire score. So if your empire was:
Delete90  11

7
A 90 with an 11 to the right and a 7 below, then yes you want the 1by2 rectangle with 90 and 11. Your last comment about a 1by3 would be true if the three numbers were arranged in a line like 79011. In that case choosing a smaller rectangle with better corners (9011) scores better.
Which points out some empire strategy: you can of course go for a really large empire, but a small empire with great corners gets you a decent score for a low risk. However, a very large squareish empire is the best scorepernumberplayed you can achieve among all the legacy elements!
One more question.
ReplyDeleteWhere is the online version alluded to in the first paragraph? I can't find it.
This site isn't "live" in the sense that I am not actively promoting yet, and I haven't finished the online version of Legacy I'm developing. In fact, this rule page has some polish coming, too. So please check back when I post the online version!
DeleteSorry to spam this post with comments, but I found another thing!
ReplyDeleteThe link in the first paragraph doesn't lead to the sample game, but to the URL "check out complete example game here". The links in the last paragraph and at the top of the page work fine.
Great catch, fixed! Thank you
ReplyDeleteMangled sentence: "The objective of the empire is to connect is to connect numbers and form a rectangular perimeter, like building a wall."
ReplyDeleteThanks, fixed it.
Delete