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Lookin' at that Engine

This blog strips down a game and analyzes what makes it go. Trappings like theme are ignored. Instead one picks apart what players do in the game to win and how they try to do it.

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Jumpin' right into the fray: Cartagena

Moshe Callen
Israel
Jerusalem
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ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ/ πλάγχθη, ἐπεὶ Τροίης ἱερὸν πτολίεθρον ἔπερσεν./...
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μῆνιν ἄειδε θεὰ Πηληϊάδεω Ἀχιλῆος/ οὐλομένην, ἣ μυρί᾽ Ἀχαιοῖς ἄλγε᾽ ἔθηκε,/...
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1. A word about this blog...

Playing a game is about having fun, but for everyone to have fun then everybody playing needs do the best that person can to win within the rules. While the goal is the striving for victory more than victory itself, that striving makes the game. I utterly reject the ideas that games are about social interaction or about immersing oneself in an experience. I want to ruthlessly crush my opponents and have them try to do the same to me-- all in good fun.

One should be asking at this point what the goal of the analysis is. In short, I want ot understand what makes good games and how I can tell if I'm dealing with a good game or not. To that end, I'm looking at the engine, kicking the tires and checking the fluids and the cables.

So in this blog I intent to pick a game and analyze what makes it go. That the game does work is a given; in that sense, this is not a review. The first victim game to pick apart in this way is a simple one but a good one: Cartagena.

2. The goal

I'm starting out with a game which is relatively simple to analyze. More complicated games will follow, although of course some games will be more complex and some less. Cartagena is a race game. Each of five players (represented by a color of meeple)
must get all six of his meeples (shown for red)
onto the path and out the other side before anyone else does.

The game has one path to victory and that's why I chose it to start with. Everybody is trying to do the same thing-- move the meeples through. This kind of symmetry represents the simplest way to achieve balance in the game, and it works well given enough player interaction to mitigate any player order advantages.

The only way for a draw to happen is if all players let themselves get stuck by running completely out of cards (which allow one to move) but since one can always create a situation so that one gets at least one card, this should not be a problem. In other words, a draw in this game might theoretically be possible, but the players would virtually have to be trying to strand themselves.

2. The cards

The cards represent the symbols on the board. Each symbol appears on 17 cards for a total of 103 cards.
Players start with the same number of cards as the number of symbols. Thereafter players spend one card to move a meeple forward to the next position where that symbol occurs which is not occupied by three meeples already, but cards can only be gained by sending a meeple backwards along the track to the next occupied position. In the latter case three meeples on a symbol act as a block so that one may gain only either one or two cards at a time.

Whether one plays with the cards to be drawn open or concealed makes negligible difference because the cards must be drawn in the same order. Thus having them open might occasionally induce a person to take more cards when that person might not otherwise and it lets other players have a fair idea of one's hand but does not otherwise have an appreciable effect on play.

Players get three actions per turn. In each action one can either move one meeple along the path by spending a card or spend a meeple back to replenish the supply of cards. Hypothetically one can imagine a player's pieces are all between groups of three so that nowhere can the player move backwards to get move cards. Then by moving two meeples forward, the player can remedy that situation, and he finally gets a card using the third action. So three actions seems like the minimum number of actions on a turn needed so that systematically stranding other players is not a viable strategy.

Therefore we have cards to go forward and going backwards to get move cards. Three actions should guarantee no player will be entirely out of the race with a minimum of foresight, and the odd number of actions simultaneously establishes that the net motion along the board is forward.

3. The board

That path consists of six identically shaped pieces (each the same on both sides) displaying one each of six distinct symbols.
The ordering of the symbols is such that each symbols occurs once only in the first, second,..., sixth place when the pieces are taken altogether. In other words, the symbols appear in the six distinct permutations where each symbol appears once in each of the six possible slots. While there is a boat
at the end, it serves no necessary function except perhaps to mark the direction pieces need to go.

So board is topologically linear and primarily (albeit not totally) unidirectional. The pieces of the board can be arranged as permutations (±1,±2,±3,±4,±5,±6) where the numbers represent the position of a given but arbitrarily chosen symbol and the opposite sign on a number represents flipping that piece. Without writing anything down and doing the math casually in my head, I believe this leads to 42 possible orderings of the symbols on the board.

The only positional advantage lies in being closer to the end goal-- going off the board. While the distribution of symbols is not uniform, it is even in the sense of being symmetric across all six symbols.

4. Moving and blocking

So far, discussion has largely focused on the actions of individual players independently of the effect on other players. Inter-player interaction in the game comes indirectly.

The primary mechanism of such interaction comes via blocking players' ability to replenish cards. Of course to do so one creates a block of three meeples on a symbol which also enables meeples going toward the occupied symbol to go farther and skip to the next such symbol.

This gives a major pro and an equally major con to such blocks. One might help an opponent more than hurt him. Of course one can and also should use groups of three to speed oneself along.

The juxtaposition of the two elements in this regard seems not as direct but it works for balance in the sense that both the pros and the cons of blocking or not apply equally to the player himself as to his opponents.

5. Nature of the balance

The balance mechanisms thus are not complicated. The same opportunities are open to everyone. Cards move one forward but getting cards moves one backwards. Blocking can hurt but can also help. The first player has the advantage of player order since this game is a race but the later players are more likely to be able to use groups of three to speed along right from the beginning.

At the same time, the game has no extraneous elements. All the actions a player can take serve toward the victory condition with arbitrary constraints. So the mechanisms of the game are sleek and clean and simple with good natural balance.

6. Degree of player control

The only element of the game over which a player does not have control (apart from the actions of other players) lies in the specific cards a player receives. Even when a player can see which cards are to be drawn next, the cards must be drawn in the same order.

Mitigating this is the fact that no cards are bad, just more or less useful to a specific player, and so the randomness of the draw is in and of itself the counterpoint to taking cards.

7. General remarks

This blog is not about reviewing the game except in the sense of assessing it in the manner of an abstract. Cartagena s pretty straightforward and works well because basically it is an abstract. Yet it serves well to generate an archetype of such analyses. Games whose analysis will be more complicated ought follow.
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Fri Sep 23, 2011 2:58 pm
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