BrettSpiel is a blog about board game design, written by game designer Brett J. Gilbert.

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One Balm For Many Fevers Found

My recent exercise in picking over all of my game designs has been paying dividends, since it has spurred me on to revisit a couple of old designs and take a critical and creative look at them.

One of these is Amongst Thieves, which in its original incarnation has several failings. Although I originally billed it as a game that supports 2–6 players, it is inescapably weak for only 2. Adding to this flaw was the way in which I had scaled the deck to fit the higher number of players. The deck split was into several ‘core’ suits, plus one smaller ‘special’ suit, and with more players more of the suits were used. But it was impossible to do this and create a deck that would always contain the correct multiple of cards, and the solution meant a fiddly removal of cards when playing with 5 players.

This part of the game was always inelegant and annoying; a part of the puzzle of designing the game that I had never properly solved.

Strokes beard

So, I had an idea. What about throwing out the requirement for supporting 2 players altogether and, at the same time, raising the upper limit to 7 players? The core of the game worked incrementally better with more players, and stretching the game to 7 certainly wasn’t going to break it.

The original deck had four core suits (each 18 cards) plus the smaller special suit (6 cards). With 2 players, two core suits plus the special suit were used, making 42 cards. With 3 or 4 players the game deck added another core suit, making 60 cards. Each player plays one card per round, so these numbers yields a neat 21 rounds for 2 players, 20 rounds for 3 players, and 15 rounds for 4 players.

You have probably noticed that 60 cards is actually a nice round number for 5 and 6 players aswell — indeed, 60 is the smallest ‘lowest common multiple’ (LCM) of 3, 4, 5 and 6 — so you are perhaps wondering what the problem was? I’d say that the problem was this: with 5 or 6 players the number of rounds would be reduced to 12 and 10 respectively, and that’s just a little too few to be interesting. That’s what the extra suit was for in the first place. But the next smallest LCM is 90, and that’s too many! (And would have necessitated a fourth suit of 30 cards.)

So, in my original game the fourth suit of 18 cards created a complete deck of 78 cards, which was fine for 6 players (13 rounds) but required an ugly 3 cards to be removed to make things square for 5 players (75 cards, 15 rounds).

Different problem…

Once I had decided to drop 2-player support and include 7 players an entirely different set of limitations presented themselves, and I began to realise that I might be able do something much smarter, although it took me a while to get there (a process not helped when I spent several hours labouring under the false impression that 7 × 12 was actually 94).

My inspiration sprung from looking again at that difference of just 3 cards between the 5- and 6-player decks (75 vs. 78 cards). I deliberately wanted to keep the new deck made up of, at all times and for all player numbers, complete suits. And there was also the need to keep the special suit, whatever its eventual size, part of the deck for all player numbers, so I couldn’t use that suit as a prop to support the switch from 75 to 78 cards.

The only possible solution, then, was to throw away another assumption about the solution, and create a deck with unequal core suits. They still need to be roughly the same size, but there is nothing in the game that demands that they are exactly the same. Combine this new approach with the obvious requirement for a fifth core suit to raise the complete deck size to support 7 players, and all the parameters of a new solution are in place.

…different solution

It’s worth stating that there is nothing in the definition of these parameters that means an acceptable solution is even possible. After all, there is essentially a set of simple but incompletely defined simultaneous equations at the heart of the problem, and exactly what constitutes an ‘acceptable’ solution is entirely in the eye of the beholder.

However, at length — and only after realising that 91 rather than 94 was a multiple of 7! — a suitably acceptable set of numbers dropped out, and here they are:

A: 17 B: 17 C: 16 D: 15 E: 13 X: 13

A, B, C, D & E are the core suits. X is the special suit. The two 17-cards suits (A & B) plus the special one (X) are part of the deck for all player numbers:

3 players: A B E X = 17 + 17 + 13 + 13 = 60 (20 rounds)
4 players: A B E X = 17 + 17 + 13 + 13 = 60 (15 rounds)
5 players: A B D E X = 17 + 17 + 15 + 13 + 13 = 75 (15 rounds)
6 players: A B C D X = 17 + 17 + 16 + 15 + 13 = 78 (13 rounds)
7 players: A B C D E X = 17 + 17 + 16 + 15 + 13 + 13 = 91 (13 rounds)

These numbers are, however, not the only possible solution. Since the A, B and X suits appear in all decks, the split of cards between them can be altered arbitrarily. It certainly makes sense to keep A and B equal in size, but they could both be 18 cards and X only 11 cards and the sums would still all work. Similarly I could drop A and B to 16 cards each (raising X to 15 cards) and better equalise the size of the five core suits, but the function of the special suit militates against this. I don’t want the proportion of cards in the special suit to begin to swamp the core suit cards with the smaller player numbers.

In conclusion

So there you have it: a rather long-winded explanation of a small problem and the even smaller victory of discovering its solution. But this is the game designer’s lot, and setting myself arcane puzzles that only I can solve (principally because I am the only one interested in solving them!) is part of the true joy of the design process. But it is a curious form of creativity, since one must visit the destination first — or at least get close enough to take a good look! — before returning to the beginning and deliberately choosing to go the long way round, as if reaching the destination without taking the most labyrinthine and intricately mapped of routes would be an abject and dishonourable failure.

And so to other designers embarked on similar journeys I say: Happy trails!

P.S. The post title, by the way, is taken from a poem called ‘An Epitaph’ by English poet A.E. Housman who, it must be said, was never the most cheerful of lyricists.

Stay, if you list, O passer by the way;
Yet night approaches; better not to stay.
 I never sigh, nor flush, nor knit the brow,
 Nor grieve to think how ill God made me, now.
Here, with one balm for many fevers found,
Whole of an ancient evil, I sleep sound.

A.E. Housman

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