Analyzing the Mirror Deck for Game Design



It's been a few years since I created the Mirror Deck and posted it on DriveThruCards. As a reminder, it's a deck of cards numbered 1 through 99, where each number can have its digits transposed, so the deck is only 54 cards. I asked some advice from other game designers recently on where to take the deck next. James Ernest was especially helpful, recommending that I look for any rarities or natural "sets" in the deck that would lend themselves to game mechanisms. 

I'm looking at how I can make a two-player trick-taking game out of the Mirror Deck.


Triangular Numbers

There are 13 triangular numbers in the deck's range, which I could mark with a triangle "suit" icon.

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91


Perfect Squares

There are 9 numbers in the deck's range, which I could mark with a square "suit" icon. 

1, 4, 9, 16, 25, 36, 49, 64, 81


Primes

There are 25 prime numbers in the deck's range, which I could mark with a "P" icon as its own suit.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97


Differences

The main hook of the Mirror Deck is how you can treat each card as a higher or lower value. It would be useful to know the maximum difference of any two inverted numbers. 

  • Difference: 0 (9 Cards): 11|11, 22|22, 33|33, 44|44, 55|55, 66|66, 77|77, 88|88, 99|99
  • Difference: 9 (9 Cards): 21|12, 32|23, 43|34, 54|45, 65|56, 76|67, 87|78, 98|89, 10|1
  • Difference: 18 (8 Cards): 31|13, 42|24, 53|35, 64|46, 75|57, 86|68, 97|79, 20|2
  • Difference: 27 (7 Cards): 41|14, 52|25, 63|36, 74|47, 85|58, 96|69, 30|3
  • Difference: 36 (6 Cards): 51|15, 62|26, 73|37, 84|48, 95|59, 40|4
  • Difference: 45 (5 Cards): 61|16, 72|27, 83|38, 94|49, 50|5
  • Difference: 54 (4 Cards): 71|17, 82|28, 93|39, 60|6
  • Difference: 63 (3 Cards): 81|18, 92|29, 70|7
  • Difference: 72 (2 Cards): 91|19, 80|8
  • Difference: 81 (1 Card): 90|9

I can use a dice face symbol to note the number of cards in each of those suits, for example the Difference:36 cards would have a ⚅ symbol because there are six cards in that set.


Multiples of 11

One thing I noticed from the beginning is that a multiple of 11 has the least flexibility in the whole deck, since it cannot create a new number by transposing its digits. In most game designs, I'd probably set this set aside with some special rules. For example...

  • A dummy leader in a two-player trick-taking game: Shuffle up the 11s into their own deck. Reveal a new card at the start of a trick. This is the lead card. 
  • Stakes of a round: The game is divided into 9 rounds, each worth progressively more points. The first round is worth 11, the second worth 22, and so on. The winner of a round takes the card into their score pile. 
  • Trump Cards: I could just say that these nine cards "beat" any other card in a trick. A trump card can only be beaten by another trump card of higher value. So 11 beats any normal trick, but 22 beats that, and 33 beats that, and so on.

I think I'll go with the last option since it keeps things flexible.


In a future post, I'll write up the rules to a trick-taking game using the Mirror Deck. Stay tuned!

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