Thursday, November 3, 2011

Fun with numbers

So I was laying in bed last night, trying to drift off to sleep and being unable to do so, so I started thinking about numbers.  In my last post, I discussed that the current version of the game had 120 cards in it, not including the Awakened or the starting Aether Surges that players will start with.  On the surface, and up until this point, it seems to have been a fairly good number for the game, but when I began to think about the future possibilities for Affinity, I have been less than happy with it.

Currently there are 36 unique cards in the game that are replicated in different amounts to make a 120 card main deck.  This deck consists of Spells and Creatures.  I have been doing some brainstorming about adding a third card type to the game, and thinking about how that would increase the size of the deck.  In addition to this, I can't predict if the game is going to be a success or not (although of course I hope it will be) so in thinking about how this hobby works and the fact that I should want to produce expansions for it, how that would also inflate the deck.

This is an issue that was encountered quite quickly in the game of Ascension.  The initial game started out with a 100 card center deck.  The first expansion added 65 new cards to this deck.  The third "expansion" is considered a stand-alone game that is not necessarily supposed to be added to the old deck (already at 165 cards) because it has 100 new cards that could potentially be added to the center deck.  265 cards is a lot to shuffle, and the amount of randomness in a game where you usually see 50-60 cards of the deck in a given game would just be too much.

So thinking about this potential problem for Affinity, since there is also a "center deck" mechanic at play, I thought about how quickly the deck would increase in size for the smallest expansion possible.  This isn't to say that I couldn't break away from the numbers that I'm about to lay out, but this is how I currently see it.

There are 120 cards in the main deck, 36 unique cards.  These cards are broken into 4 factions.  Each faction has 6 creatures and 3 spells, each of them having a number of copies in the deck based on a "rarity" system of common, uncommon and rare.  There are 5 copies of each common, 3 copies of each uncommon, and 2 copies of each rare.  This is aesthetically pleasing because it makes 30 cards for each faction, and 120 cards in the main deck.  Some nice round numbers.  Now if you assume that whenever I add cards to the deck in the manner for an expansion, I have to add an equal number of cards for each faction, and then keep the distribution of commons/uncommons/rares in the game the same for balance purposes, whenever I'm adding cards to the deck, I have to add 10 cards for each faction, or a minimum expansion size of 40 cards.  This means the first expansion would take the game to 160 cards, the second to 200, etc.

Something about this just doesn't seem acceptable to me.  Shuffling 200+ cards is not really a fun activity for anyone involved.  Not to mention, if I wanted to add a card type into the mix, I could potentially be making the base game at 160 cards before adding any expansion to the game.  Again, not what I would ideally like to be doing.

In thinking what I could do to lower the number of cards in the main deck, but keep the variety, I started with the idea of just lowering the number of copies for each card at the common/uncommon/rare levels.  There isn't a ton of room to go down with here since for a rarity system to be true to itself, you need more uncommons than rares and more commons than uncommons.  With a current 5/3/2 split, the available options are 4/3/2, 5/2/1, 4/2/1, and 3/2/1.  I had played with a 4/3/2 split in the past, and the uncommons felt just like commons and the rares didn't feel that rare.  I think a 5/2/1 split makes the commons too common, and 3/2/1 has the same problem as a 4/3/2 split, so I've decided to start playing with a 4/2/1 split.  It removes the 2nd highest amount of cards from the main deck while keeping the idea of a rarity system that I wanted.

Before deciding on this, I had to take a look at what this would do for the odds of drawing each rarity in 4/2/1 vs. 5/3/2.

4/2/1 Base Set

  • Common 4/84 or 1/21 (4.7%)
  • Uncommon 2/84 or 1/42 (2.3%)
  • Rare 1/84 (1.1%)

5/3/2 Base Set

  • Common 5/120 or 1/24 (4.2%)
  • Uncommon 3/120 or 1/40 (2.5%)
  • Rare 2/120 or 1/60 (1.7%)

4/2/1 One Expansion

  • Common 4/112 or 1/28 (3.5%)
  • Uncommon 2/112 or 1/56 (1.8%)
  • Rare 1/112 (0.9%)

5/3/2 One Expansion

  • Common 5/160 or 1/32 (3.1%)
  • Uncommon 3/160 or 1/53 (1.9%)
  • Rare 2/160 or 1/80 (1.3%)

4/2/1 Two Expansions

  • Common 4/140 or 1/35 (2.9%)
  • Uncommon 2/140 or 1/70 (1.4%)
  • Rare 1/140 (0.7%)

5/3/2 Two Expansions

  • Common 5/200 or 1/40 (2.5%)
  • Uncommon 3/200 or 1/67 (1.5%)
  • Rare 2/200 or 1/100 (1%)

I found it interesting that the commons become slightly more common and the uncommon/rares become slightly less so with a distribution of 4/2/1 over 5/3/2.  I think I can also do some interesting things when you have only one copy of a rare card vs. two without having to worry about what happens when you have two copies of the card in a 20 card deck vs. just one.  In addition, I think it will work out better for potential promotional cards (such as the ones that I'm likely to include when I Kickstart the project) since there will be much less of an impact on distribution in the deck if you add in 4 single copies of cards (assuming 1 for each region) vs. 2 of each.

Playtesting will determine if I'm correct on this theory or not, but looking at it on paper I think I will be quite happy with the change.

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