CCDD 030211 — Predictable Bear & Bimalicent Demon

Cool Card Design of the Day
Every day, I design a new card and discuss it briefly. Sometimes I will examine new possibilities for colors or mechanics, sometimes I'll re-examine existing executions and sometimes I'll just design something I think is neat.

3/02/2011 - A twitter conversation yesterday between Monty Ashley and Matt Tabak (who are both great follows for you Twitterers) began with an explanation of why you can run unlimited Relentless Rats in Commander (because the Rats ability overrides the deck-building limitation and not the other way around). That led Monty to propose the wacky ability, "For deckbuilding purposes, this card counts as two cards." I pointed out that Mishra's Bauble is basically already that card, but there are functional differences which led to the question, "If a card said, 'this counts as X cards' how big would X have to be?" The answer is two.*

The reason is actually pretty simple. From a design perspective the answer has to be 2, 4 or 10 because those are the most poetic numbers. 2 because its double, 4 because that's a normal playset or 10 for the same reason humans are drawn to decimal-based systems. For development purposes, 4 is too large and 10 is monumentally crazy. The answer must therefore be 2.*

As you can see, "counts as two cards" got my gears spinning wondering how that would work in other various situations. This interpretation is rather whole-hog and, as such, could not be keyworded or even appear on more than a cycle of rares, at best. Focusing on the original principal of the idea—a card that allows you to run a smaller deck—I came up with this much simpler execution:

Note that it's extremely unlikely anything along these lines would ever be printed because there are serious implementation problems. For example, we don't want players to have to ask a judge to check their opponent's deck every time they notice their deck is shy of 60 cards and we certainly don't want cheaters running fewer cards and telling their opponents they're running some number of these. So if these things could never be printed, why discuss them? That's what nerds call fun.

*The question that I answered above was tweaked slightly so you'd interpret it the way I did. The actual question was "If a card JUST said, 'this counts as X cards' how big would X have to be?" I'd read the "just" as simple emphasis, assuming that this new ability would be added to a card you might eventually play, be it a utility creature, a narrow answer spell or even just a land. Turns out, it becomes a particularly interesting thought exercise if you take it the way he meant it, which is literally. The card in question does nothing else. You don't want to actually draw it because you won't be able to play it.

At X=2, the card is awful. Including one gets your constructed deck down to 59 cards and playing a full playset gets it down to 56 cards, but then you have 4 cards in your deck that are literally unplayable. You can alleviate that cost by running a lot of symmetrical discard effects, but it's still not remotely worthwhile: Your chance of drawing one of the four best cards in your deck in your starting hand rises from 39.9 to 42.3% but your chance of drawing a dead card shoots from 0 to 42.3%.

At X=10, you probably only want to play one copy. Doing so increases your chance of drawing one of your four bombs to 45.7% and the chance of drawing your one useless card to 13.7%.

The curious thing about this problem is that the value of including some number of these cards in your deck increases as X grows and decreases as X grows because you become more likely to draw your blank card as you become more likely to draw the good cards in your deck. The truly optimal answer for X depends entirely on how many bombs you're looking to increase the frequency of, how negatively you value a dead card, how well you can control the damage of drawing such a dead card and how worried your deck should be about being milled.

Of course, for players who can build a six card combo, X=54 would let them build a 7-card deck and get that combo every time.

That concludes this post. What follows are some extremely boring probabilities for... uh... who likes probabilities? Just skip this. Really.

X = 1 (the baseline)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 60 -card deck: 11.7 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 60 -card deck: 39.9 %

X = 2 (a single card that counts as two)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 59 -card deck: 11.9 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 59 -card deck: 40.5 %

X = 2 (a playset of cards that count as two each)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 56 -card deck: 12.5 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 56 -card deck: 42.3 %

X = 4 (a single card that counts as four)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 57 -card deck: 12.3 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 57 -card deck: 41.7 %

X = 4 (a playset of cards that counts as four each)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 48 -card deck: 14.6 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 48 -card deck: 48 %

X = 7 (a single card that counts as seven)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 54 -card deck: 13 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 54 -card deck: 43.6 %

X = 7 (a playset of cards that counts as seven each)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 36 -card deck: 19.4 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 36 -card deck: 59.7 %

X = 10 (a single card that counts as ten)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 51 -card deck: 13.7 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 51 -card deck: 45.7 %

X = 10 (a playset of cards that counts as ten each)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 24 -card deck: 29.2 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 24 -card deck: 77.6 %

X = 15 (a single card that counts as fifteen)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 46 -card deck: 15.2 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 46 -card deck: 49.6 %

X = 20 (a single card that counts as twenty)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 41 -card deck: 17.1 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 41 -card deck: 54.2 %

X = 30 (a single card that counts as thirty)

Chance of drawing one of 1 particular card(s) in 7 draw(s) from a 31 -card deck: 22.6 %

Chance of drawing one of 4 particular card(s) in 7 draw(s) from a 31 -card deck: 66.2 %

For what it's worth (not a whole lot), the increase in the chance of drawing one of your 4 best cards finally surpasses the increase in chance of drawing your one useless card around X=26.