Magic: the Puzzling – Ravnica Answers

Posted in Feature on November 23, 2005

By Jeff Till

Time for the answers to Monday's puzzles.

Round 1, Game 3:

Round 2, Game 3:

Round 3, Game 2:

Round 4, Game 2:

Round 4, Game 3:

You have several ways of winning this game, but they are all in your deck. You can draw a single card with Terrarion, since Pithing Needle will not stop mana abilities. Your outs include:

You can manipulate your library to change the odds of drawing certain cards. Your options include:

  1. Sacrifice the Terrarion immediately.
  2. Transmute Dizzy Spell into Unholy Strength to shuffle your library, then sacrifice the Terrarion.
  3. Play Glimpse, transmute Dizzy Spell, sacrifice Terrarion.

Playing Glimpse without later randomizing your deck does not affect your odds. So which option is best?

  1. If you just sacrifice the Terrarion, you have no chance of drawing the Guildmage or Spawnbroker, since they are near the bottom of your library. This leaves you Muddle the Mixture, Dimir Infiltrator, Drift of Phantasms, Hex, or Gifts Ungiven. The probability of drawing each of these is 1/24. You also have a 1/24 chance of drawing Twisted Justice, in which case you can win if Drift of Phantasms is among the next four cards. The probability of that happening is 4/23, making the total probability of winning (1/24 * 5) + (1/24 * 4/23) = 119/552 ~ 21.6%.

  2. If you transmute Dizzy Spell and then sacrifice the Terrarion, you have 27 random cards in your library. Since you have 9 mana remaining, you can win with Golgari Guildmage, Spawnbroker, Hex, or Drift of Phantasms. The probability of drawing each of these is 1/27. In addition, if you draw Twisted Justice, you can win if Spawnbroker is among the next four cards, which has a probability of 4/26. Hence, the total probability of winning is (1/27 * 4) + (1/27 * 4/26) ~ 15.4%.

  3. If you play Glimpse the Unthinkable, you mill yourself for 10. The probability that you will mill the 2 remaining 1-mana spells in your library is 10/24 * 9/23 = 15/92. Therefore, when you transmute Dizzy Spell, you have a 15/92 chance to be left with an 18-card library, and a 77/92 chance to be left with a 17-card library. You will have seven mana remaining, so you will still win if you draw Guildmage, Spawnbroker, Hex, or Drift. Since the Guildmage and Spawnbroker are definitely still in your library, the probability of drawing each is (1/18 * 15/92) + (1/17 * 77/92) = 547/9384. Hex and Drift may be in your library or may be in the 10 cards that were milled, so the probability of drawing each is (1/28 * 15/92) + (1/27 * 77/92) = 2561/69552. The total probability of winning is therefore (2 * 547/9384) + (2 * 2561/69552) = 112459/591192 ~ 19.0%.

Your best option is therefore just to sacrifice the Terrarion right away. (I'd like to thank goblinrecruiter for pointing out a couple options I missed.)

Unfortunately, the odds were against you and you failed to draw either Hex or the Golgari Guildmage, and you lost the final game. That just reinforced the fact that Magic is both a game of skill and chance.

Bonus Puzzle:

Below is an image of something I've been constructing for quite some time now. I add one new card to the matrix each day. Can anyone figure out what it is? Feel free to post guesses in the forums.

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