Tl;DR: You have winning cards. To win, you must be able to play those cards, and have them in your hand. Your hand is randomly drawn. When might you win? How could find the answer to this (very complex) problem?
(I realize that my question isn't very formal, but I'm not exactly sure how to correctly pose the question. Feel free to edit. Also, draw3cards or Boards & Games don't like math questions)
(If you know magic, you should skip the next section, and probably the one after that, too)
- You have a 60-card deck, which has just been shuffled.
- At the beginning of the game, you draw 7 cards. From then on, each turn you draw one card.
- All cards except lands require mana to play. Mana is drawn from your mana pool. A land card on the field can be tapped (used) to add a mana of a color to your mana pool. (Mana either has a color, or is uncolored. Islands for blue mana, Swamps for black).
- Colored mana can always be turned into uncolored mana.
- Each turn, you may put no more than one land from your hand onto the field. It can immediately be tapped for mana.
- You have your Myr. As the decklist shows, you have Silver and Leaden myr, which can be tapped for Blue or Black mana, respectively. They cost two mana each, of any color.
- In the same vein, Alloy Myr grants one mana of any color, and Palladium Myr grants two uncolored mana
- You also have the Myr Galvanizer. For one mana and being tapped, it untaps all other Myr.
- If you have one Galvanizer, and your mana-myr can be tapped for more than one, you can get an extra mana
- If you have two Galvanizers, and your mana-myr can be tapped for more than one, you can have infinite mana
- If you have infinite mana, you can win with Exsanguinate (which requires two black mana - so if you have two Galvanizers and a Palladium Myr, but only one swamp, you can't win with Exsanguinate)
- ...or you could win with Blue Sun's Zenith, which requires 3 blue mana. It can also be useful without infinite mana, since it allows you to draw cards (one card for every mana of any color you pay beyond 3 blue)
- You also have three shapeshifters - Cackling Image (one mana of any color, two blue mana), Cryptoplasm (same), and Evil Twin (two uncolored, one black, one blue). All of these can make a copy of a creature on the field
- You also have Diabolic Tutor, which gives you any card you want for two black mana, two uncolored mana
- The other cards are irrelevant.
Given that you try to get mana-myr on the field first, what chances are there of winning on what turn? I realize that this is a very tricky question that probably involves quite a bit of work, so an explication of how to get an answer is almost as good an answer itself.
Also really useful would be a generalization of this.
For extra points, ideas about finding the optimal number of each card (keeping the irrelevant defensive cards, and no more than 70 cards) would be very appreciated.