## MM2: How many bounce lands is too many?

May 30, 2015 1 Comment

A lot of good players like to play as many bounce lands as they can get their hands on, but doing so also increases the risk of having to mulligan hands where your only lands are bounce lands. It may seem unlikely, but it happened to me thrice in my first 8 matches of Modern Masters 2015. (I had 3-4 bounce lands in each of those decks.) Was I just unlucky? Let’s try to quantify the risk.

An 8-person draft has about 1 copy of any given uncommon on average and there are 10 bounce lands, all at uncommon, so the typical draft will have about 10 bounce lands. This is only about 1.25 per player, but for our analysis we’ll consider decks with up to 10 bounce lands. We’ll also assume 40-card decks with 17-18 lands and where each bounceland replaces about 1.5 lands. I’m also going to ignore the case where you only have 1 bounceland and no other lands, since you wouldn’t usually keep a hand with only 1 land in most Limited games, but the risk of this does increase slightly since you’re running fewer lands in the deck.

# bounce lands |
# other lands |
P(2+ bounce lands & no other lands |

2 | 15 | 0.07% |

2 | 14 | 0.09% |

3 | 14 | 0.26% |

3 | 13 | 0.35% |

3 | 12 | 0.47% |

4 | 12 | 0.85% |

4 | 11 | 1.12% |

5 | 11 | 1.71% |

5 | 10 | 2.23% |

5 | 9 | 2.88% |

6 | 9 | 3.93% |

6 | 8 | 5.03% |

7 | 8 | 6.41% |

7 | 7 | 8.13% |

7 | 6 | 10.24% |

8 | 6 | 12.43% |

8 | 5 | 15.53% |

9 | 5 | 18.16% |

9 | 4 | 22.55% |

9 | 3 | 27.81% |

10 | 3 | 31.60% |

10 | 2 | 38.74% |

With 3 bounce lands and 14 other lands, the probability of all the lands you draw being bounce lands is only 0.26%, and with 4 bounce lands and 12 other lands, the probability only goes up to 0.85%, so the risk isn’t as high as it seemed from my small sample size. As long as you have fewer than 6 bounce lands, the probability is less than 3%, which is well worth the virtual card advantage of drawing a bounce land, and the greater density of spells in your deck. The risk involved with running 6+ bounce lands might still be worthwhile if you compare it to the lowered probability of getting stuck at 2-3 mana sources, the increased mana you have available for multikicker/X spells, and the ease of splashing cards from other colors and maximizing sunburst cards. But it’s always better to enter such situations with a good understanding the risks involved.

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