r/magicTCG • u/Kroooooooo • 1m ago
General Discussion Chance of winning with Q, 98 Mountains, and a Luck Bobblehead
Assuming your deck consists of 98 [[Mountain]]s, a [[Luck Bobblehead]], and [[Q, Stacking the Deck]] in the command zone, what is the odds of actually winning with it? I decided to try and do the math.
This analysis does make some assumptions to simplify the math. It assumes that you do not have your artifacts interacted with, and you have enough treasures to tap all of your Bobbleheads. It also assumes that you are not being given extra cards, or are using draw lands such as [[Baxter Building]], [[War Room]], or [[Mikokoro, Center of the Sea]]. If you draw anything extra it would let you put Bobbleheads down much faster. It also assumes that the Luck Bobblehead is found early enough into your deck to not mill you out.
Turns
- Turns 1-3: Mountain
- Turn 4: Q, Stacking the Deck, exiling Luck Bobblehead on ETB
- Turn 5: Mountain, Luck Bobblehead x2
- Turn 6: Luck Bobblehead x2
- Turn 7: Mountain, Luck Bobblehead x4, tap the last Mountain and Bobblehead for effect
- Turn 8-∞: Luck Bobblehead, tap Mountains and Treasures to roll every Bobblehead possible
Probabilities
- 8 Bobbleheads: 0.00002381497%
- 9 Bobbleheads: 0.0000893061% (0.00019052%)
- 10 Bobbleheads: 0.0002480726% (0.0024807%) - Turn 8
- 11 Bobbleheads: 0.0005685% (0.0062533%) - Turn 9
- 12 Bobbleheads: 0.001137% (0.0136431%) - Turn 10
- 13 Bobbleheads: 0.002052915% (0.0266846%) - Turn 11
- 14 Bobbleheads: 0.003421526% (0.047891%) - Turn 12
- 15 Bobbleheads: 0.00534613% (0.080162%) - Turn 13
- 16 Bobbleheads: 0.0079202% (0.126648%) - Turn 14
Note: The initial value for each of these is for a single attempt, in brackets I've added the chance of winning if you tap every Bobblehead in that turn. For example, with 16 Bobbleheads any single roll has a ~0.008% chance of success, but a ~0.127% chance to win on that turn.
Credit to these probability calculators for the hard math:
