![]() ![]() In this answer, I consider the question that I believe the asker is most interested in: given optimal mulligan decisions, what is the probability of drawing at least one Bazaar in time to play one on your first turn? This answer accounts for all reasonable mulligan decisions, including scrying, and for the chance of drawing one in your first draw step on the play. Probability to hit with scry: 96.1029072 %įor the curious people, here is a plot how those probabilities converged: Probability of starting with a 0 card hand and Bazar on top (including scry 1): 0.9 % Probability of starting with a 0 card hand: 4.8 % (this means no Bazaar of Baghdad was found) Probability of starting with a 1 card hand: 0.52 % Probability of starting with a 2 card hand: 1.23 % Probability of starting with a 3 card hand: 2.43 % Probability of starting with a 4 card hand: 4.79 % Probability of starting with a 5 card hand: 9.91 % Probability of starting with a 6 card hand: 22.12 % Probability of starting with a 7 card hand: 54.2 % That probability is also included in my end results. So even if I start with zero cards in hand, there is a chance that a Bazaar is in the top 2 cards of my library and (thanks to the scry) can be found within one draw step. In this situation I consider the somewhat new mulligan scry rule, which let's you scry one after mulligan. This continues until I reach the point where I reshuffle a one-card-hand, since it was considered a miss and start the game with a zero-card-hand. reshuffling the deck and drawing one card less). If I miss on both, Bazaar and Powder, than I take a mulligan (e.q. If I draw a Serum Powder, the hand is removed from the game and I draw the exact same number again. If it contains at least 1 Bazaar, the hand is considered a hit. No further assumptions regarding the deck building are required. My assumptions: The deck contains 60 cards, 4 of which are Bazaar of Baghdad and 4 are Serum Powder. I approached this question numerically and drew one billion (1,000,000,000) sample hands. ![]()
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