I picked up Vintage Dredge, and Vinatge as well, for the first time yesterday for an event where I won a Mox Jet. It was very fun. My friend told me when playing the deck to mulligan to Bazaar of Baghdad, no matter what. He said I was 93% to hit it if I was willing to mulligan to 1. It was pretty good advice. Still, that number sounded haphazard, so I wanted to know it exactly.
I've seen a lot of haphazard claims about the probability of mulliganing to bazaar in a 4 Serum Powder Vintage Dredge deck. Every single proposed answer that I've seen has just made a simulation (many incorrect already) a run it some arbitrary number of times. I've seen answers ranging from 90% to 96%
It's 94.1681291934%, but I wouldn't but stock in the last digit.
The same answer was reached by a simulation running for 10,000,000 iterations, but exactness is good. The exact solution takes a fraction of a second to run, and a large simulation takes much longer.
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The main point for me was knowing when I could complain if I didn't hit Bazaar in game 1 often enough. When you do mulligan to Bazaar, you should not get bazaar approximately every 1/(1-.942) approx = 17 games
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I picked up Vintage Dredge, and Vinatge as well, for the first time yesterday for an event where I won a Mox Jet. It was very fun. My friend told me when playing the deck to mulligan to Bazaar of Baghdad, no matter what. He said I was 93% to hit it if I was willing to mulligan to 1. It was pretty good advice. Still, that number sounded haphazard, so I wanted to know it exactly.
I've seen a lot of haphazard claims about the probability of mulliganing to bazaar in a 4 Serum Powder Vintage Dredge deck. Every single proposed answer that I've seen has just made a simulation (many incorrect already) a run it some arbitrary number of times. I've seen answers ranging from 90% to 96%
The linked program (https://github.com/Dritte/VintageDredge/blob/master/mulliganToBazaar.py) is a combinatorial calculation, not a simulation, of the solution for calculating the exact probability as proposed by a friend, Daniel Kane, PhD.
It's 94.1681291934%, but I wouldn't but stock in the last digit.
The same answer was reached by a simulation running for 10,000,000 iterations, but exactness is good. The exact solution takes a fraction of a second to run, and a large simulation takes much longer.
Department of Electrical Engineering and Computer Science
Department of Electrical Engineering and Computer Science
Department of Electrical Engineering and Computer Science