Here is the additional analysis you asked about in the podcast:
Probabilities of finding a Bazaar under the Vancouver system:
Bazaars\Powders 0 1 4 1 38.58% 41.45% 51.77% 4 86.50% 88.70% 94.18%
For the London system:
Bazaars\Powders 0 1 4 1 58.04% 62.14% 75.52% 4 97.18% 98.08% 99.57%
Methodology: I assumed you
- keep any hand with at least one Bazaar
- use Serum Powder whenever you draw it and do not have a Bazaar
- under the London system, tuck any extra Serum Powders back in your deck before any use of Serum Powder.
Mathematica source code: https://www.dropbox.com/s/np0y0maooxln4cr/mulligan.nb?dl=0
If I am reading this table correctly, it says that the probability of finding a particular/specific restricted card in your opening hand under the London system and with 4 powders is 75.52%?
I'm assuming that Bazaar is the column, and Powder the row. That's pretty astounding.
But if I am reading that table correctly, it also means that with 0 Powder, you have a 97% chance of finding Bazaar. 1 more powder gets you to 98%. 4 get you to 99.57%. That basically eliminates a game loss a tournament from the mull to oblivion.