GP Toronto: the follow up

In my previous post, I talked about how I got this hand in round 9 and was unsure whether to mulligan or not:

As suggested by Ryan Bogner, I took my decklist and generated 100 sample 6-card hands to see, on average, if what I would be mulliganing into would be better or worse than this hand. I went through each hand and decided if I would keep or mulligan, and then of the hands I would keep, I marked them as either better or worse than the original 7 (or they were inconclusive).



Here's a spreadsheet of my results, with my annotations. Feel free to play along at home and see how many of my assessments you agree or disagree with.

https://drive.google.com/file/d/0B--nsefwqmCzVTB2MVlWbU91Z00/edit?usp=sharing

I've summarized the results. Out of 100 hands:

18 hands I would mulligan.

5 hands, I'm not sure if I would mulligan or not. These hands are generally of the type where you might have one early play, but need multiple good draws to pull out of it. They are almost certainly worse than the 7 card hand.

77 hands I would keep. Of those 77:

14 hands are definitely better than this 7 card hand.
36 hands are definitely worse.
27 hands are unclear as to whether or not they're worse than the 7 card hand. These hands tend to be similar to the 5 I described above, but are firmly good enough to keep.

Additionally, I went through the 77 6 card "keep" hands and looked at how quickly they got started.

35 hands had action on turn 1, 2, or 3.
7 hands had the potential to have action before 3, but need a certain draw to do so (usually a certain color of mana).
35 hands didn't have action until turn 4 or, in some cases, turn 5.

After reviewing the data, I would definitely keep. The most oft-cited reason to mulligan is "not enough early action," and based on this data, taking a mulligan only fixes that problem 35% of the time. The other 65% you aren't improving at all or, in some cases, getting worse. (Of course, hidden in that 65% are the times where you mulligan to 5 and end up with a hand better than your 7, but I'm assuming that happens so infrequently that it is basically negligible.)

I generated the sample hands by writing my decklist into random.org, generating 100 randomized lists of my deck, and taking the top 6 cards of each list.

Thanks to Ryan Bogner for the idea to analyze sample hands, and to Tommy Ashton and Jason Ford for their assistance in analyzing some of the hands.