What are the odds of being dealt a mulligan?

It's happened to all of us, and it makes us mentally say "ouch!" (or something
stronger):  You pick up your initial seven cards, and there's not a basic
pokemon in the bunch.  So now your opponent gets to draw two additional cards,
and you will have to struggle to catch up.  Of course the odds of being dealt
a "mulligan", with no basic pokemon in your seven cards, depends on how many
basic pokemon you included in your deck.  These are the actual odds:
                          Odds
8 basic pokemon in deck:  .35      Approximately 1 in 3 chance for mulligan
9 basic pokemon in deck:  .30
10 basic pokemon in deck: .26      Approximately 1 in 4 chance for mulligan
11 basic pokemon in deck: .22
12 basic pokemon in deck: .19      Approximately 1 in 5 chance for mulligan
13 basic pokemon in deck: .16
14 basic pokemon in deck: .14
15 basic pokemon in deck: .12      Approximately 1 in 8 chance for mulligan
16 basic pokemon in deck: .10      Approximately 1 in 10 chance for mulligan
17 basic pokemon in deck: .08
18 basic pokemon in deck: .07      Approximately 1 in 15 chance for mulligan
19 basic pokemon in deck: .06
20 basic pokemon in deck: .05      Approximately 1 in 20 chance for mulligan

When building your 60-card deck, there are many factors to consider, and
"mulligan odds" is one of those factors.  You may think your ideal deck has
only eight basic pokemon, but do you really want to give your opponent two
extra cards every third game?

Bruce Long
bruce@asu.edu