How Many Basic Pokemon Should a Deck Have?
By ChallengerG (Cord0wainer@hotmail.com)
Before I begin, I should mention that this article is probably being
sent to the wrong place, as it is more suitable to your Featured Articles
section. However, as there is no address given for Featured Articles section, I
am sending it to the TCG Strategies section because it does contain an important
tip on strategy.
I really enjoy the Pokemon TCG. However, I do not enjoy losing
a game without even taking a turn. This was not a likely outcome in the
past.
These days, however, there are several decks, including Ness’s excellent
Super Crazy Sneasel (SCS) deck, that can knock out an opponent’s single Pokemon
in the 1st turn, even if that Pokemon has 80 or 90 hp. (With a full bench,
a darkness energy, and 4 plus powers, a Team Rocket Meowth has greater than 50%
chance of knocking out a 90 hp Pokemon.) For this reason, one should
design decks that do not have very high probability of starting with a single
basic Pokemon. This, of course, leads to the question how many basic
Pokemon should a deck have?
To help answer this question, I calculated the probabilities of
getting 0, 1,...,7 basic Pokemon in a 7-card opening hand, given the number of
basic Pokemon that are in the 60-card deck. The results for up to 20
basics in the deck are shown in the Table below:
Probability
for the number of Basic Pokemon in the opening hand
Basics 0 1 2 3 4 5 6 7
in Deck
1 88.33 11.67 0.00 0.00 0.00 0.00 0.00 0.00
2 77.85 20.96 1.19 0.00 0.00 0.00 0.00 0.00
3 68.46 28.19 3.25 0.10 0.00 0.00 0.00 0.00
4 60.05 33.63 5.93 0.38 0.01 0.00 0.00 0.00
5 52.54 37.53 9.01 0.88 0.03 0.00 0.00 0.00
6 45.86 40.12 12.28 1.64 0.10 0.00 0.00 0.00
7 39.91 41.61 15.60 2.65 0.21 0.01 0.00 0.00
8 34.64 42.17 18.84 3.93 0.40 0.02 0.00 0.00
9 29.98 41.97 21.90 5.44 0.68 0.04 0.00 0.00
10 25.86 41.15 24.69 7.16 1.07 0.08 0.00 0.00
11 22.24 39.83 27.16 9.05 1.57 0.14 0.01 0.00
12 19.06 38.13 29.26 11.08 2.22 0.23 0.01 0.00
13 16.28 36.14 30.98 13.21 3.00 0.36 0.02 0.00
14 13.86 33.95 32.30 15.38 3.93 0.54 0.04 0.00
15 11.75 31.63 33.22 17.55 5.02 0.77 0.06 0.00
16 9.92 29.24 33.74 19.68 6.24 1.07 0.09 0.00
17 8.34 26.84 33.90 21.73 7.61 1.45 0.14 0.01
18 6.99 24.45 33.70 23.65 9.10 1.91 0.20 0.01
19 5.82 22.12 33.18 25.41 10.70 2.47 0.29 0.01
20 4.83 19.88 32.37 26.98 12.39 3.13 0.40 0.02
For example, if you have 13 basic Pokemon in your deck, you have a 16%
chance of starting with a Mulligan (0 basics), 36% chance of starting with a
single basic, 31% of starting with 2, 13% with 3, 3% with 4, and less than 0.5%
with more than 4. The mathematical formula for the probability of getting
n basics in a 7-card opening hand out of a 60-card deck that contains b basics
is:
P(n)= 7!/[n!*(n-7)!]* Product(i=1 to 7-n) of [1-b/(b/(61-i)] *
Product(i=1 to n) of [(b+1-i)/54+n-i)]
Of course, a Mulligan is probably preferable to starting with a
single Pokemon. We can calculate the probabilities of the opening hand
once you get at least one basic, and these are given in the table
below:
Probability for the number of Basic Pokemon in the opening hand after all
Mulligans have been resolved
Basics 1 2 3 4 5 6 7
in Deck
1 100.00 0.00 0.00 0.00 0.00 0.00 0.00
2 94.64 5.36 0.00 0.00 0.00 0.00 0.00
3 89.36 10.31 0.32 0.00 0.00 0.00 0.00
4 84.18 14.85 0.95 0.02 0.00 0.00 0.00
5 79.09 18.98 1.86 0.07 0.00 0.00 0.00
6 74.11 22.69 3.02 0.18 0.00 0.00 0.00
7 69.25 25.97 4.42 0.35 0.01 0.00 0.00
8 64.52 28.83 6.01 0.61 0.03 0.00 0.00
9 59.94 31.27 7.76 0.97 0.06 0.00 0.00
10 55.50 33.30 9.65 1.44 0.11 0.00 0.00
11 51.22 34.92 11.64 2.02 0.18 0.01 0.00
12 47.11 36.15 13.70 2.74 0.29 0.01 0.00
13 43.17 37.01 15.78 3.59 0.43 0.02 0.00
14 39.42 37.49 17.85 4.57 0.62 0.04 0.00
15 35.85 37.64 19.89 5.68 0.87 0.07 0.00
16 32.47 37.46 21.85 6.93 1.19 0.10 0.00
17 29.28 36.98 23.71 8.30 1.58 0.15 0.01
18 26.29 36.23 25.43 9.78 2.05 0.22 0.01
19 23.49 35.23 26.98 11.36 2.62 0.31 0.01
20 20.89 34.01 28.34 13.02 3.29 0.42 0.02
One can see that unless a deck contains at least 12 basic Pokemon,
there is a higher than 50% chance that the opening hand will have only a single
basic. Increasing the number of basics to 16, drops that probability to
less than 1/3. Of course, if you put too many Pokemon in your deck, you
will not have enough energies or trainers. As a compromise, I would choose
14 or 15 basic Pokemon in my deck. The probability of starting with a
single card is less than 40%, and, if you do not run many evolutions, you should
have space for sufficient trainer and energy cards.
_________________________________________________________________