TCG Stats and Probability Dump

[t3h Icy]

This is a quick table of the beginning phase of Pokemon TCG. A player has a deck of 60 cards, draws 7, and must have at least 1 Basic Pokemon card in their hand. The penalty for not drawing at least 1 basic Pokemon is you must show your hand to the opponent, reshuffle, draw again, and the opponent may draw 1 or 2 additional cards if they have at least 1.

So for 1 to 60 Basic Pokemon in a deck, these are the chances of drawing at least 1 in the opening hand:

# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chance 11.66666667% 22.14689266% 31.54295733% 39.94996257% 47.45621725% 54.14360778% 60.08795492% 65.35935710% 70.02252057% 74.13707657% 77.75788585% 80.93533073% 83.71559500% 86.14093191% 88.24992053% 90.07771067% 91.65625670% 93.01454050% 94.17878375% 95.17264994% 96.01743620% 96.73225534% 97.33420830% 97.83854727% 98.25882975% 98.60706380% 98.89384478% 99.12848377% 99.31912794% 99.47287325% 99.59586949% 99.69341823% 99.77006367% 99.82967680% 99.87553304% 99.91038379% 99.93652185% 99.95584129% 99.96989179% 99.97992786% 99.98695311% 99.99175986% 99.99496436% 99.99703786% 99.99833379% 99.99911136% 99.99955568% 99.99979493% 99.99991455% 99.99996893% 99.99999068% 99.99999793% 99.99999974% 100% 100% 100% 100% 100% 100% 100%

And here's a nice chart:

SPOILER: Click to show

Edit: Thread changed into general stats and probability, rather than this post specifically.

[t3h Icy]

Drawing 2 Basic Pokemon so that the opponent cannot win on their first turn (if you only have 1 Pokemon that gets KO'd on turn 1, you had no chance to do anything).

# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chance 0% 1.18644068% 3.35476330% 6.32194162% 9.92494386% 14.01926460% 18.47752495% 23.18813966% 28.05404937% 32.99151657% 37.92898377% 42.80599219% 47.57215950% 52.18621510% 56.61509121% 60.83306845% 64.82097421% 68.56543223% 72.05816198% 75.29532614% 78.27692471% 81.00623417% 83.48929015% 85.73441201% 87.75176789% 89.55297849% 91.15075825% 92.55859217% 93.79044684% 94.86051415% 95.78298597% 96.57185842% 97.24076410% 97.80283067% 98.27056439% 98.65575687% 98.96941360% 99.22170271% 99.42192232% 99.57848503% 99.69891788% 99.78987637% 99.85717087% 99.90580386% 99.94001661% 99.96334348% 99.97867257% 99.98831093% 99.99405293% 99.99725018% 99.99888143% 99.99962093% 99.99990368% 99.99998602% 100% 100% 100% 100% 100% 100%

And a chart:

SPOILER: Click to show

Edit: Just as a fact, the inflection point occurs at 11, that is, the percentage returns for adding additional cards becomes diminishing. Or in English, after 11 cards, the amount that the chance increases per card begins to decrease.