Appendix IV

Some Deck Math

MULLIGAN CHANCE BY NUMBER OF BASIC POKÉMON IN DECK

Below is a breakdown of the percent chance your deck has of a mulligan based on the number of Basic Pokémon you’ve included in your deck. As the number of Basic Pokémon increases, the percent chance for a mulligan decreases. It is necessary to weigh the chance of a mulligan against other factors, like consistency. If you include a lot of Basic Pokémon to avoid a mulligan, it could cut into your deck’s ability to draw the cards it needs.

See also: TheMathTCG: The Probabilities Behind the Opening Hand on Six Prizes.

  
  # Basics% Chance
33%
85%
46%
05%
54%
86%
91%
64%
98%
86%

  
  # Basics% Chance
24%
06%
28%
86%
75%
92%
34%
99%
82%
83%

Chance to Draw Specific Basic Pokémon in Opening Hand by Count in Deck

  
  # Copies% Chance
67%
15%
54%
95%

CHANCE TO TOP DECK CARD BASED ON QUANTITY IN DECK AND CARDS REMAINING IN DECK

   # Cards4321
1  100%
2  100%50%
3 100%66.67%33.33%
4100%75%50%25%
580%60%40%20%
666.67%50%33.33%16.67%
757.14%42.86%28.57%14.29%
850%37.50%25%12.5%
944.44%33.33%22.22%11.11%
1040%30%20%10%
1136.36%27.27%18.18%9.09%
1233.33%25%16.67%8.33%
1330.77%23.08%15.38%7.69%
1428.57%21.43%14.29%7.14%
1526.67%20%13.33%6.67%
1625%18.75%12.5%6.25%
1723.53%17.65%11.76%5.88%
1822.22%16.67%11.11%5.56%
1921.05%15.79%10.53%5.26%
2020%15%10%5%
2119.05%14.29%9.52%4.76%
2218.18%13.64%9.09%4.55%
2317.39%13.04%8.7%4.35%
2416.67%12.5%8.33%4.17%
2516%12%8%4%

   # Cards4321
38%11.54%7.69%3.85%
81%11.11%7.41%3.7%
29%10.71%7.14%3.57%
79%10.34%6.9%3.45%
33%10%6.67%3.33%
9%9.68%6.45%3.23%
5%9.38%6.25%3.13%
12%9.09%6.06%3.03%
76%8.82%5.88%2.94%
43%8.57%5.71%2.86%
11%8.33%5.56%2.78%
81%8.11%5.41%2.7%
53%7.89%5.26%2.63%
26%7.69%5.13%2.56%
4010%7.5%5%2.5%
76%7.32%4.88%2.44%
52%7.14%4.76%2.38%
3%6.98%4.65%2.33%
09%6.82%4.55%2.27%
89%6.67%4.44%2.22%
7%6.52%4.35%2.17%
51%6.38%4.26%2.13%
33%6.25%4.17%2.08%
16%6.12%4.08%2.04%
508%6%4%2%

< Appendix III: 2021-2022 Card Legality Status (TEU-CEC) | Table of Contents | Appendix V: Pre-release Deck Building >

# Basics	% Chance
1	88.33%
2	77.85%
3	68.46%
4	60.05%
5	52.54%
6	45.86%
7	39.91%
8	34.64%
9	29.98%
10	25.86%

# Copies	% Chance
1	11.67%
2	22.15%
3	31.54%
4	39.95%

# Basics	% Chance
11	22.24%
12	19.06%
13	16.28%
14	13.86%
15	11.75%
16	9.92%
17	8.34%
18	6.99%
19	5.82%
20	4.83%

# Cards	4	3	2	1
1				100%
2			100%	50%
3		100%	66.67%	33.33%
4	100%	75%	50%	25%
5	80%	60%	40%	20%
6	66.67%	50%	33.33%	16.67%
7	57.14%	42.86%	28.57%	14.29%
8	50%	37.50%	25%	12.5%
9	44.44%	33.33%	22.22%	11.11%
10	40%	30%	20%	10%
11	36.36%	27.27%	18.18%	9.09%
12	33.33%	25%	16.67%	8.33%
13	30.77%	23.08%	15.38%	7.69%
14	28.57%	21.43%	14.29%	7.14%
15	26.67%	20%	13.33%	6.67%
16	25%	18.75%	12.5%	6.25%
17	23.53%	17.65%	11.76%	5.88%
18	22.22%	16.67%	11.11%	5.56%
19	21.05%	15.79%	10.53%	5.26%
20	20%	15%	10%	5%
21	19.05%	14.29%	9.52%	4.76%
22	18.18%	13.64%	9.09%	4.55%
23	17.39%	13.04%	8.7%	4.35%
24	16.67%	12.5%	8.33%	4.17%
25	16%	12%	8%	4%

# Cards	4	3	2	1
26	15.38%	11.54%	7.69%	3.85%
27	14.81%	11.11%	7.41%	3.7%
28	14.29%	10.71%	7.14%	3.57%
29	13.79%	10.34%	6.9%	3.45%
30	13.33%	10%	6.67%	3.33%
31	12.9%	9.68%	6.45%	3.23%
32	12.5%	9.38%	6.25%	3.13%
33	12.12%	9.09%	6.06%	3.03%
34	11.76%	8.82%	5.88%	2.94%
35	11.43%	8.57%	5.71%	2.86%
36	11.11%	8.33%	5.56%	2.78%
37	10.81%	8.11%	5.41%	2.7%
38	10.53%	7.89%	5.26%	2.63%
39	10.26%	7.69%	5.13%	2.56%
40	10%	7.5%	5%	2.5%
41	9.76%	7.32%	4.88%	2.44%
42	9.52%	7.14%	4.76%	2.38%
43	9.3%	6.98%	4.65%	2.33%
44	9.09%	6.82%	4.55%	2.27%
45	8.89%	6.67%	4.44%	2.22%
46	8.7%	6.52%	4.35%	2.17%
47	8.51%	6.38%	4.26%	2.13%
48	8.33%	6.25%	4.17%	2.08%
49	8.16%	6.12%	4.08%	2.04%
50	8%	6%	4%	2%