Box & Draft Odds

A box of one expansion holds 351 draft cards. Players shuffle them all and deal them into27 packs of 13. A standard 3-player game opens 9 of those packs, 3 per player, so 117 cards are drafted: exactly a third of the box. Blaze and Phantom boxes are built the same way.

What's in a box

Rarity	Different cards	Copies of each	Cards in a box	Per pack, on average
Legend	20	1	20	0.74
Rare	20	2	40	1.48
Uncommon	46	3	138	5.11
Common	36	4	144	5.33
Void	1	9	9	0.33
Total	123		351	13

The 4 Epic cards are not in the packs. Every player is dealt one of each before the draft and picks one of them for the Battle.

One game

Every card in the 9 open packs is drafted by someone, so between them the three players always take all 117 cards. Who ends up with which card depends on the picks, so the per-player number is the average share, not a promise.

Rarity	In the game, on average	Per player, on average	Chance a given card is in the game
Legend	6.7	2.2	33% (1 copy in the box)
Rare	13.3	4.4	56% (2 copies in the box)
Uncommon	46	15.3	70% (3 copies in the box)
Common	48	16	80% (4 copies in the box)
Void	3	1	98% (9 copies in the box)

How many will turn up

The chance of each total in one game. Pick a rarity:

Legend cards in one game (20 in the box, 6.7 on average)

1 Legend: 0.2%
1 or more: >99.9%1

2 Legend: 1.3%
2 or more: 100%2

3 Legend: 4.0%
3 or more: 98%3

4 Legend: 8.9%
4 or more: 94%4

5 Legend: 15%
5 or more: 86%5

6 Legend: 19%
6 or more: 71%6

7 Legend: 19%
7 or more: 52%7

8 Legend: 15%
8 or more: 33%8

9 Legend: 9.8%
9 or more: 18%9

10 Legend: 5.2%
10 or more: 8.6%10

11 Legend: 2.3%
11 or more: 3.3%11

12 Legend: 0.8%
12 or more: 1.1%12

13 Legend: 0.2%
13 or more: 0.3%13

Show as a table

Legend cards	Exactly	This many or more
1	0.2%	>99.9%
2	1.3%	100%
3	4.0%	98%
4	8.9%	94%
5	15%	86%
6	19%	71%
7	19%	52%
8	15%	33%
9	9.8%	18%
10	5.2%	8.6%
11	2.3%	3.3%
12	0.8%	1.1%
13	0.2%	0.3%

Rare cards in one game (40 in the box, 13.3 on average)

5 Rare: 0.1%
5 or more: >99.9%5

6 Rare: 0.4%
6 or more: 100%6

7 Rare: 1.0%
7 or more: 99%7

8 Rare: 2.3%
8 or more: 98%8

9 Rare: 4.4%
9 or more: 96%9

10 Rare: 7.3%
10 or more: 92%10

11 Rare: 10%
11 or more: 84%11

12 Rare: 13%
12 or more: 74%12

13 Rare: 14%
13 or more: 61%13

14 Rare: 14%
14 or more: 47%14

15 Rare: 12%
15 or more: 33%15

16 Rare: 8.8%
16 or more: 22%16

17 Rare: 6.0%
17 or more: 13%17

18 Rare: 3.6%
18 or more: 7.1%18

19 Rare: 1.9%
19 or more: 3.5%19

20 Rare: 0.9%
20 or more: 1.6%20

21 Rare: 0.4%
21 or more: 0.6%21

22 Rare: 0.2%
22 or more: 0.2%22

Show as a table

Rare cards	Exactly	This many or more
5	0.1%	>99.9%
6	0.4%	100%
7	1.0%	99%
8	2.3%	98%
9	4.4%	96%
10	7.3%	92%
11	10%	84%
12	13%	74%
13	14%	61%
14	14%	47%
15	12%	33%
16	8.8%	22%
17	6.0%	13%
18	3.6%	7.1%
19	1.9%	3.5%
20	0.9%	1.6%
21	0.4%	0.6%
22	0.2%	0.2%

Void cards in one game (9 in the box, 3 on average)

0 Void: 2.5%
0 or more: >99.9%0

1 Void: 12%
1 or more: 98%1

2 Void: 24%
2 or more: 86%2

3 Void: 28%
3 or more: 63%3

4 Void: 21%
4 or more: 35%4

5 Void: 10%
5 or more: 14%5

6 Void: 3.3%
6 or more: 4.0%6

7 Void: 0.7%
7 or more: 0.8%7

Show as a table

Void cards	Exactly	This many or more
0	2.5%	>99.9%
1	12%	98%
2	24%	86%
3	28%	63%
4	21%	35%
5	10%	14%
6	3.3%	4.0%
7	0.7%	0.8%

One pack

No Legend	46%
Exactly 1 Legend	37%
2 or more Legends	17%
At least 1 Rare or Legend	92%

You see every card of the 3 packs you open before anyone else picks from them: 39 cards, with a 91% chance of at least one Legend among them.

How these are worked out

The rulebook has you make the packs yourself: shuffle all 351 cards face down and deal them out13 at a time. Each number here is a hypergeometric probability for that: drawing 117 cards (a game) or 13 cards (a pack) from 351 without putting any back. The rulebook also suggests checking that Rares and Legends aren't bunched together while you shuffle, which spreads them a little more evenly between packs than pure chance would.