A card drawing simulation with 10000 trials

The average number of drawn cards required to find 5 copies of the target card is 13.5.
Mulligans: 7743, or 77.4%

Cards Drawn Games Sum
1 0 0
2 1 1
3 3 4
4 15 19
5 46 65
6 245 310
7 348 658
8 486 1144
9 621 1765
10 741 2506
11 881 3387
12 933 4320
13 946 5266
14 849 6115
15 830 6945
16 736 7681
17 593 8274
18 512 8786
19 410 9196
20 267 9463
21 194 9657
22 145 9802
23 95 9897
24 57 9954
25 26 9980
26 9 9989
27 7 9996
28 3 9999
29 1 10000
30 0 10000
31 0 10000
32 0 10000
33 0 10000
34 0 10000
35 0 10000
36 0 10000
37 0 10000
38 0 10000
39 0 10000
40 0 10000
41 0 10000
42 0 10000
43 0 10000
44 0 10000
45 0 10000
46 0 10000
47 0 10000
48 0 10000
49 0 10000
50 0 10000
Cards in deck:
Hand size:
Target cards:
Search cards:
Draw One cards:
Draw Two cards:
Desired number of  
target cards:

Keep the starting hand
if you have at least:
Target:
Search:
Draw Two:

Or:
Target:
Search:
Draw Two:
 
Trials:

Notes

Mulligan rules are for Lord of the Rings LCG, where you draw a starting hand of six cards, then choose to keep them or redraw a new set of six.

Cards that draw two cards instantly do so, which aren't counted. E.g. If my first card is a draw two, and then the 3rd card in the deck is a target card, that's effectively only one card draw to find a target card.

If you keep your hand, it will be treated as if you drew 6 cards, so there will tend to be a large statistical bump at 6 cards. If you want to turn off mulligans, set your keep targets to be 7+, which will be impossible since you have a six card starting hand.

I have 3 Light of Valinor in my 50 card deck; when should I expect to draw at least 1?
Decksize = 50, Target = 3, Search = 0, Desired = 1

I have 12 restricted attachments and 1 Word of Command in my deck with the One Ring; when should I expect to draw at least 5?
Decksize = 48 (because I get The One Ring and a Master card at the beginning), Target = 12, Search = 1, Desired = 5