A card drawing simulation with 10000 trials

The average number of drawn cards required to find 5 copies of the target card is 13.6.
Mulligans: 7834, or 78.3%

Cards Drawn Games Sum
1 0 0
2 0 0
3 0 0
4 14 14
5 38 52
6 265 317
7 355 672
8 472 1144
9 581 1725
10 783 2508
11 811 3319
12 864 4183
13 918 5101
14 896 5997
15 851 6848
16 760 7608
17 621 8229
18 546 8775
19 376 9151
20 271 9422
21 230 9652
22 151 9803
23 81 9884
24 57 9941
25 21 9962
26 22 9984
27 9 9993
28 5 9998
29 2 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