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: 7806, or 78.1%

Cards Drawn Games Sum
1 0 0
2 0 0
3 2 2
4 17 19
5 46 65
6 261 326
7 351 677
8 500 1177
9 615 1792
10 785 2577
11 825 3402
12 882 4284
13 940 5224
14 876 6100
15 815 6915
16 698 7613
17 634 8247
18 499 8746
19 415 9161
20 310 9471
21 219 9690
22 132 9822
23 69 9891
24 55 9946
25 30 9976
26 16 9992
27 4 9996
28 3 9999
29 0 9999
30 1 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