A card drawing simulation with 10000 trials

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