A card drawing simulation with 10000 trials

Cards Drawn Games Sum 1 0 0 2 1 1 3 2 3 4 13 16 5 38 54 6 245 299 7 344 643 8 486 1129 9 650 1779 10 745 2524 11 865 3389 12 936 4325 13 883 5208 14 908 6116 15 842 6958 16 684 7642 17 647 8289 18 501 8790 19 366 9156 20 304 9460 21 207 9667 22 129 9796 23 94 9890 24 50 9940 25 34 9974 26 13 9987 27 9 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