A card drawing simulation with 10000 trials

Cards Drawn Games Sum 1 0 0 2 0 0 3 4 4 4 7 11 5 37 48 6 247 295 7 317 612 8 457 1069 9 629 1698 10 754 2452 11 896 3348 12 932 4280 13 903 5183 14 872 6055 15 861 6916 16 701 7617 17 663 8280 18 453 8733 19 388 9121 20 307 9428 21 243 9671 22 143 9814 23 83 9897 24 53 9950 25 21 9971 26 22 9993 27 5 9998 28 2 10000 29 0 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