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 6 257 305 7 344 649 8 479 1128 9 620 1748 10 779 2527 11 834 3361 12 888 4249 13 895 5144 14 906 6050 15 780 6830 16 734 7564 17 631 8195 18 520 8715 19 426 9141 20 284 9425 21 220 9645 22 149 9794 23 100 9894 24 55 9949 25 28 9977 26 11 9988 27 8 9996 28 2 9998 29 1 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