Calculate odds to draw at least one card in target set from a deck with n draws.

cardodds.groovy

// calculate odds to draw at least one card in target set from a deck
// with n draws

// total size
def deckSize = 52
// cards already consumed
def burned = 0
// number of copies of card we're looking for in the deck
def targets = 4
// number of draws we have
def draws = 1
// number of redraws we have
//def mulligans = 0 FIXME

// figure out the odds
def cardsLeft = deckSize - burned
def negProb = 1.0
def p = 1.0
draws.times {
    def n = ((cardsLeft - targets) / cardsLeft)
    def y = 1.0 - n
    //printf "${cardsLeft - targets} / $cardsLeft: %.02f%% %.02f%%\n", n * 100.0, y * 100.0
    negProb -= y * p
    p = p * n
    cardsLeft -= 1
}
printf "%.02f%%\n", (1.0 - negProb) * 100.0

// sanity check: simulate it
def hits = 0
10000.times {
    def deck = (0..<deckSize).toList()[0..-(burned + 1)]
    Collections.shuffle(deck)
    def drawn = deck.take(draws)
    if (drawn.any { (0..<targets).contains(it) }) {
        hits++
    }
}
printf "%.02f%%\n", new BigDecimal(hits) / 100