iki-kartli-poker.kojo

// 4.2 Practice Problem 1
/* In a drastically simplified poker game, you're dealt just two cards.
 * If you get a pair—that is, if the two cards are of the same denomination—you receive $50.
 * If you get a "flush"—two cards of the same suit—the payoff is $10.
 * What's the expected value of the game?
 */

def pow(base: Int, exp: Int): BigInt = if (exp < 1) 1 else base * pow(base, exp - 1)
def fac(n: Int): BigInt = if (n < 2) 1 else n * fac(n - 1)
def seqRep(n: Int, k: Int): BigInt = pow(n, k)
def seqUniq(n: Int, k: Int): BigInt = if (k < 1) 1 else if (k < 2) n else n * seqUniq(n - 1, k - 1)
def colUniq(n: Int, k: Int): BigInt = seqUniq(n, k) / fac(k)
def colRep(n: Int, k: Int): BigInt = colUniq(n + k - 1, k)
val choose = colUniq _
clearOutput
val numAll = choose(52, 2).toInt // 1326
val numPair = choose(4, 2) * choose(13, 1) // 78
val numFlush = choose(4, 1) * choose(13, 2) // 312
val pPair = numPair.toDouble / numAll // 0.06
val pFlush = numFlush.toDouble / numAll // 0.24  (12 / 51)
// expected value is 50 * 78 / 1326 + 10 * 312 / 1326
val expected = 50 * pPair + 10 * pFlush // 5.3
println("Expected payoff is " + round(expected, 1))

// 5.2 Practice Problems
/* Suppose you're playing two-card poker, and you're dealt two cards at random from a deck;
 * we'll say you have a mini-flush if they're the same suit, and a mini-straight if their
 * denominations are in sequence. 
 * NOTE: For the purposes of this problem, an ace-2 is NOT considered a mini-straight.
 */

val numStr = (13 - 1) * // no straight starting with ace
    4 * // num suits for the first (say 5)
    4 // num consequent cards (5 of any suit)
val pStr = numStr / numAll.toDouble // 0.145

val pStrGivenFlush = 12.0 / choose(13, 2).toDouble // 0.154
val pFlushGivenStr = 1 / 4.0 // 0.25

val msg = "Getting a straight v a flush are " +
    (if (pStrGivenFlush > pStr) "positively " else "negatively ") +
    "correlated."
println(msg)

assert(pFlushGivenStr > pFlush, "test + correlation")