洗牌的非正态抽样

Question

我有一个脚本，它使用 sample() 将一副牌洗牌到四手 - 如下所示。

这个脚本产生正态分布的手部分裂。也就是说，一套花色中的 13 张牌在四手牌中的分布将在 21.6% 的情况下为“4432”，在 15.5% 的情况下为“5442”，... - 请参见此处：https://en.wikipedia.org/wiki/Contract_bridge_probabilities#Hand%20pattern%20probabilities。

有没有办法让sample() 给出非正态分布，例如展平轮廓，使双手的分布偏离预期概率？ sample() 可以采用加权参数，但看不到如何使用它来实现我的目标。或者，是否有其他采样功能可以提供此功能？

谢谢，

TC

# Set up
library(tidyverse)
set.seed(123)

# Build pack
pack <- expand.grid(rank = c("A", 2:9, "T", "J", "Q", "K"), suit = c("S", "H", "D", "C")) %>%
  as_tibble(.name_repair = "minimal") %>%
  mutate(card = paste(suit, rank, sep = "-"))

# Divide cards into hands
for (i in 1:4) {
  temp <- sample(pack$card, 13, replace = FALSE) %>%
    as_tibble(.name_repair = "minimal") %>%
    separate(value, sep = "-", into = c("suit", "rank")) %>%
    mutate(
      suit = factor(suit, levels = c("S", "H", "D", "C")),
      rank = factor(rank, levels = c("A", "K", "Q", "J", "T", 9:2, " "))
    ) %>%
    arrange(suit, rank) %>%
    unite("card", sep = "-")

  assign(glue::glue("hand{i}"), temp)
  
  pack <- pack %>%
    filter(!card %in% unname(unlist(temp)))
}

# Reassemble pack
pack <- hand1 %>% 
  cbind(hand2) %>%
  cbind(hand3) %>%
  cbind(hand4) %>% 
  rename(N = 1, E = 2, S = 3, W = 4)

Answer 1

您可以按如下方式简化创建套牌、洗牌和发牌的过程：

# Create the deck
Suit <- c("S", "H", "D", "C")
Rank <- c("A", 2:9, "T", "J", "Q", "K")
Deck <- data.frame(Rank=rep(Rank, 4), Suit=rep(Suit, each=13))

# Shuffle and deal
Shuffle <- Deck[sample(nrow(Deck)), ]  # Shuffle the deck
Hand <- factor(rep(c("N", "E", "S", "W"), 13), levels=c("N", "E", "S", "W"))
Deal <- data.frame(Hand, Shuffle)

现在 deal 是一个显示每手牌的数据框。按花色获取牌的分布：

xtabs(~Suit+Hand, Even)
#     Hand
# Suit N E S W
#    C 3 3 3 4
#    D 3 3 4 3
#    H 3 4 3 3
#    S 4 3 3 3

拿到手：

split(Deal, Deal$Hand)
# $N
#    Hand Rank Suit
# 12    N    Q    S
# 2     N    2    S
# 37    N    J    D
# 49    N    T    C
# 43    N    4    C
# 17    N    4    H
# 33    N    7    D
# 26    N    K    H
# 13    N    K    S
# 44    N    5    C
# 18    N    5    H
# 46    N    7    C
# 11    N    J    S
.  .  .  .  .

由于您提到了手型概率，因此展示如何凭经验生成它们可能会有所帮助：

HPP <- function() {
    Shuffle <- Deck[sample(nrow(Deck)), ]  # Shuffle the deck
    Hand <- factor(rep(c("N", "E", "S", "W"), 13), levels=c("N", "E", "S", "W"))
    Deal <- data.frame(Hand, Shuffle)
    tbl <- xtabs(~Suit+Hand, Deal)
    return(unname(apply(tbl, 1, function(x) paste(sort(x, decreasing=TRUE), collapse="-"))))
}

X <- replicate(1000, HPP())
HP <- prop.table(sort(table(X), decreasing=TRUE))
as.matrix(HP)
#            [,1]
# 4-4-3-2 0.22200
# 5-3-3-2 0.14925
# 5-4-3-1 0.12075
# 4-3-3-3 0.11225
# 5-4-2-2 0.10775
# 6-3-2-2 0.05175
# 6-4-2-1 0.04850
#  .  .  .  .

要按花色获得更“均匀”的牌分布，您必须打破洗牌的随机分布，例如，我们可以洗牌中的排名值，但保留花色的顺序：

Even <- Deck
Even$Rank <- c(replicate(4, sample(Rank)))
Even <- data.frame(Hand, Even)

现在卡值会有所不同，但花色的分配总是一样的。