note-1: basic calculations

aft_null

  1. 起手牌牌型总数：1326

    choose(52,2)
    ## [1] 1326

  2. 起手牌拿到至少一张特定点数的牌，例如(A,X)或(A,A)的概率：14.93%

    1 - choose(48,2)/choose(52,2)
    ## [1] 0.1493213

  3. 起手牌是任意两单张，在flop提升为一对的概率：28.96%

    choose(44,2)*3*2/choose(50,3)
    ## [1] 0.2895918

  4. 起手牌是任意两单张，在flop未击中任何对子的概率：67.57%

    choose(44,3)/choose(50,3)
    ## [1] 0.6757143

  5. 起手牌是任意两单张，在flop提升为两对的概率：2.02%

    3*3*(52-4-4)/choose(50,3)
    ## [1] 0.02020408

  6. 起手牌是任意两单张，在flop成为天葫芦的概率：0.09%

    choose(3,2)*choose(3,1)*2/choose(50,3)
    ## [1] 0.0009183673

  7. 起手牌是任意两单张，在flop成为四条的概率：0.01%

    2/choose(50,3)
    ## [1] 0.0001020408

  8. 任意两单张例如(A,K)，一直看到river，至少击中一对的概率：48.74%

    1 - choose(44,5)/choose(50,5)
    ## [1] 0.4874323

  9. 起手牌拿到特定口袋对子(AA或KK)的概率：0.45%

    choose(4,2) / 1326
    ## [1] 0.004524887

  10. 起手牌拿到任意口袋对子(AA或22等)的概率：5.88%

    choose(4,2) * 13 / 1326
    ## [1] 0.05882353

  11. 起手牌拿到口袋对子QQ+的概率：1.36%

    choose(4,2)*3/choose(52,2)
    ## [1] 0.01357466

  12. 起手牌拿到口袋对子JJ+的概率：1.81%

    choose(4,2)*4/choose(52,2)
    ## [1] 0.01809955

  13. 起手牌拿到口袋对子TT+的概率：2.26%

    choose(4,2)*5/choose(52,2)
    ## [1] 0.02262443

  14. 起手牌拿到两张K+（包含口袋对子）的概率：2.11%

    (6*2+16)/choose(52,2)
    ## [1] 0.02111614

  15. 起手牌拿到两张Q+（包含口袋对子）的概率:4.98%

    (6*3+16*3)/choose(52,2)
    ## [1] 0.04977376

  16. 起手牌拿到两张J+（包含口袋对子）的概率：9.05%

    (6*4+16*6)/choose(52,2)
    ## [1] 0.09049774

  17. 起手牌拿到两张T+（包含口袋对子）的概率：14.33%

    (6*5+16*10)/choose(52,2)
    ## [1] 0.1432881

  18. 任意口袋对子在flop击中Set的概率(标准计算)：11.51%

    choose(48,2)*2/choose(50,3)
    ## [1] 0.115102

  19. 在4-9人局中，口袋对子在flop击中暗三条(Set)的概率：13%，13.6%，14.2%，14.97%，15.7%，16.6%

    playerNum <- c(4:9)
blockNum <- 0   ## 此处范围为0到2
probFlopSet <- choose((52 - playerNum*2 -2),2)*(2 - blockNum) / choose((52 - playerNum*2),3)
PFS <- round(probFlopSet,3)
## print(PFS)
## plot(playerNum,PFS)
library(ggplot2)
data <- data.frame(
  category = playerNum,
  value = PFS,
  x = playerNum,
  y = PFS,
  family = PFS
)

ggplot(data, aes(x =playerNum, y = value)) +
  geom_point(stat = "identity") +
  geom_text(aes(label = (paste0(PFS*100,"%"))),nudge_y = 0.05,size = 3)+
  coord_cartesian(ylim = c(0, 1)) +
  scale_y_continuous(labels = scales::percent) +
  labs(y = "PFS") +
  labs(title = paste("Hit set on flop"),subtitle = "by aft_null")

  20. 在4-9人局中，口袋对子在turn上击中Set的概率：4.88%,5.13%,5.41%,5.71%,6.06%,6.45%

    playerNum <- c(4:9)
probTurnSet <- 2 / (52 -playerNum*2 - 3)
PTS <- round(probTurnSet,4)
## print(PTS)

library(ggplot2)

data <- data.frame(
  category = playerNum,
  value = PTS,
  x = playerNum,
  y = PTS,
  family = PTS
)

ggplot(data, aes(x =playerNum, y = value)) +
  geom_point(stat = "identity") +
  geom_text(aes(label = (paste0(PTS*100,"%"))),nudge_y = 0.05,size = 3)+
  coord_cartesian(ylim = c(0, 1)) +
  scale_y_continuous(labels = scales::percent) +
  labs(y = "PTS") +
  labs(title = paste("Hit set on turn"),subtitle = "by aft_null")

  21. 在4-9人局中，口袋对子在river击中Set的概率：5%,5.26%,5.56%,5.88%,6.25%,6.67%

    playerNum <- c(4:9)
probRiverSet <- 2 / (52 - playerNum*2 - 4)
PRS <- round(probRiverSet,4)
## print(PRS)

library(ggplot2)

data <- data.frame(
  category = playerNum,
  value = PRS,
  x = playerNum,
  y = PRS,
  family = PRS
)

ggplot(data, aes(x =playerNum, y = value)) +
  geom_point(stat = "identity") +
  geom_text(aes(label = (paste0(PRS*100,"%"))),nudge_y = 0.05,size = 3)+
  coord_cartesian(ylim = c(0, 1)) +
  scale_y_continuous(labels = scales::percent) +
  labs(y = "PRS") +
  labs(title = paste("Hit set on river"),subtitle = "by aft_null")

  22. 口袋对子在flop击中四条(Quads)的概率：0.24%

    48 / choose(50,3)
    ## [1] 0.00244898

  23. 口袋对子preflop ALL IN， 走到river击中Set或Quads的概率：18.4% + 0.82% = 19.2%

    (choose((48),4) * 2 + choose(48,3))  / choose(50,5)
    ## [1] 0.1918367

  24. 起手牌是Suited的概率：23.5%

    choose(13,2) * 4 / 1326
    ## [1] 0.2352941

  25. 在4-9人局中，Suited在flop击中Flush,也就是“天金”的概率：1.2%,1.4%,1.7%,2%,2.8%

    playerNum <- c(4:9)
probFlopFlush <- choose(11,3) / choose((52 - playerNum*2),3)
PFF <- round(probFlopFlush,3)
## print(PFF)

library(ggplot2)

data <- data.frame(
  category = playerNum,
  value = PFF,
  x = playerNum,
  y = PFF,
  family = PFF
)

ggplot(data, aes(x =playerNum, y = value)) +
  geom_point(stat = "identity") +
  geom_text(aes(label = (paste0(PFF*100,"%"))),nudge_y = 0.05,size = 3)+
  coord_cartesian(ylim = c(0, 1)) +
  scale_y_continuous(labels = scales::percent) +
  labs(y = "PFF") +
  labs(title = paste("Hit flush on flop"),subtitle = "by aft_null")

  26. 在4-9人局中，Suited在flop形成同花听牌后,在转牌圈击中Flush，也就是“一脚着”的概率：22%,23.1%,24.3%,25.7%,27.3%,29%

    playerNum <- c(4:9)
blockNum <- 0
probTurnFlush <- (9 - blockNum) / (52 - playerNum*2 - 3)
PTF <- round(probTurnFlush,3)
## print(PTF)

library(ggplot2)

data <- data.frame(
  category = playerNum,
  value = PTF,
  x = playerNum,
  y = PTF,
  family = PTF
)

ggplot(data, aes(x =playerNum, y = value)) +
  geom_point(stat = "identity") +
  geom_text(aes(label = (paste0(PTF*100,"%"))),nudge_y = 0.05,size = 3,check_overlap = FALSE)+
  coord_cartesian(ylim = c(0, 1)) +
  scale_y_continuous(labels = scales::percent) +
  labs(y = "PTF") +
  labs(title = paste("Hit flush on turn"),subtitle = "by aft_null")

  27. 在4-9人局中，Suited在翻牌圈形成同花听牌后,在turn或river击中同花Flush的概率：39.51%,41.3%,43.24%,45.38%,47.73%,50.32%

    playerNum <- c(4:9)
blockNum <- 0 ## 对手手握阻挡牌总数 ##
probTRF <- 1 - choose(52-playerNum*2-3-9+blockNum,2)/choose(52-playerNum*2-3,2)
PTRF <- round(probTRF,4)
## print(PTRF)

library(ggplot2)

data <- data.frame(
  category = playerNum,
  value = PTRF,
  x = playerNum,
  y = PTRF,
  family = PTRF
)

ggplot(data, aes(x =playerNum, y = value)) +
  geom_point(stat = "identity") +
  geom_text(aes(label = (paste0(PTRF*100,"%"))),nudge_y = 0.05,size = 3)+
  coord_cartesian(ylim = c(0, 1)) +
  scale_y_continuous(labels = scales::percent) +
  labs(y = "PTRF") +
  labs(title = paste("Hit flush on turn or river"),subtitle = "by aft_null")

  28. Suited手牌，于preflop ALL IN，在river击中Flush的概率：8.42%

    choose(11,3)*choose(47,2)/choose(50,5)
    ## [1] 0.08418367

  29. Suited 连张手牌，在flop至少击中一对、或者Straight听牌、以及Flush听牌的概率：34.85%

    choose(23,2)*27/choose(50,3) ## 6张同点数补牌+8张顺子听牌补牌+11张同花色补牌-2张共同补牌，其余27张是无关牌
    ## [1] 0.3485204

  30. 任意两张手牌在flop击中Quads的概率：0.024%

    ## 白皮书 P26 E.2.4.15 b) ##
## 13种四条 + 另外48种单张牌*（翻牌的第三张牌）##
13*48/choose(52,5)  ## 等价于随机选择5张牌，其中4张牌的点数相同的概率 ##
    ## [1] 0.000240096

  31. 已经拿到特定口袋对子，翻牌圈击中金刚的概率：0.24%

    1*48/choose(50,3) 
    ## [1] 0.00244898

  32. 已经拿到特定口袋对子，假设无论如何都要看到河牌，击中金刚的概率：0.8%

    1*choose(48,3)/choose(50,5)  ## 5张公牌，有两张与口袋对子同点数凑成金刚，其余3张任意组合 ##
    ## [1] 0.008163265