问鱿鱼游戏第7集及模拟

EN

squid_bridge1 <- function(players, n, prob) {
  if (players == 0 | n == 18) {
    # All players have died or we have reached the end
    return(players)
  }
  
  jump <- rbinom(1, 1, prob)
  
  if (jump == 0) {
    # Player died
    return(squid_bridge1(players - 1, n, prob))
  }

  if (jump == 1 & n < 18) {
    # Player lives and advances 1 space
    return(squid_bridge1(players, n + 1, prob))
  } 
}

squid_bridge2 <- function(players, n, prob, previous) {
  if (players == 0 | n == 18) {
    # The game ends if there are no players or they have reached the end
    return(players)
  }
  
  if (previous == 0) {
    # The previous guess was wrong, but now the players know where to go next
    return(squid_bridge2(players, n + 1, prob, previous = 1))
  }
  
  jump <- rbinom(1, 1, prob)
  
  if (jump == 0) {
    # Player died
    return(squid_bridge2(players - 1, n, prob, previous = 0))
  }
  
  if (jump == 1 & n < 18) {
    # Move is correct. Advance 1 space
    return(squid_bridge2(players, n + 1, prob, previous = 1))
  } 
}

not_stupid <- function() {
  x <- runif(1, 0, 1)
  if (x <= 0.1) {
    return(FALSE)
  } else {
    return(TRUE)
  }
}

squid_bridge3 <- function(players, n, prob, previous) {
  if (players == 0 | n == 18) {
    # The game is over because there are no players left or they reached the end
    return(players)
  }
        
  if (previous == 0) {
    # The previous guess was wrong, but now the players know where to go next
    return(squid_bridge3(players, n + 1, prob, previous = 1))
  }
  
  if (!not_stupid()) {
    return(squid_bridge3(players - 1, n, prob, previous = 1))
  }
  
  jump <- rbinom(1, 1, prob)
  
  if (jump == 0) {
    # Player died because of either choosing wrong or a self-inflicted loss
    return(squid_bridge3(players - 1, n, prob, previous = 0))
  }
  
  if (jump == 1 & n < 18) {
    # Move is correct. Advance 1 space
    return(squid_bridge3(players, n + 1, prob, previous = 1))
  } 
}

set.seed(123)
trials <- 10000
players <- 16
squid1 <- replicate(trials, squid_bridge1(players, 0, 0.5))
squid2 <- replicate(trials, squid_bridge2(players, 0, 0.5, 1))
squid3 <- replicate(trials, squid_bridge3(16, 0, 0.5, 1))

df <- tibble(squid1 = squid1,
             squid2 = squid2,
             squid3 = squid3) %>%
  pivot_longer(cols = c(squid1, squid2, squid3))

ggplot(data = df,
       aes(x = value)) +
  geom_histogram(bins = 10,
                 binwidth = 1,
                 fill = "cornflowerblue",
                 color = "black") +
  facet_wrap(~name,
             nrow = 3) +
  xlab("# of players to make it to the end") +
  scale_x_continuous(breaks = seq(0, 16, by = 1),
                     labels = seq(0, 16, by = 1))

apply(apply(matrix(rgeom(16*1e6,.5)+1,nc=16),1,cumsum)>18,1,mean)
#with details:
#rgeom(16*1e6,.5)+1 for 16 x 10⁶ geometric simulations when
#the outcome is the number of attempts till "success",
# "success" included
#,1,cumsum) for the number of steps till 16th "success"
#)>18 for counting the cases when a player manages to X the bridge
#1,mean) for finding the probability of each of the players to X

sum(1-pnbinom(size=1:16,q=17:2,prob=.5))
#Explanation:
#pnbinom is the Negative Binomial cdf
#with size the number of "successes"
#q the integer at which the cdf is computed
#prob is the Negative Binomial probability parameter
#Because nbinom() is calibrated as the number of attempts
#before "success", rather than until "success", the value of
#q decreases by one for each player in the game

##########
# Game ○ △ □ 
##########
squidd7<-function(N_Fields,N_Players,p_new_field){
  Players<-data.frame(id = 1:N_Players, alive=rep(1,N_Players),Field=0)
  
    for(i in 1:N_Players){
      while (Players[i,"alive"]==TRUE && max(Players$Field)< N_Fields) { 
        Players[i,"Field"]=Players[i,"Field"]+1  # Jump onto the next Field
        Players[i,"alive"]=rbinom(1,1,p_new_field)# Fall or repeat
      }
      Players[i+1,"Field"]=Players[i,"Field"] # next player starts where prior player died
    }
  Players<-Players[1:N_Players,] # cosmetic because i do i+1 in the prior line
  # Print me some messages
  if(!any(Players$alive>0)){
      cat("Players loose!")
    } else {
    cat(" \n After", max(Players$Field),"goal was reached! ")
    cat("Players",Players[Players$alive==1,"id"], "survive")
    }
  
  return(Players)
}


squidd7(18,16,0.5)

###########
# simulation ○ △ □
###########
results<-data.frame(matrix(0, nrow = 100, ncol = 20))
for(x in 1:ncol(results)){
     for (i in 1:nrow(results)) {
    Players<-squidd7(x+7,16,0.5)
    results[i,x]<-sum(Players$alive)
  }
}
###########
## Results ○○□□○ △ □
sdt<-apply(results,2,sd) # standart devation 
mn<-apply(results,2,mean) # ○ △ □

boxplot(results,xlab ="n Steps ",names = 8:27,ylab="N Survivors of 16 ")
points(mn,type="l")
points(sdt,type="l")

colors<-colorRampPalette(c(rgb(0,1,0,0.4),
                           rgb(1,1,0,0.4),
                           rgb(1,0,0,0.4)), alpha = TRUE)(21)


plot(density(results$X1),type="n",xlim=c(-1,17),ylim=c(0,0.30),
     main="○ △ □ ",
     sub="○ △ □ ○ △ □ ○ △ □",
     xlab="number of survivors")
for( i in 1:21){
polygon(density(results[,i]),col= colors[i])
}
legend(15,0.31,title="Steps",legend=8:28,fill=colors,border = NA,
       y.intersp = 0.5,
       cex = 0.8, text.font = 0.3)