R中的蒙特卡罗骰子模拟

Question

Hi I am trying to solve a problem where a player has $10. A coin is flipped, if the player calls it correctly he earns $1, if he is incorrect he loses $1. What are the odds that he will reach $0 before he reaches $20? How long on average does the game last? How much does he have on average after 25 flips? I am supposed to use a Monte Carlo Method in R to code for this, but I am a beginner and not totally sure where to start-- here's what i was thinking

game <- function() {
x=10 ## $10
y=0 ## number of times player gets $20
z =0 ## number of times player loses money
 result<- sample(1:2,1, replace = TRUE)
if (result==1) {
x=x+1 } ## money goes up, 1 represents player calling correct coin
else{
x=x-1 }
if (x= 20) { 
y = y+1} ### dont know how to stop trials
if(x=0){
z=z+1}

I am pretty lost on how to code this but here is an idea. Basically i want to simulated a 50/50 simulation and see how often y occurs and z occurs. I'm not sure how to run a certain number of trials or stop when i reach 20 or 0.... Thanks for any help.

Answer 1

Ahh, a version of theGambler's Ruin .

Anyhow, it seems as if you have yet to use loops (like for and while ) in R, which is strange since it is quite far in the semester.

The below will enable you to run the simulation to answer your questions.

# Set configuration
money = 10  # $10

B = 100         # Number of games to play

y = 0           # Number of times player gets $20 from ALL games run
z = rep(0, B)   # Number of times player loses money per game
r = rep(0, B)   # Number of rounds played per game
a = rep(0, B)   # Value on the 25th turn per game (not the average!)

# Start playing games!
for(i in 1:B){

  # Reset settings for each game. 

  # Make it reproducible by setting a seed. 
  set.seed(1337+i)

  # Set Counter
  count = 1

  # Set game
  x = money

  while( x > 0 ){

    # Perform the draw
    result = sample(1:2,1, replace = TRUE)

    # 1 means the player wins!
    if(result == 1) {
      x = x + 1 

    } else { # 2 - The player loses!
      x = x - 1 

      # Increment Player Loss
      z[i] = z[i] + 1
    }

    # Increase round calculation
    r[i] = r[i] + 1

    count = count + 1

    # After 25 flips, how much is left? 
    if(count == 25){
      a[i] = x
    }

    # Reset to zero? 
    if(x == 20){
      y = y + 1

      # End game
      break;
    }

  }

}