genshin impact wish simulator (DTMC)

# Genshin Impact wish simulator
# "Walking through wish space, 160 primos at a time"

# Based on a discrete-time Markov chain.
# Essentially a dumbed-down version of gacha in Genshin.
# TODO: actually make banners and add names
# TODO: simulate losing and winning 50/50, useful for event banners.

init <- function() { # Reset the simulator.
  x <<- 0 # 4* pity
  y <<- 0 # 5* pity
  vx <<- c() # vector for tallying 4* pity
  vy <<- c() # vector for tallying 5* pity
  vt <<- c() # vector for showing the tier of item obtained
}

wishonce <- function() { # Use one wish.
  iter() # iterate once; takes care of vt.
  vx <<- append(vx,x) # add new x
  vy <<- append(vy,y) # and new y
}

wish <- function(w) { # Use w wishes.
  for (i in 1:w) {
    wishonce() # this takes care of vx and vy as well
  }
}


iter <- function() { # Iterate once.
  r <- runif(1,0,1) # Draw a random number, uniformly dist. on [0,1]
  if(x < 9 && y < 89) {
     if(r <= .943) { # getting a 3*
       x <<- x + 1
       y <<- y + 1
       vt <<- append(vt,3)
     } else if(r <= .994) { # getting a 4*
       x <<- 0
       y <<- y + 1
       vt <<- append(vt,4)
     } else { # getting a 5*
       x <<- x + 1
       y <<- 0
       vt <<- append(vt,5)
     }
  } else if(x >= 9 && y < 89) {
    if(r <= .994) { # getting 4* by hard pity
      x <<- 0
      y <<- y + 1
      vt <<- append(vt,4)
    } else { # getting a 5*
      x <<- x + 1
      y <<- 0
      vt <<- append(vt,5)
    }
  } else if(y == 89) { # getting a 5* by hard pity
    x <<- x + 1
    y <<- 0
    vt <<- append(vt,5)
  } else { # do nothing... this shouldn't happen.
    print("Something is off!")
    vt <<- append(vt,0)
  }
}

init() # and make sure to init the sim!