Playset_Drawing_Testing.R

#Playset Drawing Simulations (to determine how best to model ICR chances for rare playsets)
#Written: 2021-0704 by Emil Karpinski

#Setting up some variables
#cards - tracks the cards that have been obtained in each method (no duplicates)
#ItCount - tracks how many random ICRs were needed to complete each set (i.e. 1:100 x 4 in the Four_Off method; 1:400 x 1 in the Individual Card method)
#Iteration - tracks how many times you've gotten an ICR
#i and a - general all purpose counters for the while and for loops

cards <- vector()
ItCount <- vector()
iteration <- 0
i <- 0

#Does 1000 simulations tracking the time needed to obtain a set of 100 rares (in full playsets, 4 of each). This is done two ways.
#The first way simulates more closely the actual game. It requires you to collect 4x 100 rares, represented by the numbers 1:100 (i.e. requires four instances of the value 1, four instances of the value 2, ..., four instances of the value 100).
#The second way treats each rare as unique; so the first rare playset requires values 1, 2, 3, and 4. This way is easier to code, but takes longer.

#Sets up the loop for the 1000 simulations
for (a in 1:10000)
{
  #Runs until the set is complete - denoted by the flag (i) changing from 0 to 1
  while (i < 1)
  {
    #Counts how many times we've been through this loop. i.e. how many times have we drawn a card and checked if we have it     or not.
    iteration <- iteration + 1

    #Samples a random number from 1:100 (where 100 is the number of rares). Replace does nothing here.
    x <- sample(1:100, 1, replace=T)

    #Checks if the chosen number has been drawn less than 4 cards. If so then it adds that entry to the list of cards drawn (cards vector).
    #Then checks to see if there are 400 entries in that vector (which would denote a full playset of all 100 rares). If so it trips the i flag to leave the loop.
    if (sum(cards == x) < 4)
    {
      cards <- c(cards,x)

      #Records the iterations at which unique cards (i.e. those for which we don't have a playset are drawn)


      if (length(cards) == 400)
      {
        i <- 1
      }
    }

  }

  #Extends the vector ItCount (stores the number of draws it took to get a full playset - i.e. iteration), and adds the last value of iteration to it.
  ItCount <- c(ItCount, iteration)

  #Cleans up the cards vector (sets it to empty), sets iterations to 0, and resets the flag to re-enable the while loop.
  cards <- vector()
  iteration <- 0
  i <- 0
}

#Since I copied and pasted the above in the below version, I'm just creating a new vector here (Four_Off_Comp_Count) to store the values within ItCount so I don't need to Ctrl+F and replace it in the loops below. Then wipe ItCount so it can be used in the second batch of simulations.
Four_Off_Comp_Count <- ItCount
ItCount <- vector()

#Sets up the loop for 1000 simulations
for (b in 1:10000)
{
  #As before
  while (i < 1)
  {
    #As before, but not sampling from the numbers 1:400 with sets of 4 representing a playset.
    x <- sample(1:400, 1, replace=T)

    #As before, but checks if that number is present. If it isn't it's added, and we check to see all 400 unique entries are present. If so the i flag gets set     to 1 to escape the loop.
    if (sum(cards == x) < 1)
    {
      cards <- c(cards,x)

      if (length(cards) == 400)
      {
        i <- 1
      }
    }
    #Regardless iterations are increased by 1
    iteration <- iteration + 1
  }

  #Stores the number of cards you needed to draw to get a complete set of 400 rares.
  ItCount <- c(ItCount, iteration)

  #Resets everything like before
  cards <- vector()
  iteration <- 0
  i <- 0

}
#For consistencies sake, also outputting the values in ItCount to a vector for this method, then wiping it.
Ind_Card_Comp_Count <- ItCount
ItCount <- vector()

#outputs some basic summary stats for the two approaches.
summary(Four_Off_Comp_Count)
summary(Ind_Card_Comp_Count)

plot(Four_Off_Comp_Count, type = "p", xlab = "Simulation Number", ylab = "Iterations", main = "Draws until Rare Completion", col = "blue", ylim = c(400,6000))
points(Ind_Card_Comp_Count, col = "red")

lines(c(c(1:10000)), rep(mean(Four_Off_Comp_Count), 10000), col = "yellow", lwd = 3)
lines(c(c(1:10000)), rep(mean(Ind_Card_Comp_Count), 10000), col = "green", lwd = 3)