# R script to simulate chain length during a UASF chain split

# 0. Variables
t <- 60 # time in minutes when to calculate the likelihood of a reorg
n <- 1000 # number of times the simulation runs
p <- 20 # minority UASF chain in percentage points


# 1. Create vectors
chaina <- 1:n
chainb <- 1:n

# 2.1 Minority chain length simulation
for (i in 1:length(chaina)) {

  observationa <- rexp(n,1/(1000/p)) # exponential function to calculate block arrive intervals
  cumulativea <- 1:n # create vector

  for (j in 1:length(observationa)){
    cumulativea[j] <- sum(observationa[1:j])
  } # sum up block arrival intervals

  chaina[i] <- min(which(cumulativea[] > t))
} # check how long the chain is at time t

# 2.2 Majority chain length simulation
for (i in 1:length(chainb)) {

  observationb <- rexp(n,1/(1000/(100-p)))
  cumulativeb <- 1:n

  for (j in 1:length(observationb)){
    cumulativeb[j] <- sum(observationb[1:j])
  }

  chainb[i] <- min(which(cumulativeb[] > t))
}

# 3. Compare the two chains
all <- data.frame(chaina, chainb)
all$x <- ifelse(chaina > chainb, TRUE, FALSE)
sum(all$x == TRUE)

# Notes:
# The script only compares the chain lengths.
# There is also the chance that a chain re-organized well before time t
# Therefore this script systematically UNDERESTIMATES the chance of a re-org

# @LeoAW https://liongrass.hk