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tft_reroll_calcs.R
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tft_reroll_calcs.R
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#' ---
#'Title: TFT Reroll Calculations (Set 8)
#'Author: Richard Liu
#'Output: PDF
#'---
rm(list = ls())
library(itertools2)
library(data.table)
library(dplyr)
library(ggplot2)
library(readxl)
library(openxlsx)
library(randtests)
library(Matrix)
library(matrixcalc)
library(RColorBrewer)
# ================ SET POOL STATS FOR CURRENT PATCH ==============
UnitPoolSize <- as.matrix(c(29, 22, 18, 12, 10))
colnames(UnitPoolSize) <- "Unit Copies Per Tier"
rownames(UnitPoolSize) <- 1:5
NumUnits <- as.matrix(c(13, 13, 13, 12, 8))
rownames(NumUnits) <- 1:5
colnames(NumUnits) <- "Unique Units Per Tier"
ExpToLevel <- c(0, 2, 6, 10, 20, 36, 56, 80, 0)
ShopProbMat <- matrix(c(1, 0, 0, 0, 0,
1, 0, 0, 0, 0,
.75, .25, 0, 0, 0,
.55, .3, .15, 0, 0,
.45, .33, .2, .02, 0,
.25, 0.4, .3, .05, 0,
.19, .30, .35, .15, .01,
.16, .20, .35, .25, .04,
.09, .15, .3, .3, .16),
nrow=9, ncol=5, byrow=T, dimnames=list(1:9, 1:5))
# ================ DEFINE HELPER FUNCTIONS ===============
# Generate ordered list of keys for all unit permutations given vector of how many looking for
# Current implemented conditions: "any" and "all"
# To get all absorbing states at the end: start with the base order {(0,0), (0,1), ..., (1,0)} (reversed StarscapeTFT)
# then take all absorbing permutations and throw them to the end with the same general ordering
getOrderedPermutations <- function(lookingfor, condition="any"){
if(!is.numeric(lookingfor)){
stop("Expected numeric vector")
}
final_lookingfor <- lookingfor
rangeslist <- lapply(final_lookingfor, function(x) seq(0,x))
perms <- do.call(iproduct, rangeslist) # Default ordering is fine
perms_df <- do.call(rbind, as.list(perms))
perms_df <- data.table(perms_df)
# Absorbing vector conditions
if(condition == "any"){
absorb_inds <- apply(perms_df[, 1:ncol(perms_df)], 1, function(x) any(x >= lookingfor))
}
else if(condition == "all"){
absorb_inds <- apply(perms_df[, 1:ncol(perms_df)], 1, function(x) all(x >= lookingfor))
}
else if(grepl("any", condition, fixed=T)){ # any "n" hit condition
num <- as.numeric(trimws(sub("any ", "", condition, fixed=T)))
absorb_inds <- apply(perms_df[, 1:ncol(perms_df)], 1, function(x) sum(x >= lookingfor) >= num)
}
else{ stop("This termination condition has not been implemented yet!") }
# print(perms_df)
# print(absorb_inds)
# print(lookingfor)
# print(perms_df[!absorb_inds,,drop=F])
# stop()
# Move absorbing rows to the end
perms_df_ordered <- rbind(perms_df[!absorb_inds,,drop=F], perms_df[absorb_inds,,drop=F]) # Drop=F against 1-col edge case
absorb_cutoff_ind <- nrow(as.data.frame(perms_df[!absorb_inds,,drop=F])) + 1
# Convert to array of character vectors
perms_char <- as.vector(apply(perms_df_ordered, 1, paste0, collapse=","))
return(list(perms_char, absorb_cutoff_ind))
}
# Define function for computing transition probability
getStepTransitionProb <- function(base_state, step_state, player_lvl, unit_lvl, num_taken_unit, num_taken_other_unit,
ShopProbMat, UnitPoolSize, NumUnits){
state_diff <- step_state - base_state
# If step size 0, return error (0 step is 1-sum(all steps))
if(sum(state_diff) == 0){
stop("getStepTransitionProb: Don't make me compute the 0-step it's too hard!")
}
# If chosen step, then allow step size of 3
if(sum(state_diff) != 1){
return(0)
} else{ # Default is step size of 1
unit_ind <- which(state_diff == 1)
}
# Compute probability of step
total_pool_lvl <- UnitPoolSize[unit_lvl] * NumUnits[unit_lvl] - num_taken_unit - num_taken_other_unit - base_state[unit_ind]
units_left <- UnitPoolSize[unit_lvl]-num_taken_unit-base_state[unit_ind]
# Edge cases: total pool lvl size is 0, units left is negative
# Default return 0
if (total_pool_lvl <= 0){
return(0)
} else if(units_left < 0){
return(0)
}
step_prob <- ShopProbMat[player_lvl, unit_lvl] * units_left/total_pool_lvl
return(step_prob)
}
# Computes the complete number of "other" units taken from a lvl pool, including the other searched-for units
# of the same level.
getStatePoolTakenOther <- function(perm_num, unit_lvls, unit_index, num_taken, num_taken_other){
unit_lvl <- unit_lvls[unit_index]
other_inds <- which(unit_lvls == unit_lvl) # Will find at least one
other_inds <- other_inds[other_inds != unit_index]
if(length(other_inds) == 0){
return(num_taken_other[unit_lvl])
}
else{
base_taken <- sum(num_taken[other_inds])
state_taken <- sum(perm_num[other_inds])
tot_taken <- base_taken + state_taken + num_taken_other[unit_lvl]
return(tot_taken)
}
}
# Generalized function for 1 slot transition matrix
# Matrix[0,0] will represent the initial state (set by user)
createOneSlotMatrix <- function(ordered_perms, absorb_cutoff, player_lvl, unit_lvls, num_taken, num_taken_other, initial_state,
ShopProbMat, UnitPoolSize, NumUnits){
mat_dim <- length(ordered_perms)
one_slot_transition_mat <- matrix(rep(0, mat_dim^2), nrow=mat_dim,ncol=mat_dim)
# Adjust num_taken by initial_state
num_taken <- num_taken + initial_state
# Set matrix row and column names
row.names(one_slot_transition_mat) <- ordered_perms
colnames(one_slot_transition_mat) <- ordered_perms
# Fill out probabilities one section at a time
# Absorbed states: identity matrix
for(i in absorb_cutoff:nrow(one_slot_transition_mat)){
one_slot_transition_mat[i,i] <- 1
}
# Other transitions: Q and R
# Loop through string permutations and get list of feasible steps (max 1 step away from any state)
# Then set probability based on pool size, lvl, and num units out
for(perm in ordered_perms[1:absorb_cutoff-1]){
perm_num <- charPermToNumeric(perm)
# Set of feasible steps is just +1 to any element, within the permutation bounds
for(i in 1:length(perm_num)){
# Edge case: perm num is length 1
if(i < 1){
next
}
stepi <- perm_num
stepi[i] <- stepi[i] + 1
stepi_char <- paste0(stepi, collapse=",")
if (!(stepi_char %in% colnames(one_slot_transition_mat))){
next
}
# Compute probability of step and assign to matrix
unit_lvl_i <- unit_lvls[i]
num_taken_i <- num_taken[i]
num_taken_other_i <- getStatePoolTakenOther(perm_num, unit_lvls, i, num_taken, num_taken_other)
# Check if proposed step is within bounds
one_slot_transition_mat[perm, stepi_char] <- getStepTransitionProb(perm_num, stepi, player_lvl,
unit_lvl_i, num_taken_i,
num_taken_other_i, ShopProbMat,
UnitPoolSize, NumUnits)
}
# 0 step is just 1 - sum of all other steps
one_slot_transition_mat[perm, perm] <- 1 - sum(one_slot_transition_mat[perm,])
}
return(one_slot_transition_mat)
}
# Fundamental Matrix: expected number of visits to state j starting from state i before being absorbed
# Input: Q matrix (sub-matrix of absorbing Markov chain with absorbing rows/cols removed)
# Formula: (I-Q)^-1
# Expected number of steps before being absorbed when starting in state i = sum of row i
getFundamentalMatrix <- function(Q){
id_mat <- diag(nrow(Q))
fund_mat <- solve(id_mat - Q)
return(fund_mat)
}
# Compute probability of going from one state to the other in N steps
getNStepProb <- function(oneslotmat, state1_num, state2_num, N){
Nstepmat <- matrix.power(oneslotmat, N)
state1_ind <- paste0(state1_num, collapse=",")
state2_ind <- paste0(state2_num, collapse=",")
return(Nstepmat[state1_ind, state2_ind])
}
# PDF: Prob hit in exactly N slots f(k) = Q^(k-1)R (makes sense: odds of getting to step before then hitting)
# CDF: Prob hit within N slots F(k) = 1 - Q^k_1_ (Can also be sum of absorbed states for Q^k)
generateDistributionData <- function(oneslotmat, absorb_cutoff){
Q <- oneslotmat[1:absorb_cutoff-1, 1:absorb_cutoff-1]
T0 <- oneslotmat[1:absorb_cutoff-1,absorb_cutoff:ncol(oneslotmat)] # 1-step probs to absorption
cdf_probs <- c()
# Generate CDFs up until 99%: PDF(k) = CDF(k) - CDF(k-1)
i <- 1
cdf_i <- 0
generate <- T
cdf_mat <- oneslotmat
while(generate){
if (cdf_i >= 0.99 | i == 500){ # Cap at 500 calcs
if (i %% 5 == 0){# Enforce multiple of 5 for shops calc
generate <- F
}
}
cdf_i <- sum(cdf_mat[1,absorb_cutoff:ncol(cdf_mat)])
cdf_probs <- c(cdf_probs, cdf_i)
cdf_mat <- cdf_mat %*% oneslotmat
i <- i+1
}
cdf_data <- setDT(data.frame("CDF" = cdf_probs, "Step" = 1:length(cdf_probs)))
cdf_data$PDF <- cdf_data$CDF - shift(cdf_data$CDF)
cdf_data$PDF[1] <- cdf_data$CDF[1] # At the first step the CDF and PDF are the same
# Create indicator for 25-75 percentile
cdf_data$Perc_Range <- as.numeric(cdf_data$CDF >= 0.25 & cdf_data$CDF <= 0.75)
cdf_data[CDF > .75, Perc_Range := 2,]
return(cdf_data)
}
# Plots PDF by different aggregations: gold, shops, identity
# Imitate StarscapeTFT's pretty graphs and color the 25% to 75% CDF region
plotPDF <- function(distribution_data, x_by){
if(x_by == "identity"){ # Plot data as is
plt <- ggplot(data=distribution_data, aes(x=Step, y=PDF)) + geom_bar(aes(fill=factor(Perc_Range)), stat="identity", width=1) +
labs(x="Shop Slots", y="Probability of Hitting", title="PDF: P(Hit) vs # Shop Slots") +
scale_x_continuous(breaks=scales::pretty_breaks(n=10)) +
scale_fill_manual(name="Percentile Ranges", labels=c("<25%", "25%-75%", ">75%"), values=c("#293352", "#3A75A2", "#3DBFFE"),
limits=c(0,1,2))
return(plt)
}
else if(x_by == "Gold"){
grouped_dat <- distribution_data[,.(PDF=sum(PDF), Perc_Range=round(mean(Perc_Range))), Step-0:4] # 5 shops every 2 gold
grouped_dat$Gold <- 1:nrow(grouped_dat)
gold_breaks <- pretty(seq(0,tail(grouped_dat$Gold,1)), n=10)
gold_labels <- as.character(2*gold_breaks)
plt <- ggplot(data=grouped_dat, aes(x=Gold, y=PDF)) + geom_bar(aes(fill=factor(Perc_Range)), stat="identity", width=1) +
labs(x="Gold", y="Probability of Hitting", title="PDF: P(Hit) vs Gold Spent") +
scale_x_continuous(breaks= gold_breaks, labels=gold_labels) + #Hacky way but works for our purposes
scale_fill_manual(name="Percentile Ranges", labels=c("<25%", "25%-75%", ">75%"), values=c("#293352", "#3A75A2", "#3DBFFE"),
limits=c(0,1,2))
return(plt)
}
else if(x_by == "Shops"){
grouped_dat <- distribution_data[,.(PDF=sum(PDF), Perc_Range=round(mean(Perc_Range))), Step-0:4] # 5 shops every 2 gold
grouped_dat$Shops <- 1:nrow(grouped_dat)
plt <- ggplot(data=grouped_dat, aes(x=Shops, y=PDF)) + geom_bar(aes(fill=factor(Perc_Range)), stat="identity", width=1) +
labs(x="Shops", y="Probability of Hitting", title="PDF: P(Hit) vs # Shops") +
scale_x_continuous(breaks=scales::pretty_breaks(n=10)) +
scale_fill_manual(name="Percentile Ranges", labels=c("<25%", "25%-75%", ">75%"), values=c("#293352", "#3A75A2", "#3DBFFE"),
limits=c(0,1,2))
return(plt)
}
else {
stop(paste("Have not implement by", x_by, "yet!", sep=" "))
}
}
plotCDF <- function(distribution_data, x_by){
if(x_by == "identity"){ # Plot data as is
plt <- ggplot(data=distribution_data, aes(x=Step, y=CDF)) + geom_bar(aes(fill=factor(Perc_Range)), stat="identity", width=1) +
labs(x="Shop Slots", y="Probability of Hitting", title="CDF: P(Hit) vs # Shop Slots") +
scale_x_continuous(breaks=scales::pretty_breaks(n=10)) +
scale_fill_manual(name="Percentile Ranges", labels=c("<25%", "25%-75%", ">75%"), values=c("#293352", "#3A75A2", "#3DBFFE"),
limits=c(0,1,2))
return(plt)
}
else if(x_by == "Gold"){
grouped_dat <- distribution_data[,.(CDF=max(CDF), Perc_Range=round(mean(Perc_Range))), Step-0:4] # 5 shops every 2 gold
grouped_dat$Gold <- 1:nrow(grouped_dat)
gold_breaks <- pretty(seq(0,tail(grouped_dat$Gold,1)), n=10)
gold_labels <- as.character(2*gold_breaks)
plt <- ggplot(data=grouped_dat, aes(x=Gold, y=CDF)) + geom_bar(aes(fill=factor(Perc_Range)), stat="identity", width=1) +
labs(x="Gold", y="Probability of Hitting", title="CDF: P(Hit) vs Gold Spent") +
scale_x_continuous(breaks= gold_breaks, labels=gold_labels) + #Hacky way but works for our purposes
scale_fill_manual(name="Percentile Ranges", labels=c("<25%", "25%-75%", ">75%"), values=c("#293352", "#3A75A2", "#3DBFFE"),
limits=c(0,1,2))
return(plt)
}
else if(x_by == "Shops"){
grouped_dat <- distribution_data[,.(CDF=max(CDF), Perc_Range=round(mean(Perc_Range))), Step-0:4] # 5 shops every 2 gold
grouped_dat$Shops <- 1:nrow(grouped_dat)
plt <- ggplot(data=grouped_dat, aes(x=Shops, y=CDF)) + geom_bar(aes(fill=factor(Perc_Range)), stat="identity", width=1) +
labs(x="Shops", y="Probability of Hitting", title="CDF: P(Hit) vs # Shops") +
scale_x_continuous(breaks=scales::pretty_breaks(n=10)) +
scale_fill_manual(name="Percentile Ranges", labels=c("<25%", "25%-75%", ">75%"), values=c("#293352", "#3A75A2", "#3DBFFE"),
limits=c(0,1,2))
return(plt)
}
else {
stop(paste("Have not implement by", x_by, "yet!", sep=" "))
}
}
# Function to check any possible nonsense with the requested scenario
# Output: list(TRUE/FALSE, error message)
validateScenario <- function(player_lvl, num_taken_other, unit_lvls, num_taken, lookingfor, initial_state,
ShopProbMat, UnitPoolSize, NumUnits, chosen){
# == Validate base data first ==
# Check if base data completely filled out
if (any(is.na(ShopProbMat)) | any(is.na(UnitPoolSize)) | any(is.na(NumUnits))){
return(list(FALSE, "Please finish filling out the pool size and reroll probabilities."))
}
# Reroll probabilities must be non-negative
if (any(ShopProbMat < 0)){
return(list(FALSE, "Reroll probabilities must be non-negative."))
}
# Reroll probabilities must sum to 1 per level
if (!(all(rowSums(ShopProbMat) == 1))){
faulty_reroll_rows <- which(rowSums(ShopProbMat) != 1)
faulty_reroll_char <- paste0(faulty_reroll_rows, collapse=", ")
return(list(FALSE, paste("Reroll probabilities must sum to 1. Please adjust for level(s):", faulty_reroll_char)))
}
# Unit pool size must be positive
if (any(UnitPoolSize <= 0)){
return(list(FALSE, "Unit pool sizes must all be positive."))
}
# Num units must be positive
if (any(NumUnits <= 0)){
return(list(FALSE, "Number of units must all be positive."))
}
# Check if unit pool size large enough
unit_availability_check <- sapply(1:length(unit_lvls), function(x)
(num_taken[x] + lookingfor[x] + initial_state[x]) <= UnitPoolSize[unit_lvls[x]])
if (!all(unit_availability_check)){
faulty_unit_ind <- which(!unit_availability_check)
unit_ind_char <- paste0(faulty_unit_ind, collapse = ", ")
return(list(FALSE, paste("Can't hit copies of units that don't exist. Please adjust the 'Copies Others Own' and",
"'Total Copies Wanted' fields for unit(s):",
unit_ind_char)))
}
# Check if tier pool size large enough
tier_taken <- num_taken_other
for (i in 1:length(unit_lvls)){
unit_lvl <- unit_lvls[i]
tier_taken[unit_lvl] <- tier_taken[unit_lvl] + num_taken[i] + lookingfor[i] + initial_state[i]
}
tier_pool_check <- sapply(1:length(tier_taken), function(x) tier_taken[x] <= UnitPoolSize[x]*NumUnits[x])
if (!all(tier_pool_check)){
faulty_tier <- which(!tier_pool_check)
tier_char <- paste0(faulty_tier, collapse = ", ")
return(list(FALSE, paste("Your scenario involves more units than exist in the tier pools. Please adjust the scenario for tier(s):",
tier_char)))
}
# All unique units being looked for are excluded from the num_taken_other count
other_taken <- num_taken_other
for (i in 1:length(unit_lvls)){
unit_lvl <- unit_lvls[i]
other_taken[unit_lvl] <- other_taken[unit_lvl] + UnitPoolSize[unit_lvl]
}
other_taken_check <- sapply(1:length(other_taken), function(x) other_taken[x] <= UnitPoolSize[x]*NumUnits[x])
if (!all(other_taken_check)){
faulty_tier <- which(!other_taken_check)
tier_char <- paste0(faulty_tier, collapse = ", ")
return(list(FALSE, paste("You currently have too many units taken out of the pool,",
"given the number of units you are looking for, for tier(s):",
tier_char)))
}
# Check if player level adequate for unit level
available_unit_lvls <- which(ShopProbMat[player_lvl,] > 0)
player_lvl_check <- sapply(unit_lvls, function(x) x %in% available_unit_lvls)
if (!all(player_lvl_check)){
fauly_unit_ind <- which(!player_lvl_check)
faulty_unit <- paste0(fauly_unit_ind, collapse = ", ")
return(list(FALSE, paste("Player level too low to hit unit(s):", faulty_unit)))
}
# Check if total looking for is non-positive
positive_check <- sum(lookingfor) > 0
if (!positive_check){
return(list(FALSE, paste("Please select a positive number of copies to hit.")))
}
return(list(TRUE, "passed validation!"))
}
charPermToNumeric <- function(perm){
return(as.numeric(unlist(strsplit(perm, ","))))
}
getExpToLevel <- function(lvl, ExpToLevel){
return(ExpToLevel[lvl])
}
# Use fundamental matrix to get the expected number of shops before hitting
getExpectedShopsToHit <- function(oneslotmat, absorb_cutoff){
q <- oneslotmat[1:absorb_cutoff-1, 1:absorb_cutoff-1]
# Check if q is scalar
if (length(q) == 1){
expected_slots <- 1/(1-q)
expected_shops <- round(expected_slots/5)
}
else{
fundamental_mat <- getFundamentalMatrix(q)
expected_slots <- sum(fundamental_mat[1,]) + 1
expected_shops <- round(expected_slots/5)
}
return(expected_shops)
}
# ======================== TESTING =======================
# player_lvl <- 4
# num_taken_other <- c(0,0,0,0,0) # this is ordered by level
# unit_lvls <- c(1,1,1)
# num_taken <- c(6,6,6)
# lookingfor <- c(1,1,1) # THIS IS NOW LOOKING FOR ON TOP OF INITIAL STATE INSTEAD OF TOTAL
# condition <- "all"
# initial_state <- c(3,3,3)
#
# test_validate <- validateScenario(player_lvl, num_taken_other, unit_lvls, num_taken, lookingfor, initial_state,
# ShopProbMat, UnitPoolSize, NumUnits)
# print(test_validate[[2]])
#
# ordered_ret <- getOrderedPermutations(lookingfor, condition)
# ordered_perms <- ordered_ret[[1]]
# absorb_cutoff <- ordered_ret[[2]]
# one_slot_transition_mat <- createOneSlotMatrix(ordered_perms, absorb_cutoff, player_lvl, unit_lvls, num_taken, num_taken_other, initial_state,
# ShopProbMat, UnitPoolSize, NumUnits)
#
# # Q <- one_slot_transition_mat[1:absorb_cutoff-1, 1:absorb_cutoff-1]
# n_shops <- getExpectedShopsToHit(one_slot_transition_mat, absorb_cutoff)
#
# # Test pdf plots
# dist_data <- generateDistributionData(one_slot_transition_mat, absorb_cutoff)
# plotCDF(dist_data, x_by="Shops")
# plotPDF(dist_data, x_by="Shops")
#
# # Test chosen hit conditions -------------------------
# test_validate <- validateChosenScenario(player_lvl, num_taken_other, unit_lvls, num_taken, initial_state,
# ChosenProbMat, UnitPoolSize, NumUnits, chosen)
# print(test_validate[[2]])
# expected_shops <- getChosenExpectedShopsToHit(initial_state, player_lvl, unit_lvls, num_taken, num_taken_other,
# ChosenProbMat, UnitPoolSize, NumUnits, ChosenProb)
#
# # Test pdf plots
# dist_data <- generateChosenDistributionData(initial_state, player_lvl, unit_lvls, num_taken, num_taken_other,
# ChosenProbMat, UnitPoolSize, NumUnits, ChosenProb)
# plotCDF(dist_data, x_by="Shops")
# plotPDF(dist_data, x_by="Shops")