lottery.jl

### A Pluto.jl notebook ###
# v0.19.27

#> [frontmatter]
#> title = "Hotspot Analysis"
#> date = "2023-08-24"

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ bd481c9c-352b-11ee-2340-1d554ffed22a
using XLSX

# ╔═╡ ea4f446e-2a32-4b33-b202-0ee906a1fc26
using DataFrames

# ╔═╡ a487c1a4-19ba-4ac0-b593-0bf3fc6fcf77
using Plots

# ╔═╡ 8cf48b45-64fd-477d-a569-0c5fd182c89b
using Pipe

# ╔═╡ a784788c-6b14-4cba-be69-ff386c6ea702
using Statistics

# ╔═╡ 20568aff-1720-4dd0-ba88-e75ee2d2b711
using Distributions

# ╔═╡ 0c539612-0de0-4f06-87a8-7fbe9d3136ea
using StatsPlots

# ╔═╡ 9fd349a9-4133-479c-ae75-d8335c038b37
using HypothesisTests

# ╔═╡ 2abd4d89-6c36-431f-95cc-b83889e2ef0b
using Glob

# ╔═╡ cb4b7e67-d3cd-4407-b310-94ab9b2cf527
using PlutoUI

# ╔═╡ d9f5fae6-867c-4c35-9b4a-feed1840bd24
using Dates

# ╔═╡ 47f7ffef-9f69-4a08-afb3-d541b429e1b1
using SHA

# ╔═╡ ca3e1383-a461-4c14-86c4-ab1ab9694aeb
using Formatting

# ╔═╡ 42a7a1cf-e636-4e34-8ca8-c3456a5bf54e
using StatsBase

# ╔═╡ 663877a2-f975-4bfa-a88f-977a0c3c9204
md"""
# Exhibit: Analysis of Randomness of Hot Spot Results
Neal Fultz, <neal@njnm.co>
"""

# ╔═╡ 63de8a85-fcdd-4823-996b-1acaf9082ac9
md"""
## Preamble
"""

# ╔═╡ 19ac3edc-455b-48b4-aad5-3abc189de685
HTML("""
<style>
@media print {
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	body :has(#noprintcode:checked) pluto-input {
		display:none !important
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	body :has(#noprintmd:checked) pluto-cell :has(div.markdown) + pluto-input {
		display:none !important
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	div.cm-editor div[aria-live="polite"]  {
		display:none !important
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}
</style>
<div class=noprint>
    <header> Extra print options</header>
    <input type="checkbox" id="noprintempty" name="noprintempty" checked />
    <label for="noprintempty">Hide empty output</label>
    <input type="checkbox" id="noprintmd" name="noprintmd" checked />
    <label for="noprintmd">Hide markdown code</label>
    <input type="checkbox" id="noprintcode" name="noprintcode"  />
    <label for="noprintcode">Hide *all* code</label>
</div>
""")

# ╔═╡ 142a4519-3228-42b8-84bb-43b4c759c74b
md"""
Select a data file:
"""

# ╔═╡ 90a7d7d7-f973-462b-a46c-e7801bdf277d
@bind xlsx  Select(glob("*.xlsx"))

# ╔═╡ 4cff819e-677b-4340-b40e-65c1172fe1c6
begin
	checksum = open(xlsx) do f
		bytes2hex(sha2_256(f))
	end
	md""
end

# ╔═╡ ca48fd62-8e6b-4d02-ba48-dd9ade8c1638
begin 
	df = DataFrame(XLSX.readtable(xlsx, 1))
	rename!((x) -> replace(x, r"\s" => "_"), df)
	N = nrow(df)
	first, last = df.Draw_Date[1], df.Draw_Date[N]

	# Fix types for specific draws
	for j in 1:20
		if eltype(df[!, 4+j]) == Any
			df[!, 4+j] = parse.(Int, df[!, 4+j])
		end
	end
	
	md""
end

# ╔═╡ 20b19473-c99e-4077-aa53-d100717da9d2
md"""
* using $xlsx
* SHA2-256: $(checksum)
* Analyzing $N draws from $first - $last
* Executed on $(Dates.today())
"""

# ╔═╡ f77d8762-ebe5-4552-adb6-86a92dc805e8
md"""
## Exploratory Data Analysis

"""

# ╔═╡ 60af1b15-d99e-43ff-8ad7-d16a5b376132
md"""
### Distribution of Winning Numbers over Spots 
"""

# ╔═╡ 35d0869d-7eb0-492a-8ff8-6974a2ce2cb9
begin
	m = zeros(Int, 20, 80)
	for j in 1:20
		for i in 1:nrow(df)
			m[j,df[i,4+j]] += 1
		end
	end
	md""
end

# ╔═╡ 16661133-822a-4241-967e-eaeae2de5850
heatmap(m, xaxis=("Win Number"), yaxis=("Spot"), c=[:yellow, :blue, :red])

# ╔═╡ 889951a9-a704-4f90-9a28-0b2a8f736291
begin
	cov11 = 1 - mean( round(N*1/80 - 1.96*sqrt(1/80*79/80*N), RoundDown) 
						.<= m .<
					  round(N*1/80 + 1.96*sqrt(1/80*79/80*N), RoundUp)
				)
	cov11 = sprintf1("%6.3f%%", cov11*100)
	md"RR of $cov11"
end

# ╔═╡ 4ea47b75-8ad9-463c-8548-f59a23e7d0cb
md"""
### Distribution of Winning Numbers
"""

# ╔═╡ 4e17b54b-1443-4934-99cb-a3dfe1846e40
begin
	h = sum(m, dims=1)
	bar(vec(h), legend=false, xaxis="Win Number", yaxis="Frequency", yformatter=:plain)
	hline!([N*.25 - 1.96*sqrt(.25*.75*N)], linestyle=:dash, color=:red)
	hline!([N*.25 + 1.96*sqrt(.25*.75*N)], linestyle=:dash, color=:red)
end

# ╔═╡ b8691296-659c-4920-bcd6-a05f8453f14c
begin
	cov12  = 1-mean(
		round(N*.25 - 1.96*sqrt(.25*.75*N), RoundDown)
		.<	h .<= 
		round(N*.25 + 1.96*sqrt(.25*.75*N), RoundUp)
	)
	cov12 = sprintf1("%6.3f%%", cov12*100)
	md"RR of $cov12"

end

# ╔═╡ dbaeae8b-75b5-4f43-84a8-04dacaaebc13
md"""
### Statistical Summaries
"""

# ╔═╡ a7372374-d23f-479f-ab2f-e6d5b2a48a7b
summary_stat = @pipe  df |> 
  select(_, :Draw_Date, r"Win_Num_") |>
  stack(_, Not(:Draw_Date)) |>
  transform(_, :variable => (x -> replace.(x, r"Win_Num_" => "Spot ")) => :Spot) |>
  groupby(_, :Spot) |>
  combine(_, 
	  :value => length => :N,
	  :value => mean => :Mean,
	  :value => std => :SD,
	  :value => minimum => :Min,
	  :value => (x -> quantile(x, .25)) => :Q1,
	  :value => median => :Median,
	  :value => (x -> quantile(x, .75)) => :Q3,
	  :value => maximum => :Max,
	  
  )

# ╔═╡ 16e67dc3-ba02-4388-8613-e7c1bd1bc48c
md"""
#### Spot Set Mean QC
"""

# ╔═╡ 4d32ad01-a98c-4cab-b2ab-a73529ec3470
begin

	ssmqc = @pipe  df |> 
	  transform(_, :Draw_Date => ((x) -> (eachindex(df[!, :Draw_Date]) .- 1) .÷ 100  ) => :idx) |>
	  groupby(_, :idx) |> 
	  combine(_,  5:24 .=> mean) |> 
	  rename((x) -> replace(x, r"Win_Num_|_mean" => ""), _) |>
	  stack(_, Not(:idx)) |>
	  transform(_, :variable => ((x) -> parse.(Int, x) .+ rand(length(x))./2 .- 1/2)  => :spot )

	cov21  = 1 - mean((40.5-4.526) .<= ssmqc[!,:value] .<= (40.5+4.526))
	cov21 = sprintf1("%6.3f%%", cov21*100)
	md"RR of $cov21"

end

# ╔═╡ 43866a08-d4b7-46e2-b3f8-6a3e9e38fd90
begin
	scatter(ssmqc[!,:spot], ssmqc[!, :value], legend=false, xaxis="Spot", yaxis="Sample Mean")
	hline!([40.5-4.526], linestyle=:dash, color=:red)
	hline!([40.5+4.526], linestyle=:dash, color=:red)
end

# ╔═╡ eb9c437f-32a5-4ed2-a031-385e4c682cd1
md"""
#### Day Average QC
"""

# ╔═╡ 36bee5a7-b2ef-4189-986b-c0681a8c1948
begin

	daqc = @pipe  df |> 
	  groupby(_, :Draw_Date) |> 
	  combine(_,  5:24 .=> mean) |> 
	  rename((x) -> replace(x, r"Win_Num_|_mean" => ""), _) |>
	  stack(_, Not(:Draw_Date)) |>
	  transform(_, :variable => ((x) -> parse.(Int, x)) => :spot )

	md""
end

# ╔═╡ 3455fc6c-bbdb-4a53-ac87-65a0a737aee6
begin
	daqc2 = @pipe  df |> 
	  select(_, :Draw_Date, :Draw_Nbr, r"Win_Num_") |>
	  stack(_, Not(:Draw_Date, :Draw_Nbr)) |>
	  groupby(_, [:Draw_Date, :Draw_Nbr]) |>
	  combine(_, :value => mean) |>
	  groupby(_, :Draw_Date) |>
	  combine(_, :value_mean => mean => :m,
		         :value_mean => length => :n,
		         :value_mean => (x -> std(x)/sqrt(length(x) - 1)) => :se) |>
	  transform(_, [:se, :n] => ( (se,n) -> se .* quantile.(TDist.(n .- 1), 1-.025) ) => :w) |>
	  transform(_, [:m, :w] => ((m, w) -> (@. m-w < 40.5 < m+w )) => :out)
	
	cov22 = 1 - mean(daqc2.out)
	cov22 = sprintf1("%6.3f%%", cov22*100)

	md"RR of $cov22"
end

# ╔═╡ c037e2e5-11fb-4701-aea1-a6c8879bc4aa
begin
	theme(:ggplot2)
	@df filter( :out => identity, daqc2) sticks(:Draw_Date, :m .- :w, 
		fillrange=(:m .+ :w), 
				linecolor = 1,
		xaxis="Date", yaxis="Day Average", plot_title="95% CI for Mean Winning Number"
	)
	@df filter( :out => !, daqc2) sticks!(:Draw_Date, :m .- :w, 
		fillrange=(:m .+ :w), 
				linecolor = 2
	)
	hline!([40.5], linecolor=:grey, linestyle=:dash)
	@df daqc2 scatter!(:Draw_Date, :m, legend=false, #yerror=:w, legend
		markercolor = 2 .- :out, markerstrokecolor=:auto,
		markersize=1.7
	)  

end

# ╔═╡ 9da09e5f-0fc6-4676-af90-6159e1f47856
md"""
Points not covered:
"""

# ╔═╡ 9bb035f5-9d9c-4e10-b190-551ecee1bb39
filter( :out => x -> !x, daqc2)

# ╔═╡ 70752728-d0ac-4634-b5de-81e187eabbd9
md"""
### Trace Plots
"""

# ╔═╡ 510ac63c-ed6e-42a7-9e59-5b1190e3b45f
begin
    s1 = df[1:50, r"Win_Num"] |> Matrix
	s2 = df[500:549, r"Win_Num"] |> Matrix
	raw_mat = df[!, Between(:Win_Num_1, :Win_Num_20)] |> Matrix
	md""
end

# ╔═╡ 2bd18cf5-36fd-4b49-a352-4f234541a1a6
plot(s1 |> transpose |> vec, legend=false, xaxis="", yaxis="Draw", plot_title="Seq 1 Trace: Rounds 1-50")

# ╔═╡ b1f29364-87f2-4ecc-9ced-24fa20157e1b
plot(s2 |> transpose |> vec, legend=false, xaxis="", yaxis="Draw", plot_title="Seq 2 Trace: Rounds 500-549")

# ╔═╡ 6e79b91f-4060-4041-92b5-54c5a44a4529
begin
	draw_mean =  @pipe  df |> 
	  select(_, :Draw_Nbr, r"Win_Num_") |>
	  stack(_, Not(:Draw_Nbr)) |>
	  groupby(_, :Draw_Nbr) |>
	  combine(_, :value => mean => :m)
	
	plot(draw_mean[!, :Draw_Nbr], draw_mean[!,:m], legend=false, xaxis="Draw ID Number", yaxis="Round Average",xformatter=:plain)
end

# ╔═╡ 0974071a-f86c-425e-ab07-77e4f22dd34b
begin 
	draw_day =  @pipe  df |> 
	  select(_, :Draw_Date, r"Win_Num_") |>
	  stack(_, Not(:Draw_Date)) |>
	  groupby(_, :Draw_Date) |>
	  combine(_, :value => mean => :m)
	md""
end

# ╔═╡ 9b6a89b7-2b64-4c16-8195-128bb1796c54
plot(draw_day[!, :Draw_Date], draw_day[!,:m], legend=false, xaxis="Day", yaxis="Daily Average")

# ╔═╡ 0d8c0915-e550-4782-b4a2-250918236e4f
md"""
### Lag Plot
"""

# ╔═╡ 5c673bc0-a3bc-4d2d-a4c1-e1d2f882321c
begin
	s1lag = s1 |> Matrix |> transpose |> vec
	scatter(s1lag[1:end-1], s1lag[2:end], legend=false, markeralpha=.6,
	 xaxis="Seq 1 Lag 1", yaxis="Seq 1", plottitle="Within-Round")
	
	plot!(1:80, 1:80, color=:red, linestyle=:dash)
end

# ╔═╡ 2557b636-886d-4176-a193-2787084ff6a3
begin
	s2lag = s2 |> Matrix |> transpose |> vec
	scatter(s2lag[1:end-1], s2lag[2:end], legend=false, markeralpha=.6,
	 xaxis="Seq 2 Lag 1", yaxis="Seq 2", plottitle="Within-Round")
	
	plot!(1:80, 1:80, color=:red, linestyle=:dash)
end

# ╔═╡ d9f5495c-8c9f-4c23-9a9d-20af77242a9f
begin
	s1lagT = s1 |> Matrix  |> vec
	#s1lagT = df[1:1000, :Win_Num_1]
	scatter(s1lagT[1:end-1], s1lagT[2:end], legend=false, markeralpha=.6,
	 xaxis="Seq 1 Lag 1", yaxis="Seq 1", plottitle="Between-Round")
	
	plot!(1:80, 1:80, color=:red, linestyle=:dash)
end

# ╔═╡ 16abd8b9-30e4-4fb0-a39a-fe9b0821d984
begin
	s2lagT = s2 |> Matrix  |> vec
	scatter(s2lagT[1:end-1], s2lagT[2:end], legend=false, markeralpha=.6,
	 xaxis="Seq 2 Lag 1", yaxis="Seq 2", plottitle="Between-Round")
	
	plot!(1:80, 1:80, color=:red, linestyle=:dash)
end

# ╔═╡ d2d8edad-187d-434e-9c49-bb30cfa460ea
md"""
### ACF Plot
"""

# ╔═╡ a13cbb76-d2fd-47c7-a3d3-d17a40658c56
begin
	plot(s1 |> transpose |> vec |> autocor, 
		line=:stem, ylimits=(-.1, .1), yaxis="ACF", legend=false, plot_title="Seq 1 (By Round)")
	hline!([1.96/sqrt(1000)], color=:red, linestyle=:dash)
	hline!([-1.96/sqrt(1000)], color=:red, linestyle=:dash)
end

# ╔═╡ 14083b10-a7e1-4ac3-941e-92eb1339629a
begin
	plot(df[!,r"Win_Num"] |> Matrix |> transpose |> vec |> autocor, 
		line=:stem, ylimits=(-.01, .01), yaxis="ACF", legend=false,  plot_title="All  (By Round)")
	hline!([1.96/sqrt(N*20)], color=:red, linestyle=:dash)
	hline!([-1.96/sqrt(N*20)], color=:red, linestyle=:dash)
end

# ╔═╡ 0bc09e9d-7366-43f0-95f6-f639ab415ea9
begin
	plot(s1  |> vec |> autocor, 
		line=:stem, ylimits=(-.1, .1), yaxis="ACF", legend=false,  plot_title="Seq 1 (By Spot)")
	hline!([1.96/sqrt(1000)], color=:red, linestyle=:dash)
	hline!([-1.96/sqrt(1000)], color=:red, linestyle=:dash)
end

# ╔═╡ 309e6156-99a2-4591-802e-ff6c3f8eb621
begin
	plot(df[!,r"Win_Num"] |> Matrix  |> vec |> autocor, 
		line=:stem, ylimits=(-.01, .01), yaxis="ACF", legend=false,  plot_title="All  (By Spot)")
	hline!([1.96/sqrt(N*20)], color=:red, linestyle=:dash)
	hline!([-1.96/sqrt(N*20)], color=:red, linestyle=:dash)
end

# ╔═╡ b116f2e5-80a2-4495-882e-2f1e06074f63
md"""
## Formal Tests
"""

# ╔═╡ 5a1b8f71-9bbb-4169-b751-261d8727e9d4
md"""
### $\chi^2$ Goodness of Fit
"""

# ╔═╡ e925c3e9-9abe-4a22-84b6-4dab4780da6c
begin
	dist = Binomial(N, 1.0/80)
	p_spot_win = 0.0*m
	for ix in CartesianIndices(m)
		p_spot_win[ix] = pvalue(ChisqTest([m[ix], nrow(df) - m[ix]], [1/80, 79/80]))
	end
	md""
end

# ╔═╡ 1b6c6766-a3a0-4b39-9b2f-1d22be8f19d4
begin
	long_p = stack(hcat(DataFrame(spot=1:20), DataFrame(p_spot_win, :auto)), Not(:spot))
	long_p.Win_Num = parse.(Int, replace.(long_p.variable, "x" => ""))
	md""
end

# ╔═╡ 6b7f00cb-1bb8-4345-a2aa-59a9a30b577a
begin

	@df long_p scatter(
		:Win_Num, :value, legend=false, 
		markercolor=[(p > .05 ? 1 : 2) for p in :value],
		markeralpha=.6,
		plot_title="1600 tests, Spot X Win Num",
		xaxis="Win Number",
		yaxis="p"
	)
	hline!([.05], linestyle=:dash, linecolor=:red)
end

# ╔═╡ 0531f93e-b28a-40ab-afa2-19d1f7f00b90
begin
	cov311 = mean(long_p[!,:value] .<= .05)
	cov311 = sprintf1("%6.3f%%", cov311*100)
	md"""
	RR of $cov311
	"""
end

# ╔═╡ e6ebcbc1-4d91-4261-a9f6-4c94b939d6a3
begin
	dist2 = Binomial(nrow(df), 1.0/4)
	#p_num = cdf.(dist2, sum(m, dims=1))[1,:] |> two_side

	p_round_win = zeros(80)
	for i in enumerate(sum(m, dims=1))
		i, s = i
		p_round_win[i] = pvalue(ChisqTest([s, nrow(df) - s], [1/4, 3/4]))
	end

	scatter(1:80, p_round_win, legend=false,
			markercolor=[(p > .05 ? 1 : 2) for p in p_round_win],
		markeralpha=.6,
		plot_title="80 tests, Win Num in Round",
		xaxis="Win Number",
		yaxis="p"

	)
	hline!([.05], linestyle=:dash, linecolor=:red)

end

# ╔═╡ 51663667-f34c-4195-aa61-0bef1267bfd1
begin
	cov312 = mean(p_round_win .<= .05)
	cov312 = sprintf1("%6.3f%%", cov312*100)
	md"""
	RR of $cov312
	"""
end

# ╔═╡ f5526ada-f62f-4af8-ada6-81769eb755c8
begin
	dist3 = DiscreteUniform(1,80)

	gdf = @pipe df |> 
	  transform(_, :Draw_Nbr => (x -> repeat(1:10, inner=length(x) ÷ 10)) => :i) |>
	  groupby(_, :i)

	spot = []
	p3 = []
	
	for i in enumerate(gdf)
		i, x = i
		for j in 1:20

			table = @pipe x |> groupby(_, names(x)[j+4]) |> combine(_, nrow)
			
			p_val = pvalue(ChisqTest(table.nrow))

			push!(spot, j)
			push!(p3, p_val)
		end
	end

#	p3 = DataFrame(spot=spot, value=p3)

	scatter(spot, p3, legend=false,
			markercolor=[(p > .05 ? 1 : 2) for p in p3],
		markeralpha=.6,
		plot_title="200 tests, Spots (10 chunks)",
		xaxis="Spot",
		yaxis="p"

	)
	hline!([.05], linestyle=:dash, linecolor=:red)

end

# ╔═╡ b236037e-b052-4189-89ec-d2c3f4cfa60e
begin
	cov313 = mean(p3 .<= .05)
	cov313 = sprintf1("%6.3f%%", cov313*100)
	md"""
	RR of $cov313
	"""
end

# ╔═╡ ded1d93d-1a90-457d-88c5-bf46f91be1b1
md"""
#### KS Tests
"""

# ╔═╡ 1a49d4ef-dd82-4fd8-a52c-26062a8981b3
@doc ExactOneSampleKSTest

# ╔═╡ 2b5d4bf4-c762-4612-b3df-9326093019df
md"Spot-by-number"

# ╔═╡ 63980b7e-0e22-4a06-ac67-c2d1b2679960
ApproximateOneSampleKSTest(p_spot_win |> vec, Uniform())

# ╔═╡ a505a05c-64d0-4ecc-8271-6ebb14d3bba1
md"Win Number in Round"

# ╔═╡ c17713de-7798-44a5-8698-772c92db2c5c
ApproximateOneSampleKSTest(p_round_win |> vec, Uniform())

# ╔═╡ 58169563-26ef-4460-bf5b-546844ad6a6e
md"Spot (10 chunks)"

# ╔═╡ dab99337-f3dc-41f1-8e45-66450cd6363f
ApproximateOneSampleKSTest(Float64.(p3)  |> vec, Uniform())

# ╔═╡ a2d38a3e-a7f1-4c24-920c-42afb4d6d929
md"""
### Wald Wolfowitz R Test
"""

# ╔═╡ 2e12980b-ab4b-4fc1-aea8-b34f23a69aec
function wwr_test2(raw_mat, K, T=true, threshold=40.5)
	"""
    Goes across draws. Eg K = 10 => Spot1[1:200], Spot1[201:400], ..., Spot2[1:200]
	"""

	T = T ? identity : transpose
	wwr = []
	slice = nothing

	raw_mat = T(raw_mat) |> vec
	
	for i in 1:(K*20):size(raw_mat)[1]
		e = min(i + K*20-1, size(raw_mat)[1])

		slice = raw_mat[i:e]  .> threshold
		push!(wwr, WaldWolfowitzTest(slice ) |> pvalue)
	end
	K, prod(size(slice)), length(wwr), mean(wwr .<= .05)
end

# ╔═╡ b9fb424b-462e-4fb5-9a91-8761c01cb3f9
function wwr_test(raw_mat, K, T=false, threshold=40.5)
	"""
    Split into groups of K draws. Walk either by row or by column.
	"""

	T = T ? identity : transpose
	wwr = []
	slice = nothing
	
	for i in 1:K:size(raw_mat)[1]
		e = min(i + K-1, size(raw_mat)[1])
		slice = raw_mat[i:e,:]  .> threshold
		push!(wwr, WaldWolfowitzTest(slice |> Matrix |> T |> vec) |> pvalue)
	end
	K, prod(size(slice)), length(wwr), mean(wwr .<= .05)
end

# ╔═╡ d2cff83f-11f9-453d-9885-4328571204d6
md"""
#### Rejection Rates for WWR / Round First
"""

# ╔═╡ 4f14cc60-b424-4807-adcc-6ac47e1f9b5b
DataFrame([
  wwr_test(raw_mat, 10, false)
  wwr_test(raw_mat, 20, false)
  wwr_test(raw_mat, 50, false)
  wwr_test(raw_mat, 100, false)
  wwr_test(raw_mat, 200, false)
], ["Rounds", "Draws", "Tests", "RR"])

# ╔═╡ 0b6c3b88-1497-49c7-8322-ff32b308b1e0
md"""
#### Rejection Rates for WWR / Spot First
"""

# ╔═╡ 83d784e5-4f9c-47c0-9125-968591a7cb0a
DataFrame([
  wwr_test2(raw_mat, 10, true)
  wwr_test2(raw_mat, 20, true)
  wwr_test2(raw_mat, 50, true)
  wwr_test2(raw_mat, 100, true)
  wwr_test2(raw_mat, 200, true)
], ["Rounds", "Draws", "Tests", "RR"])

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
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"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
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[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.1+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.15.0+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.2+0"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.6+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.39.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.5.0+0"

[[deps.ZipFile]]
deps = ["Libdl", "Printf", "Zlib_jll"]
git-tree-sha1 = "f492b7fe1698e623024e873244f10d89c95c340a"
uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea"
version = "0.10.1"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+0"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.5+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.29.0+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+0"
"""

# ╔═╡ Cell order:
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# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002