In vjcitn/play4YES: probability illustrations with playing cards

A deck of cards as an R vector

library(play4YES)
set.seed(1234)  # reproducible
deck = build_deck()
deck

Is it a fair deck?

table(suits(deck), faces(deck))

Make a biased deck:

bdeck = deck
bdeck[3] = bdeck[18]
table(suits(bdeck), faces(bdeck))

Fairness assessed by top card in a series of deals

We'll use the built-in function sample to simulate shuffles of the deck. top_card gives the card at top of deck.

shuffle = sample
top_card = function(x) x[1]
t1 = top_card(shuffle(deck))
t1
suits(t1)

Using the fair deck

We'll take the top cards for each of 100 shuffles and examine the suit.

table( replicate(100, suits(top_card(shuffle(deck)))) )

We should see about 25 for each suit. Are we close enough?

Using the biased deck

table( replicate(100, suits(top_card(shuffle(bdeck)))) )

Increasing the "sample size"

Variability can mask structural bias. If we create statistics based on more observations, we can start to unearth it.

table( replicate(10000, suits(top_card(shuffle(deck)))) )
table( replicate(10000, suits(top_card(shuffle(bdeck)))) )

A finer-grained problem: the face, not the suit

There are 4 different suits, but 13 different faces. Is the bias discernible with this procedure?

table( replicate(100, faces(top_card(shuffle(deck)))) )
table( replicate(100, faces(top_card(shuffle(bdeck)))) )

If we make 10000 shuffles, we expect each face to appear 10000/13 = 769.230.... times.

tfair <- table( replicate(10000, faces(top_card(shuffle(deck)))) )
tfair
tbias <- table( replicate(10000, faces(top_card(shuffle(bdeck)))) )
tbias

We can plot the observed frequencies of appearance of each face.

library(beeswarm)
beeswarm(list(fair=tfair,biased=tbias), ylab="Top card face frequencies")

With the biased deck, one face has depleted frequency, one enhanced.

vjcitn/play4YES documentation built on Feb. 28, 2022, 12:48 a.m.