R: Counting the Frequencies of Coin Flips - r

Question

I am working with the R programming language.
I simulated this dataset which contains 1000 coin flips - then I calculated the number of "2 Flip Sequences":
Coin <- c('H', 'T')
Results = sample(Coin,1000, replace = TRUE)
My_Data = data.frame(id = 1:1000, Results)
Pairs = data.frame(first = head(My_Data$Results, -1), second = tail(My_Data$Results, -1))
Final = as.data.frame(table(Pairs))
first second Freq
1 H H 255
2 T H 245
3 H T 246
4 T T 253
I am curious - is it possible to extend the above code for "3 Flip Sequences"?
For example - I tried modifying parts of the code to see how the results change (and hoped to stumble across the correct way to write this code):
# First Attempt
Pairs = data.frame(first = head(My_Data$Results, -1), second = head(My_Data$Results, -1) , third = tail(My_Data$Results, -1))
Final = as.data.frame(table(Pairs))
first second third Freq
1 H H H 255
2 T H H 245
3 H T H 0
4 T T H 0
5 H H T 0
6 T H T 0
7 H T T 246
8 T T T 253
# Second Attempt
Pairs = data.frame(first = head(My_Data$Results, -1), second = tail(My_Data$Results, -1) , third = tail(My_Data$Results, -1))
Final = as.data.frame(table(Pairs))
first second third Freq
1 H H H 255
2 T H H 0
3 H T H 0
4 T T H 245
5 H H T 246
6 T H T 0
7 H T T 0
8 T T T 253
I am not sure which of these options are correct?
In general, I am looking to understand the logic as to how I can adapt the above code for an "arbitrary number of coin flips" (e.g. "4 flip sequences", "5 flip sequences", etc.)
Also, this might not be the most efficient way to calculate these frequencies - I would also be interested in learning about other ways that might be more efficient ( e.g. as the overall size of the data increases).
Thanks!

Answer 1

It might be helpful to work with strings.
coin <- c("H", "T")
results <- sample(coin, 1000, replace = TRUE)
Then to get sequence counts (assuming overlapping sequences also count) for triples, we could do something like:
triples <- table(
sapply(
1:(length(results) - 3),
function(i) sprintf(
"%s%s%s",
results[i],
results[i + 1],
results[i + 2]
)
)
)
which gives me something like:
HHH HHT HTH HTT THH THT TTH TTT
132 129 138 115 129 124 116 114
This idea could be generalized fairly easily, for example:
n_sequences <- function(n, results) {
helper <- function(i, n) if (n < 1) "" else sprintf(
"%s%s",
helper(i, n - 1),
results[i + n - 1]
)
result <- data.frame(
table(
sapply(
1:(length(results) - n + 1),
function(i) helper(i, n)
)
)
)
colnames(result) <- c("Sequence", "Frequency")
result
}
For example:
n_sequences(5, results)
Gives me something like:
Sequence Frequency
1 HHHHH 34
2 HHHHT 31
3 HHHTH 36
4 HHHTT 31
5 HHTHH 35
6 HHTHT 36
7 HHTTH 20
8 HHTTT 37
9 HTHHH 35
10 HTHHT 34
11 HTHTH 41
12 HTHTT 27
13 HTTHH 27
14 HTTHT 24
15 HTTTH 34
16 HTTTT 30
17 THHHH 31
18 THHHT 36
19 THHTH 36
20 THHTT 26
21 THTHH 34
22 THTHT 32
23 THTTH 31
24 THTTT 27
25 TTHHH 32
26 TTHHT 28
27 TTHTH 25
28 TTHTT 31
29 TTTHH 33
30 TTTHT 31
31 TTTTH 30
32 TTTTT 20

Answer 2

You could first cut along 3 + 1 breaks, split it along the levels. The interaction can now be tabled to get the result.
My_Data$cut3 <- cut(seq_len(nrow(My_Data)), seq.int(1, nrow(My_Data), length.out=3 + 1), include.lowest=TRUE)
(res <- interaction(split(My_Data$Results, My_Data$cut3)) |> table() |> as.data.frame())
# Var1 Freq
# 1 H.H.H 51
# 2 T.H.H 58
# 3 H.T.H 43
# 4 T.T.H 49
# 5 H.H.T 38
# 6 T.H.T 51
# 7 H.T.T 64
# 8 T.T.T 46
To get the desired output, we can strsplit Var1.
strsplit(as.character(res$Var1), '\\.') |> do.call(what=rbind) |>
cbind.data.frame(res$Freq) |> setNames(c('first', 'second', 'third', 'Freq'))
# first second third Freq
# 1 H H H 51
# 2 T H H 58
# 3 H T H 43
# 4 T T H 49
# 5 H H T 38
# 6 T H T 51
# 7 H T T 64
# 8 T T T 46
Note, that nrow of your data should be divisible by 3.
Edit
To generalize, we may write a small function.
f <- \(x, n) {
ct <- cut(seq_len(nrow(x)), seq.int(1L, nrow(x), length.out=n + 1L), include.lowest=TRUE)
res <- interaction(split(x$Results, ct)) |> table() |> as.data.frame()
strsplit(as.character(res$Var1), '\\.') |> do.call(what=rbind) |>
cbind.data.frame(res$Freq) |> setNames(c(LETTERS[seq_len(n)], 'Freq'))
}
f(My_Data, 4)
# A B C D Freq
# 1 H H H H 13
# 2 T H H H 25
# 3 H T H H 18
# 4 T T H H 17
# 5 H H T H 18
# 6 T H T H 15
# 7 H T T H 21
# 8 T T T H 24
# 9 H H H T 26
# 10 T H H T 15
# 11 H T H T 16
# 12 T T H T 18
# 13 H H T T 22
# 14 T H T T 18
# 15 H T T T 10
# 16 T T T T 24
Data:
set.seed(42)
My_Data <- data.frame(id=1:1200, Results=sample(c('H', 'T'), 1200, replace=TRUE))

Answer 3

A slightly generalized solution with tidyverse tools. Change the sets variable for longer or shorter sequences.
coin <- c("H", "T")
sets <- 4
rolls <- 10000
results <- sample(coin, sets * rolls, rep = TRUE)
named_results <- purrr::map_chr(
0:(rolls - 1),
~ paste0(results[(sets * .x + 1):(sets * .x + sets)],
collapse = ""
)
)
dplyr::count(tibble::tibble(x = named_results), x)
with output
# A tibble: 16 x 2
x n
<chr> <int>
1 HHHH 629
2 HHHT 627
3 HHTH 638
4 HHTT 599
5 HTHH 602
6 HTHT 633
7 HTTH 596
8 HTTT 661
9 THHH 631
10 THHT 589
11 THTH 633
12 THTT 647
13 TTHH 660
14 TTHT 637
15 TTTH 623
16 TTTT 595
sets = 8 would give something like
# A tibble: 256 x 2
x n
<chr> <int>
1 HHHHHHHH 37
2 HHHHHHHT 36
3 HHHHHHTH 43
4 HHHHHHTT 35
5 HHHHHTHH 38
6 HHHHHTHT 27
7 HHHHHTTH 32
8 HHHHHTTT 28
9 HHHHTHHH 33
10 HHHHTHHT 38
# ... with 246 more rows