In rolkra/tidydice: Simulates Dice Rolls and Coin Flips
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
Introduction
A basic understanding of probability and statistics is crucial for data understanding and discovery of meaningful patterns. A great way to teach probability and statistics is to start with an experiment, like rolling a dice or flipping a coin.
This package simulates rolling a dice and flipping a coin. Each experiment generates a tibble. Dice rolls and coin flips are simulated using sample(). The properties of the dice can be changed, like the number of sides. A coin flip is simulated using a two sided dice. Experiments can be combined with the pipe-operator.
tidydice package on Github: https://github.com/rolkra/tidydice
Setup
As the tidydice-functions fits well into the tidyverse, we load the dplyr-package. For quick visualisations we use the explore-package. To create more flexible graphics, use ggplot2.
library(tidydice)
library(dplyr)
library(explore)
Roll a dice
Example
6 dice are rolled 3 times using roll_dice(). The result of the dice-experiment is visualised using plot_dice().
set.seed(123)
roll_dice(times = 6, rounds = 3) %>%
plot_dice()
Roll a dice once
The output of roll_dice() is a tibble. Each row represents a dice roll. Without parameters, a dice is rolled once. You can use plot_dice() to visualise the result.
```{R echo=TRUE}
set.seed(123)
roll_dice()
```{R echo=TRUE, fig.width=6, fig.height=1}
set.seed(123)
roll_dice() %>% plot_dice()
Success is defined as result = 6 (as default), while result = 1..5 is not a success. In this case the result is 2, so it is no success.
Define success
If we would define result = 2 and result = 6 as success, it would be treated as success.
```{R echo=TRUE}
set.seed(123)
roll_dice(success = c(2,6))
#### Unfair dice
As default, the dice is fair. So every result (0..6) has the same probability. If you want, you can change this.
```{R echo=TRUE}
set.seed(123)
roll_dice(prob = c(0,0,0,0,0,1))
In this case we created a dice that always gets result = 6 (with 100% probability)
Untypically dice
As default the dice has 6 sides. If you want you can change this. Here we use a dice with 12 sides. result now can have a value between 1 and 12. But result = 6 is still the default success.
```{R echo=TRUE}
set.seed(123)
roll_dice(sides = 12)
#### Roll a dice 4 times
```{R echo=TRUE}
set.seed(123)
roll_dice(times = 4)
```{R echo=TRUE, fig.width=6, fig.height=1}
set.seed(123)
roll_dice(times = 4) %>% plot_dice()
We get 1 success
#### Define rounds
```{R echo=TRUE}
set.seed(123)
roll_dice(times = 4, rounds = 2)
```{R echo=TRUE, fig.width=6, fig.height=2}
set.seed(123)
roll_dice(times = 4, rounds = 2) %>% plot_dice()
Rolling the dice 4 times is repeated. In the first round we got 1 success, in the secound round 2 success.
#### Use agg
A convenient way to aggregate the result, is to use the agg parameter. Now we get one line per round.
```{R echo=TRUE}
set.seed(123)
roll_dice(times = 4, rounds = 2, agg = TRUE)
You can aggregate by hand too using dplyr.
```{R echo=TRUE}
set.seed(123)
roll_dice(times = 4, rounds = 2) %>%
group_by(experiment, round) %>%
summarise(times = n(),
success = sum(success))
#### Visualise result
You can use any package/tool you like to visualise the result. In this example we use the explore-package.
```{R echo=TRUE, fig.height=4, fig.width=7}
set.seed(123)
roll_dice(times = 100) %>%
explore(result, title = "Rolling a dice 100x")
In 15% of the cases we got a six. This is close to the expected value of 100/6 = 16.67%
If we increase the times parameter to 10000, the results are more balanced.
```{R echo=TRUE, fig.height=4, fig.width=7}
set.seed(123)
roll_dice(times = 10000) %>%
explore(result, title = "Rolling a dice 10000x")
#### Visualise success
If we repeat the experiment rolling a dice 100x with rounds = 100, we get the distribution with a peak at about 17 (16.67 is the expected value)
```{R echo=TRUE, fig.height=4, fig.width=7}
set.seed(123)
roll_dice(times = 100, rounds = 100, agg = TRUE) %>%
explore(success,
title = "Rolling 100 dice 100x",
auto_scale = FALSE)
If we increase rounds from 100 to 10000 we get a more symmetric shape. We see that success below 5 and success above 30 are very unlikely.
```{R echo=TRUE, fig.height=4, fig.width=7}
set.seed(123)
roll_dice(times = 100, rounds = 10000, agg = TRUE) %>%
explore(success,
title = "Rolling 100 dice 10000x",
auto_scale = FALSE)
This shape is already very close to the binomial distribution
```{R echo=TRUE, fig.height=4, fig.width=7}
binom_dice(times = 100) %>%
plot_binom(title = "Binomial distribution, rolling 100 dice")
```{R echo=TRUE}
set.seed(123)
roll_dice(times = 100, rounds = 10000, agg = TRUE) %>%
mutate(check = ifelse(success < 5 | success > 30, 1, 0)) %>%
count(check)
In only 4 of 10000 (0.04%) cases success is below 5 or above 30. So the probability to get this result is very low.
We can check that with the binomial distribution too:
```{R echo=TRUE}
binom_dice(times = 100) %>%
filter(success < 5 | success > 30)
```{R echo=TRUE}
binom_dice(times = 100) %>%
filter(success < 5 | success > 30) %>%
summarise(check_pct = sum(pct))
The probability to get this result is 0.04% (based on the binomial distribution).
#### Combine experiments
Let's add an experiment, where you have 10 extra dice. The shape of the distribution changes.
```{R echo=TRUE, fig.height=4, fig.width=7}
set.seed(123)
roll_dice(times = 100, rounds = 10000, agg = TRUE) %>%
roll_dice(times = 110, rounds = 10000, agg = TRUE) %>%
explore(success,
target = experiment,
title = "Rolling a dice 100/110x",
auto_scale = FALSE)
You can add as many experiments as you like (as long they generate the same data structure)
Adding an experiment with times = 150 will generate a smaller but wider shape.
```{R echo=TRUE, fig.height=4, fig.width=7}
set.seed(123)
roll_dice(times = 100, rounds = 10000, agg = TRUE) %>%
roll_dice(times = 110, rounds = 10000, agg = TRUE) %>%
roll_dice(times = 150, rounds = 10000, agg = TRUE) %>%
explore(success,
target = experiment,
title = "Rolling a dice 100/110/150x",
auto_scale = FALSE)
#### Binomial distribution
Rolling a dice 100x, a result between 10 and 23 has a probability of over 94%
```{R echo=TRUE, fig.height=4, fig.width=7}
binom_dice(times = 100) %>%
plot_binom(highlight = c(10:23))
Flip a coin
Internally the package handles coins as dice with only two sides. Success is defined as result = 2 (as default), while result = 1 is not a success.
Flip a coin 10x
```{R echo=TRUE}
set.seed(123)
flip_coin(times = 10)
In this case the result are 6x 2 and 4x 1. We can use the describe() function of the explore-package to get a good overview.
```{R echo=TRUE}
set.seed(123)
flip_coin(times = 10) %>%
describe(success)
Or just use the agg-parameter
```{R echo=TRUE}
set.seed(123)
flip_coin(times = 10, agg = TRUE)
#### Define rounds
The parameter rounds can be used like in roll_dice().
```{R echo=TRUE}
set.seed(123)
flip_coin(times = 10, rounds = 4, agg = TRUE)
Visualise result
```{R echo=TRUE, fig.height=4, fig.width=7}
set.seed(123)
flip_coin(times = 10, rounds = 4) %>%
plot_coin()
#### Combine experiments
```{R echo=TRUE}
set.seed(123)
flip_coin(times = 10, agg = TRUE) %>%
flip_coin(times = 15, agg = TRUE)
Binomial Distribution
```{R echo=TRUE}
binom_coin(times = 10)
```{R echo=TRUE, fig.height=4, fig.width=7}
binom_coin(times = 10) %>%
plot_binom(title = "Binomial distribution,\n10 coin flips")
Dice design
Default settings
set.seed(123)
roll_dice(times = 6) %>%
plot_dice()
Change color
set.seed(123)
roll_dice(times = 6) %>%
plot_dice(fill = "black", line_color = "white", point_color = "white")
set.seed(123)
roll_dice(times = 6) %>%
plot_dice(fill = "lightblue", fill_success = "gold")
set.seed(123)
roll_dice(times = 6) %>%
plot_dice(fill = "darkgrey",
fill_success = "darkblue",
line_color = "white",
point_color = "white")
Dice type
set.seed(123)
roll_dice(times = 6) %>%
plot_dice(detailed = TRUE)
set.seed(123)
roll_dice(times = 6) %>%
plot_dice(detailed = FALSE)
Limits
plot_dice() is limited to 1 experiment with max. 10 times x 10 rounds.
set.seed(123)
roll_dice(times = 10, rounds = 10) %>%
plot_dice(detailed = FALSE, fill_success = "gold")
Force
You can force a result using force_dice() and force_coin().
force_dice(1:6) %>%
plot_dice()
force_dice(rep(6, times = 6)) %>%
plot_dice()
We can combine two foreced dice rolling using the pipe operator and the parameter round.
force_dice(rep(5, times = 3), round = 1) %>%
force_dice(rep(6, times = 3), round = 2)
set.seed(123)
force_dice(rep(6, times = 3)) %>%
roll_dice(times = 3)
In the first experiment we get 3 times a 6 (forced), but in the second experiment none.
Using Dice Formula
If you want to do more complex dice rolls, use roll_dice_formula()
# roll 1 dice with 6 sides
roll_dice_formula(dice_formula = "1d6", seed = 123)
roll_dice_formula(
dice_formula = "4d6", # 4 dice with 6 sides
success = 15:24, # success is defined as sum between 15 and 24
seed = 123 # random seed to make it reproducible
)
# roll 4 dice with 6 sides
roll_dice_formula(
dice_formula = "4d6", # 4 dice with 6 sides
rounds = 10, # repeat 10 times
success = 15:24, # success is defined as sum between 15 and 24
seed = 123 # random seed to make it reproducible
)
roll_dice_formula(
dice_formula = "4d6e3", # 4 dice with 6 sides, explode on a 3
rounds = 5, # repeat 5 times
success = 15:24, # success is defined as sum between 15 and 24
seed = 123 # random seed to make it reproducible
)
roll_dice_formula(
dice_formula = "4d6+1d10", # 4 dice with 6 sides + 1 dice with 10 sides
rounds = 1000) %>% # repeat 1000 times
explore_bar(result, numeric = TRUE) # visualise result
Other examples for dice_formula:
1d6 = roll one 6-sided dice1d8 = roll one 8-sided dice1d12 = roll one 12-sided dice2d6 = roll two 6-sided dice1d6e6 = roll one 6-sided dice, explode dice on a 63d6kh2 = roll three 6-sided dice, keep highest 2 rolls3d6kl2 = roll three 6-sided dice, keep lowest 2 rolls4d6kh3e6 = roll four 6-sided dice, keep highest 3 rolls, but explode on a 61d20+4 = roll one 20-sided dice, and add 41d4+1d6 = roll one 4-sided dice and one 6-sided dice, and sum the results
rolkra/tidydice documentation built on Feb. 9, 2023, 9:09 a.m.
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knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
Introduction
A basic understanding of probability and statistics is crucial for data understanding and discovery of meaningful patterns. A great way to teach probability and statistics is to start with an experiment, like rolling a dice or flipping a coin.
This package simulates rolling a dice and flipping a coin. Each experiment generates a tibble. Dice rolls and coin flips are simulated using sample(). The properties of the dice can be changed, like the number of sides. A coin flip is simulated using a two sided dice. Experiments can be combined with the pipe-operator.
tidydice package on Github: https://github.com/rolkra/tidydice
Setup
As the tidydice-functions fits well into the tidyverse, we load the dplyr-package. For quick visualisations we use the explore-package. To create more flexible graphics, use ggplot2.
library(tidydice) library(dplyr) library(explore)
Roll a dice
Example
6 dice are rolled 3 times using roll_dice(). The result of the dice-experiment is visualised using plot_dice().
set.seed(123) roll_dice(times = 6, rounds = 3) %>% plot_dice()
Roll a dice once
The output of roll_dice() is a tibble. Each row represents a dice roll. Without parameters, a dice is rolled once. You can use plot_dice() to visualise the result.
```{R echo=TRUE} set.seed(123) roll_dice()
```{R echo=TRUE, fig.width=6, fig.height=1}
set.seed(123)
roll_dice() %>% plot_dice()
Success is defined as result = 6 (as default), while result = 1..5 is not a success. In this case the result is 2, so it is no success.
Define success
If we would define result = 2 and result = 6 as success, it would be treated as success.
```{R echo=TRUE} set.seed(123) roll_dice(success = c(2,6))
#### Unfair dice
As default, the dice is fair. So every result (0..6) has the same probability. If you want, you can change this.
```{R echo=TRUE}
set.seed(123)
roll_dice(prob = c(0,0,0,0,0,1))
In this case we created a dice that always gets result = 6 (with 100% probability)
Untypically dice
As default the dice has 6 sides. If you want you can change this. Here we use a dice with 12 sides. result now can have a value between 1 and 12. But result = 6 is still the default success.
```{R echo=TRUE} set.seed(123) roll_dice(sides = 12)
#### Roll a dice 4 times
```{R echo=TRUE}
set.seed(123)
roll_dice(times = 4)
```{R echo=TRUE, fig.width=6, fig.height=1} set.seed(123) roll_dice(times = 4) %>% plot_dice()
We get 1 success
#### Define rounds
```{R echo=TRUE}
set.seed(123)
roll_dice(times = 4, rounds = 2)
```{R echo=TRUE, fig.width=6, fig.height=2} set.seed(123) roll_dice(times = 4, rounds = 2) %>% plot_dice()
Rolling the dice 4 times is repeated. In the first round we got 1 success, in the secound round 2 success.
#### Use agg
A convenient way to aggregate the result, is to use the agg parameter. Now we get one line per round.
```{R echo=TRUE}
set.seed(123)
roll_dice(times = 4, rounds = 2, agg = TRUE)
You can aggregate by hand too using dplyr.
```{R echo=TRUE} set.seed(123) roll_dice(times = 4, rounds = 2) %>% group_by(experiment, round) %>% summarise(times = n(), success = sum(success))
#### Visualise result
You can use any package/tool you like to visualise the result. In this example we use the explore-package.
```{R echo=TRUE, fig.height=4, fig.width=7}
set.seed(123)
roll_dice(times = 100) %>%
explore(result, title = "Rolling a dice 100x")
In 15% of the cases we got a six. This is close to the expected value of 100/6 = 16.67%
If we increase the times parameter to 10000, the results are more balanced.
```{R echo=TRUE, fig.height=4, fig.width=7} set.seed(123) roll_dice(times = 10000) %>% explore(result, title = "Rolling a dice 10000x")
#### Visualise success
If we repeat the experiment rolling a dice 100x with rounds = 100, we get the distribution with a peak at about 17 (16.67 is the expected value)
```{R echo=TRUE, fig.height=4, fig.width=7}
set.seed(123)
roll_dice(times = 100, rounds = 100, agg = TRUE) %>%
explore(success,
title = "Rolling 100 dice 100x",
auto_scale = FALSE)
If we increase rounds from 100 to 10000 we get a more symmetric shape. We see that success below 5 and success above 30 are very unlikely.
```{R echo=TRUE, fig.height=4, fig.width=7} set.seed(123) roll_dice(times = 100, rounds = 10000, agg = TRUE) %>% explore(success, title = "Rolling 100 dice 10000x", auto_scale = FALSE)
This shape is already very close to the binomial distribution
```{R echo=TRUE, fig.height=4, fig.width=7}
binom_dice(times = 100) %>%
plot_binom(title = "Binomial distribution, rolling 100 dice")
```{R echo=TRUE} set.seed(123) roll_dice(times = 100, rounds = 10000, agg = TRUE) %>% mutate(check = ifelse(success < 5 | success > 30, 1, 0)) %>% count(check)
In only 4 of 10000 (0.04%) cases success is below 5 or above 30. So the probability to get this result is very low.
We can check that with the binomial distribution too:
```{R echo=TRUE}
binom_dice(times = 100) %>%
filter(success < 5 | success > 30)
```{R echo=TRUE} binom_dice(times = 100) %>% filter(success < 5 | success > 30) %>% summarise(check_pct = sum(pct))
The probability to get this result is 0.04% (based on the binomial distribution).
#### Combine experiments
Let's add an experiment, where you have 10 extra dice. The shape of the distribution changes.
```{R echo=TRUE, fig.height=4, fig.width=7}
set.seed(123)
roll_dice(times = 100, rounds = 10000, agg = TRUE) %>%
roll_dice(times = 110, rounds = 10000, agg = TRUE) %>%
explore(success,
target = experiment,
title = "Rolling a dice 100/110x",
auto_scale = FALSE)
You can add as many experiments as you like (as long they generate the same data structure)
Adding an experiment with times = 150 will generate a smaller but wider shape.
```{R echo=TRUE, fig.height=4, fig.width=7} set.seed(123) roll_dice(times = 100, rounds = 10000, agg = TRUE) %>% roll_dice(times = 110, rounds = 10000, agg = TRUE) %>% roll_dice(times = 150, rounds = 10000, agg = TRUE) %>% explore(success, target = experiment, title = "Rolling a dice 100/110/150x", auto_scale = FALSE)
#### Binomial distribution
Rolling a dice 100x, a result between 10 and 23 has a probability of over 94%
```{R echo=TRUE, fig.height=4, fig.width=7}
binom_dice(times = 100) %>%
plot_binom(highlight = c(10:23))
Flip a coin
Internally the package handles coins as dice with only two sides. Success is defined as result = 2 (as default), while result = 1 is not a success.
Flip a coin 10x
```{R echo=TRUE} set.seed(123) flip_coin(times = 10)
In this case the result are 6x 2 and 4x 1. We can use the describe() function of the explore-package to get a good overview.
```{R echo=TRUE}
set.seed(123)
flip_coin(times = 10) %>%
describe(success)
Or just use the agg-parameter
```{R echo=TRUE} set.seed(123) flip_coin(times = 10, agg = TRUE)
#### Define rounds
The parameter rounds can be used like in roll_dice().
```{R echo=TRUE}
set.seed(123)
flip_coin(times = 10, rounds = 4, agg = TRUE)
Visualise result
```{R echo=TRUE, fig.height=4, fig.width=7} set.seed(123) flip_coin(times = 10, rounds = 4) %>% plot_coin()
#### Combine experiments
```{R echo=TRUE}
set.seed(123)
flip_coin(times = 10, agg = TRUE) %>%
flip_coin(times = 15, agg = TRUE)
Binomial Distribution
```{R echo=TRUE} binom_coin(times = 10)
```{R echo=TRUE, fig.height=4, fig.width=7}
binom_coin(times = 10) %>%
plot_binom(title = "Binomial distribution,\n10 coin flips")
Dice design
Default settings
set.seed(123) roll_dice(times = 6) %>% plot_dice()
Change color
set.seed(123) roll_dice(times = 6) %>% plot_dice(fill = "black", line_color = "white", point_color = "white")
set.seed(123) roll_dice(times = 6) %>% plot_dice(fill = "lightblue", fill_success = "gold")
set.seed(123) roll_dice(times = 6) %>% plot_dice(fill = "darkgrey", fill_success = "darkblue", line_color = "white", point_color = "white")
Dice type
set.seed(123) roll_dice(times = 6) %>% plot_dice(detailed = TRUE)
set.seed(123) roll_dice(times = 6) %>% plot_dice(detailed = FALSE)
Limits
plot_dice() is limited to 1 experiment with max. 10 times x 10 rounds.
set.seed(123) roll_dice(times = 10, rounds = 10) %>% plot_dice(detailed = FALSE, fill_success = "gold")
Force
You can force a result using force_dice() and force_coin().
force_dice(1:6) %>% plot_dice()
force_dice(rep(6, times = 6)) %>% plot_dice()
We can combine two foreced dice rolling using the pipe operator and the parameter round.
force_dice(rep(5, times = 3), round = 1) %>% force_dice(rep(6, times = 3), round = 2)
set.seed(123) force_dice(rep(6, times = 3)) %>% roll_dice(times = 3)
In the first experiment we get 3 times a 6 (forced), but in the second experiment none.
Using Dice Formula
If you want to do more complex dice rolls, use roll_dice_formula()
# roll 1 dice with 6 sides roll_dice_formula(dice_formula = "1d6", seed = 123)
roll_dice_formula( dice_formula = "4d6", # 4 dice with 6 sides success = 15:24, # success is defined as sum between 15 and 24 seed = 123 # random seed to make it reproducible )
# roll 4 dice with 6 sides roll_dice_formula( dice_formula = "4d6", # 4 dice with 6 sides rounds = 10, # repeat 10 times success = 15:24, # success is defined as sum between 15 and 24 seed = 123 # random seed to make it reproducible )
roll_dice_formula( dice_formula = "4d6e3", # 4 dice with 6 sides, explode on a 3 rounds = 5, # repeat 5 times success = 15:24, # success is defined as sum between 15 and 24 seed = 123 # random seed to make it reproducible )
roll_dice_formula( dice_formula = "4d6+1d10", # 4 dice with 6 sides + 1 dice with 10 sides rounds = 1000) %>% # repeat 1000 times explore_bar(result, numeric = TRUE) # visualise result
Other examples for dice_formula:
1d6= roll one 6-sided dice1d8= roll one 8-sided dice1d12= roll one 12-sided dice2d6= roll two 6-sided dice1d6e6= roll one 6-sided dice, explode dice on a 63d6kh2= roll three 6-sided dice, keep highest 2 rolls3d6kl2= roll three 6-sided dice, keep lowest 2 rolls4d6kh3e6= roll four 6-sided dice, keep highest 3 rolls, but explode on a 61d20+4= roll one 20-sided dice, and add 41d4+1d6= roll one 4-sided dice and one 6-sided dice, and sum the results
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