In the previous post we saw rolling a single dice D6. Now we'll roll two dice together. Rolling two dice results in larger numbers and a different distribution of results. The following code will create two D6 dice to simulate the way we roll a pair of dice:
from die import Die
from plotly.graph_objs import Bar, Layout
from plotly import offline
# Create two D6 dice.
die_1 = Die()
die_2 = Die()
# Make some rolls, and store results in a list.
results = []
for roll_num in range(1000):
result = die_1.roll()+ die_2.roll()
results.append(result)
# Analyze the results.
frequencies = []
max_result = die_1.num_sides + die_2.num_sides
for value in range(2, max_result+1):
frequency = results.count(value)
frequencies.append(frequency)
# Visualize the results.
x_values = list(range(2, max_result+1))
data = [Bar(x=x_values, y=frequencies)]
x_axis_config = {'title': 'Result','dtick': 1}
y_axis_config = {'title': 'Frequency of Result'}
my_layout = Layout(title='Results of rolling two D6 dice 1000 times',xaxis=x_axis_config, yaxis=y_axis_config)
offline.plot({'data': data, 'layout': my_layout}, filename='d6_d6.html')
In our program each time we roll the pair, we’ll add the two numbers (one from each die) and store the sum in results. After creating two instances of Die, we roll the dice and calculate the sum of the two dice for each roll. The largest possible result (12) is the sum of the largest number on both dice, which we store in max_result. The smallest possible result (2) is the sum of the smallest number on both dice. When we analyze the results, we count the number of results for each value between 2 and max_result.
When creating the chart, we include the dtick key in the x_axis_config dictionary. This setting controls the spacing between tick marks on the x-axis. Now that we have more bars on the histogram, Plotly’s default settings will only label some of the bars. The 'dtick': 1 setting tells Plotly to label every tick mark.
When we run this program, the following output is shown on the browser:
The above graph shows the approximate results you’re likely to get when you roll a pair of D6 dice. As you can see, you’re least likely to roll a 2 or a 12 and most likely to roll a 7. This happens because there are six ways to roll a 7, namely: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6 and 1.
What if we roll a pair of dice of different sizes? let's take a D6 and D10 and see what happens when
we roll them 50,000 times. The code is shown below:
from plotly.graph_objs import Bar, Layout
from plotly import offline
from die import Die
# Create a D6 and a D10.
die_1 = Die()
die_2 = Die(10)
# Make some rolls, and store results in a list.
results = []
for roll_num in range(50_000):
result = die_1.roll() + die_2.roll()
results.append(result)
# Analyze the results.
frequencies = []
max_result = die_1.num_sides + die_2.num_sides
for value in range(2, max_result+1):
frequency = results.count(value)
frequencies.append(frequency)
# Visualize the results.
x_values = list(range(2, max_result+1))
data = [Bar(x=x_values, y=frequencies)]
x_axis_config = {'title': 'Result', 'dtick': 1}
y_axis_config = {'title': 'Frequency of Result'}
my_layout = Layout(title='Results of rolling a D6 and a D10 50000 times',
xaxis=x_axis_config, yaxis=y_axis_config)
offline.plot({'data': data, 'layout': my_layout}, filename='d6_d10.html')
To make a D10, we pass the argument 10 when creating the second Die instance and change the first loop to simulate 50,000 rolls instead of 1000. The output of this program is shown below:
Instead of one most likely result, there are five. This happens because there’s still only one way to roll the smallest value (1 and 1) and the largest value (6 and 10), but the smaller die limits the number of ways you can generate the middle numbers: there are six ways to roll a 7, 8, 9, 10, and 11. Therefore, these are the most common results, and you’re equally likely to roll any one of these numbers.
As as exercise try to make a program for rolling three Dice and plot the results. See you soon with another topic which will be related to downloading data sets from online sources.
from die import Die
from plotly.graph_objs import Bar, Layout
from plotly import offline
# Create two D6 dice.
die_1 = Die()
die_2 = Die()
# Make some rolls, and store results in a list.
results = []
for roll_num in range(1000):
result = die_1.roll()+ die_2.roll()
results.append(result)
# Analyze the results.
frequencies = []
max_result = die_1.num_sides + die_2.num_sides
for value in range(2, max_result+1):
frequency = results.count(value)
frequencies.append(frequency)
# Visualize the results.
x_values = list(range(2, max_result+1))
data = [Bar(x=x_values, y=frequencies)]
x_axis_config = {'title': 'Result','dtick': 1}
y_axis_config = {'title': 'Frequency of Result'}
my_layout = Layout(title='Results of rolling two D6 dice 1000 times',xaxis=x_axis_config, yaxis=y_axis_config)
offline.plot({'data': data, 'layout': my_layout}, filename='d6_d6.html')
In our program each time we roll the pair, we’ll add the two numbers (one from each die) and store the sum in results. After creating two instances of Die, we roll the dice and calculate the sum of the two dice for each roll. The largest possible result (12) is the sum of the largest number on both dice, which we store in max_result. The smallest possible result (2) is the sum of the smallest number on both dice. When we analyze the results, we count the number of results for each value between 2 and max_result.
When creating the chart, we include the dtick key in the x_axis_config dictionary. This setting controls the spacing between tick marks on the x-axis. Now that we have more bars on the histogram, Plotly’s default settings will only label some of the bars. The 'dtick': 1 setting tells Plotly to label every tick mark.
When we run this program, the following output is shown on the browser:
The above graph shows the approximate results you’re likely to get when you roll a pair of D6 dice. As you can see, you’re least likely to roll a 2 or a 12 and most likely to roll a 7. This happens because there are six ways to roll a 7, namely: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6 and 1.
What if we roll a pair of dice of different sizes? let's take a D6 and D10 and see what happens when
we roll them 50,000 times. The code is shown below:
from plotly.graph_objs import Bar, Layout
from plotly import offline
from die import Die
# Create a D6 and a D10.
die_1 = Die()
die_2 = Die(10)
# Make some rolls, and store results in a list.
results = []
for roll_num in range(50_000):
result = die_1.roll() + die_2.roll()
results.append(result)
# Analyze the results.
frequencies = []
max_result = die_1.num_sides + die_2.num_sides
for value in range(2, max_result+1):
frequency = results.count(value)
frequencies.append(frequency)
# Visualize the results.
x_values = list(range(2, max_result+1))
data = [Bar(x=x_values, y=frequencies)]
x_axis_config = {'title': 'Result', 'dtick': 1}
y_axis_config = {'title': 'Frequency of Result'}
my_layout = Layout(title='Results of rolling a D6 and a D10 50000 times',
xaxis=x_axis_config, yaxis=y_axis_config)
offline.plot({'data': data, 'layout': my_layout}, filename='d6_d10.html')
To make a D10, we pass the argument 10 when creating the second Die instance and change the first loop to simulate 50,000 rolls instead of 1000. The output of this program is shown below:
Instead of one most likely result, there are five. This happens because there’s still only one way to roll the smallest value (1 and 1) and the largest value (6 and 10), but the smaller die limits the number of ways you can generate the middle numbers: there are six ways to roll a 7, 8, 9, 10, and 11. Therefore, these are the most common results, and you’re equally likely to roll any one of these numbers.
As as exercise try to make a program for rolling three Dice and plot the results. See you soon with another topic which will be related to downloading data sets from online sources.
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