With all the dice rolling, is there a way to use probability in games like Dungeons & Dragons to improve your odds? There sure is.
The tips below will help you calculate some basic probabilities. Once you see how it works, you can apply it to any type of game.
Probability Basics
How do I calculate the odds of a 1d20 result?
The odds of a single dice roll are 1/the number of sides. So for a d20, each outcome is 5%, which means:

The odds of rolling a 7 are 5%.
To get the odds of a range of numbers, simply add up all the probabilities. For instance, you have a 6 out of 20 chance of rolling 1520, so:

The odds of rolling 1520 are 30% (6 outcomes * 5%)
Calculating Damage Probabilities
What is the most likely result of 2d6 (or any damage combination)?
Use this website to calculate more complicated dice rolls. Type in “output 2d6” and you’ll see a chart of probabilities. You’ll need to note these results. With a 2d6 for example:

You have a 44.5% chance to roll between 68. (I added up the the percentages of the three most likely results, 68. This gives you a sense of how likely a number will fall within this range.)

Repeat this exercise to understand the probability of doing damage for all your attack types, and notate the results on your sheet. (For items with bonuses, try “output 2d8 +1”, for instance).
Saving Throws
You have three chances to pass a DC 16 check. How do you know your odds of success?
Some trap checks require multiple roles like this. For this exercise, we’ll use a binomial distribution calculator. Good news — it’s a lot simpler than it sounds.

The probability of a DC16 check is 5/20, because only five numbers on a d20 will pass. Enter “5/20” in the first box.

We have three chances. Enter “three” in the second box.

We only need one success. Enter “one” in the second box.

Easy! We have a 57.8% chance of passing this check.
Combat probability in games like Dungeons & Dragons
How does advantage affect rolls?
A lot. The TLDR; on this is that you should take advantage very seriously. If you have it or can give it to someone else, make sure you’re attacking. If you have disadvantage, you might want to retreat. For example, you have less than a 9% chance of rolling higher than 15 with disadvantage. The chart here explains it in more detail.
Understanding Your Opponents
Technically you shouldn’t know the weaknesses of a specific monster. That would be metagaming. But is it metagaming to know the average weaknesses of all monsters in the Monster Manual?

On average, monsters will be weakest against saves that target these attributes (in this order): Int, Cha, Wis. If you can attack a monster with something that requires an Int save, you’re statistically likely to be targeting a weakness.
Probability of avoiding resistance
The fine people of the Internet have analyzed the average resistances in the Monster Manual:

Fire and poison are the most common monster resistances. You have the highest likelihood of encountering a monster with resistance to these types of attacks.

Radiant and Force are the least likely monster resistances. If you use these attacks, you’re likely safe.
A Probability Chart Example
Here’s a chart for a simple cleric that you can use as a guide. You would need to create a chart based on your unique character.
Guiding Bolt  Average damage: 14 (1216) Average attack roll: 20.5 average 
Spiritual Weapon  Average damage: 23.5 (2225) Average attack roll: 20.5 average 
Spirit Guardians  Average damage: 13.5 (1314) Average attack roll: 15% likely WIS save (Targets multiple) 
Flame Strike  Average damage: 28 (2729) Average attack roll: 15% likely DEX save (Targets multiple) 
Insect Plague  Average damage: 22 (2024) Average attack roll: 15% likely CON save (Targets multiple) 
Blade Barrier  Average damage: 33 (3134) Average attack roll: 15% likely DEX save (Targets multiple) 
Word of Radiance  Average damage: 10.5 (912) Average attack roll: 15% likely CON save (Targets multiple) 
Sacred Flame  Average damage: 13.5 (1215) Average attack roll: 15% likely save DEX 
A chart that shows average damage of various spells, plus the likely saving saving throws.
Helpful Probability Tools for Games like Dungeons & Dragons

Anydice – a general dice probability calculator

Best saves to use for targeting monsters

Binomial Distribution Calculator for determining DC checks
* Photo by Alperen Yazgı on Unsplash