# Know your roll with Dicegraph.

## Visualize dice roll outcomes, plan accordingly, and game on.

The Dicegraph Probability Engine (or Dicegraph for short) is a statistical modeling tool—which is a fancy way of saying it’s a tool that shows you the likelihood of every possible outcome when you roll a set of dice.

Way beyond statistical averages, Dicegraph shows you exactly how likely any given outcome is, and empowers you to make smarter, better-informed decisions in your gaming.

## How does it work? Choose your role to learn more.

Tabletop wargaming is the birthplace of Dicegraph, and we built this tool to help you optimize your strategies before your units ever hit the battlefield. Here’s an example:

With Dicegraph, you select how many dice you’re rolling, how many sides those dice have, and any rules needed to calculate success or failure. This gives you a clear visual of the likely outcomes, and lets you model more complex rolls made in sequence. But we’ll get to that later.

For now: Your 10 infantry have 10 laser shots, which hit on a d6 roll of 4+.

We can see that the likeliest outcome is 5 successful hits. Just this knowledge can help you make decisions about equipment, opponents, or even types of units in your army. But let’s dig deeper.

Your opponent’s space orks are wounded by lasers on a d6 roll of 5+. So we take the likelihood of success for every shot, then calculate the likelihood of those shots wounding, which looks something like this:

Our odds are getting narrower. Orks aren’t heavily armored, but say they have a chance to save against a wound on a d6 roll of 6.

This shows us that the most likely outcome is one dead ork (36.16%), and there's only a 15.18% chance of taking out 3 or more. Not the greatest odds, but a wealth of information to help you equip yourself for success and make smarter decisions on the field.

Balance is critical for every game, especially when you’re running or designing them.

Dicegraph helps you ensure your next Dungeons and Dragons encounter, your new campaign, or your in-progress top-secret tabletop game is fair, balanced, and just the right amount of challenging for your players. Here’s an example:

You’re a DIY dungeon master who wants to run a new homebrew encounter for your party, but you’re not sure if the monster you’ve made will be too powerful for your players.

With Dicegraph, you can model the outcome of a monster’s attacks against a given player, and see if the probability of potential damage is acceptable—or if it sends you running for the hills.

Say your new monster gets two attacks, each of which hit on a d20 roll of 12+. Each attack does 2d8 damage. How much damage could happen on a single turn?

We can see that this monster is most likely to deal 9 damage to a player, but has a non-negligible chance (10.96%) of dealing at least 18 damage, which is nothing to shake a staff at.

Visualizing these outcomes can help you make more informed decisions about your game, optimize outcomes before playtesting, and create all-around happier players.

For game masters and designers, additional support for the complexities possible in base-d20 systems, like modifiers (think 2d6+2 damage instead of 2d6), combining multiple models (two very different characters attacking the same monster), and branching results (critical hits on a 20) are all on the roadmap.

Maybe you’re not a tabletop gamer or RPG addict, but you’re curious about the implications of statistical modeling like this. You’re in the right place! Here’s a totally non-game-related example:

Let's imagine we have a dam with a fish ladder, and ten fish at the bottom of the dam.

A fish only has a 50% chance of making it through a step in the ladder, which we represent as a roll of 5 or higher on a ten-sided die.

We have three steps in our ladder.

At the top of the damn, the fish will spawn and each will have between 1 and 10 baby fish.

How many baby fish will we have at the end? It's possible that we will have 0 baby fish – if none of the fish make it through the ladder. It's also possible that we will have 100 baby fish — if all of the fish make it through and they all have 10 baby fish each.

We can see that the chance of 0 baby fish is 8.7%, while the chance of 100 baby fish is so vanishingly small that it's basically 0%. Between those two extremes we have the chance of any given outcome, and the chance of *at least* some outcome. The chance of 0 or more baby fish is 100%, while the chance of 10 or more is 50.66%.

Check out the other examples to see how this might apply to gameplay or game design, or dive in and give it a shot yourself!

## What’s all this goodness cost?

**Dicegraph is free to use for modeling rolling outcomes.** To save, search, and share your statistical models, though, we ask for a modest $3/month.