Designer’s Corner: Mack Martin on Game Theory of Dice

Dice are one of the most common game tools in all of table top gaming. There is a lot to cover when it comes to dice. Lets go!

By Mack Martin

Rolling dice is one of the simplest ways to generate a random number. Some games use a deck of cards, and that has its own merits and flaws. It’s important, as a game developer, to think about each type of dice, and how they will be used. It’s not about “what is best”, as that’s a matter of opinion. Instead, it’s about know what effect the dice have on a game.

When a player rolls a die, or a pool of dice, he is committing to an outcome. He knows that once the dice are rolled, he can’t take his action back. It’s the moment where he looks in Schrodinger’s box hoping to find a cuddly kitten. This generates excitement. This is where a players maneuvering, plotting, and planning can all come together, increasing his odds at success.

This article will be a little stream of consciousness. Please don’t hesitate to post a response, and if any of this is a topic you want me to expound upon, let me know! So here are some things to mull when deciding on what dice to use:

Number of Faces
Most dice have a numeric sequence, such as 1 to 6. When rolling these dice, the number of faces increases the maximum possible number and the average number, but not the lowest number. This opens up some math options, bigger usually being better. A bigger weapon in DnD has a bigger die for damage, for instance.

When a player is expected to roll multiple types of dice, it is best to have him rolling as few dice as possible. This is really just a cost issue. A wargame could, in theory, make use of many sizes of dice, but the design team needs to be certain that they don’t expect every player to have 20+ of each die type. That would quickly get cost-prohibitive. Instead, games like DnD expect each player to have one or two of each die type.

Dice Shape
Each die type has a unique shape. On a flat surface, such as a table or game board, the shape of the die really isn’t much of a concern. They will be clear to read once they come to rest. However, wargames involve uneven surfaces, and that gets tricky. This is one of the reasons why so many wargames use d6′s. The d6 typically rolls “uncocked” more often than d8′s or d10′s. The ninety degree angle really helps prevent many of these issues.

The Odds
This is where dice pools, roll process, modifiers… all that good stuff, changes everything. Dice allow for resolution of multiple events simultaneously (such as 20 orks shooting at once). The more dice rolled, the more likely the player will roll towards average. 30 dice that succeed on a 5 or better, are extremely like to generate between 9 and 11 successes. These are all “success engine” decisions, where the designer must decide how “swingy” he wants his game to be. Sometimes swingy is good (like in a party game) and sometimes it will annoy players.

Skirmish style wargames, like Malifaux, can use a deck of cards, as they don’t need many events resolved at the same time. Dice are just another random generator to these games. Additionally, a deck of cards that isn’t recycled until all the cards are used provide a set amount of “luck” to a player, which can help to normalize the “bad rolls”. It won’t solve it all ,but it helps.

Die Pools vs. Additive Dice
This is a simple distinction, but I need to briefly talk about the differences here. In a dice pool system, each die is independent. In an RPG this means that more dice is better, as each dice is attempting to score a success. The same is true in a wargame, each dice typically representing one units attacks (or several dice in the pool representing those attacks). The target number for each dice is adjusted based on the difficulty of the challenge or the players skill. The number of dice can either be skill, or rate of fire, ect. Basically there are two scales that can be adjusted to get the odds in line with what the designer wants.

Additive dice are rolled and added together, such as 2d6. These system uses fewer dice, and creates a probability curve. Fewer dice still come close to “the middle” and it’s a fairly predictable system. Warmachine uses this in conjunction with modifiers and scaling target numbers to create a variety of probabilities with just a few dice.
Both systems are fine, they just perform in different ways, and a designer needs to know what effect he is shooting for. It really just adds to the “feel” of the game, and either system can be equally well balanced. There are other systems, but they are rare enough to not really go into.

Another simple way to adjust the odds. On a d6, each +1 is a bonus 16.66% chance at success. While modifiers are easy for the player, to many modifiers can cause confusion (or forgetfulness, which is almost worse). I prefer to just apply one modifier, usually the highest of both good and bad, that sort of thing. No modifiers is best, if you can find another way to handle it, or reactive modifiers. It’s far better for an opponent to say “I’m using my shimmer stone, this attack you’ve just declared is at a -1″ that way it isn’t forgotten. Modifiers are a good tool, just be careful how you use them, they can get out of hand.

Target Numbers
This is where dice succeed or fail. This is the number a die must equal or exceed to count as a success. I recommend equal or succeed, instead of succeed. Players tend to view die rolls a bit like money. If you have 5 dollars, you can buy a 5 dollar success. It’s really just a terminology thing, it shouldn’t alter your game design mathematical spread at all.

Typically, a target number of 1/3 or 1/2 is a good starting point. This gives you a lot of wiggle room both up, and down. If you start with 1/3 success, you are telling the player that things are harder for their units or characters, however. In an RPG, most players should feel confident that a “standard” check (like a typical attack) should succeed about 50% of the time, more if they are combat focused. A non-combat check (like knowing history, or spotting a hidden door) should probably have about a 2/3 success chance. Players like to feel like their characters are competent, for the most part.

For miniatures games, I like a 40% to 60% chance at success as a baseline. This gives plenty of up and down movement for defining models in an interesting way without the outcome being certain.

Success and Failure
The purpose of a die roll, is often to see if a player will succeed. This can be as simple as moving spaces on a board, where success is landing on the right space, or simply going as far along the track as possible. In a wargame this roll can feature a series of rolls, where final success isn’t determined until the end of the series.

I wonder how many pictures of Jennifer Tilly playing poker I can use…

A player is always spending a resource when he makes a die roll. In a wargame a unit only has so many actions, so a player is choosing to use one of those actions to make a die roll. He has to assess his odds of success, and make the roll blind, knowing that failure is possible. His goal is to make failure as unlikely as possible.

It is equally important that a player have a chance at success, however slim. No matter the odds against a player, he needs to have a chance for the die roll to come in his favor. If it doesn’t, he will feel defeated by the system, not his opponent. That’s seldom an outcome a designer wants.

If a die roll doesn’t contain a chance for failure, there isn’t any risk. This can be fine, if you’re using a die to determine a random factor (like the weather) or building a scenario. When a die roll is just a random generator, it needs to effect all players equally. When you roll a non-failure dice separately for each player the roll still has a chance at failure, it just becomes harder to see. If both players are rolling separately for weather, for instance, it is a victory if one player generates “light breeze” and the other gets “all your units are struck by lightning.”

So there are some random thoughts on dice, and how each can be used. It’s a good starting point, if you want to know more about a certain topic mentioned here, please let me know! -Mack

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