Randomness

from the editor.

a homebrew game designer’s method for defeating randomness.

games of all types typically can be reduced to some measure in two categories: chance and skill. the more luck apparent, the less dependent on skill a game is, and vice versa. randomness is more prevalent in childrens’ games (where complex strategy isn’t necessarily accessible, and can’t hold a child’s attention span besides) and in games of chance, such as gambling.

 

this is all explored thoroughly in ian schrieber and brenda brathwaite’s book challenges for game designers. for anyone interested in designing games – either digital or “analog” – it’s a read well worth it, and has been invaluable in developing my own course material.

 

i’ve wrestled with this concept quite a bit personally, in developing games over the past year and a half or so. i enjoy randomness as a component of gameplay to an extent, such as in developing random maps, resource component compositions, or even player turn order. i’ve fallen out of love with rolling dice, unfortunately, which flies in the face of my youth (as a Dungeons & Dragons aficionado). dice are disappearing from my own game designs as a result.

 

recently, i updated a game design in just such a way, reducing randomness and increasing strategy and planning within the gameplay as it unfolds.

 

to quickly sum up the game concept for this example: players run across the city in search of items to pick up and then drop off at a central location, and each item had a variable chance of success, based upon a value assigned to that individual item, the applicable ability score of the player, and a die roll.

 

the following features were based on random chance in the original state of the game in question. the players used an 8-sided die to determine the following:

  • the location of new items as they were generated

  • the chance to pick up an item when the player made an attempt

  • the chance to steal an already-acquired item from another player in the game

 

several pivotal aspects of the game depended on a single die roll; in this situation, there is an equal probability for any one number on that die to be rolled (trust me on this…either that or think about it real hard: there is definitely an equal chance of rolling a 1 or rolling a 5 or rolling an 8, it makes no difference).

 

one of my playtesters loves skill-based decision-making in games, and he loathed the gameplay; his feedback consisted of what amounted to, “the theme is great, the mechanics suck.” i took his words to heart, and did some hard thinking to reduce chance and increase skill. at the same time, i personally desired a randomly-generated framework within which all players had a level playing field to start, but altered this through their own personal actions, strategy, and choices. i took on two options.

 

probability, and option 1: “success” die rolls

 

this is a method that modifies probability by multiplication. by increasing the number of random generators (dice), and identifying a range of numbers that constitute a success, you can increase the likelihood of a desired result even with a random generator that has equal probability of generating any one available number.for example, let’s look at a normal 6-sided die. there are six different possible outcomes when you roll it:

 

1, 2, 3, 4, 5, 6

 

however, when two 6-sided dice are rolled and their numbers are added together, there are a total of 36 possible combinations, and when the two dice are added together they sum is 2, 12, or a number in-between.

 

why does it work this way? because there are more combinations of 2 numbers from 1 to 6 that add up to 7 (6 different combinations) than they add up to 2 or 12 (only one combination each). for a more detailed description of the probability of rolling two 6-sided dice,have a look at this link, from everyone’s favourite information source.

 

what does that tell us? that the more dice you roll at once, the more likely it is you’ll end up with a sum somewhere in the mid-range (where there are more combinations that add up to a given number) as opposed to those further away from the mean number(s). with two dice the chart is ‘triangular’ while with additional dice, a ‘bell curve’ of possible results emerges in a chart. it’s all very fascinating, if you’re into mathematics at all.

 

for option 1, i wanted to use a similar range of probability to determine player success, but factor in individual die rolls instead of the sum of the rolls. the first step is to determine what a ‘successful’ die roll would be for players. i set this result as rolling a 4, 5, or 6 on a single 6-sided die. basically, the player has a 50% chance of being successful for any one die roll. this is called a “success.” there’s a rather popular role-playing game system that follows this mechanic, allowing players to determine their ability to complete a complex task by rolling several dice and tallying up successes. essentially, you are reducing the 6 possible outcomes to 2 different results.

 

next i changed the target numbers of the items to the number of successes required to pick up the item. finally, i changed the ability scores of the players to reflect the number of dice rolled to determine their number of successes. here’s an example:

 

the target number to pick up the Widget is 3. the player must use Strength to determine whether or not they can pick up the Widget. the player’s Strength score is 3. the player rolls three 6-sided dice; results are a 2, a 4, and a 5. since the player rolled only two successes, they were unable to pick up the Widget.

 

it’s a very simple system, and it reduces the probability of way-out results. the probability of either outcome (a “success” or failure/”non-success”) is now a 1-in-2 chance, as opposed to 1-in-6. to make it more challenging, simply add additional successes required. for any one die roll, you have a 50% chance of producing the desired result; by upping it to requiring two successes, that likelihood decreases (i’m no mathematician, but just think about it: you have to beat a 50% chance for one roll, then beat a 50% chance on another roll…that’s not easy).

 

any way you slice it, more successes = less likely; it’s a tougher number of successes to meet. higher target rolls are for tougher objectives.

 

later, i will discuss the way i developed to generate the locations of newly-placed items. meanwhile, i set aside this model after some preliminary testing in order to examine another option.

 

option 2: player “action cards”

 

for this option, a few modifications were also in order. the game would be altered in a number of different ways from the original to make this work.first off, a “city deck” would be created. the city deck would be comprised of 16 cards, 2 each of numbers 1 through 8. it would be used to generate a number of previously-random variables:

  • location of new items: draw a card, and place the item on that location

  • target numbers for items: draw a card, and that number is the target number

  • target numbers for special, more difficult encounters (such as the in-game police encounters): draw two cards and add them together to generate a result

     

secondly, a “player deck” would be created for each player (up to 4). these decks are composed 13 cards: 3 of each number 1 through 4, and 1 numbered 5. to use the deck, the cards are shuffled, and the player is dealt 5 cards from their own deck to use whenever they need to determine any variable results. once they’re out of cards, they draw 5 more. if the player deck is exhausted, the player will shuffle all discarded cards to rebuild their player deck, and draw as needed.

 

using this new system, let’s see how the previous example would play out.

 

the player moves their piece to the location to see if they can pick up the Widget. the player draws a card from the city deck, and comes up with a 6; the related ability score is Strength. the player’s Strength ability score is 2, meaning they can use two cards from their current hand to meet or exceed 6 (the target number). the player selects a 2 and a 4 card from their hand. the sum meets or exceeds the target number of 6, so the player takes the Widget, then discards the two cards they played.

 

i elected to go with option 2 (the card system), for several worthwhile reasons.

 

game layout remains the same. there are 8 locations in the original game; to keep things consistent, i would have needed to use 8-sided dice which would throw everything outta whack, or modify the probability of rolling 2 six-sided dice to determine locations of new items. It seemed to me that sticking with dice would have added some non-essential bulk to the game. the city deck is simpler.

 

eliminates “dice runs.” even when dealing with a spread of dice to determine successes, there’s the possibility of rolling the same number several times in a row. players might experience a “run of bad luck” or a series of “lucky rolls” or “hot dice” or whatever. meanwhile, the result is that—particularly when determining locations—multiple rolls would need to be generated. if cards are used instead, there’s a probability that modifies to lesser chances the more a player draws cards. here’s a simpler way of saying it:

the city deck has two cards of each number in it. So there’s an equal likelihood that any one of the numbers would be drawn at first. However, once any number is drawn, the probability of drawing that number again instantly reduces…you can’t draw more than two 4’s from a deck that has only two 4’s in it to begin with. The result is that there’s a greater likelihood of drawing different numbers each time.

 

a lot less math. just because i like math (on occasion, in moderation) doesn’t mean everyone else does.

 

the city deck is a one-stop-shop for all in-game variables. Everything on the non-player side of things can be determined using the city deck.

 

there are a few things i predict will happen with the game when i playtest it with the new card mechanic.

 

players will pay more attention. I remember playing the game in a recent testing session; i really hadn’t paid any attention to my ability score and how it linked up with an item i wanted to snatch up. I simply rolled over the space, then worried about the corresponding ability score. in this version, corpse locations do not necessarily change, but the ability scores linked to them do. players will have to keep track of their own ability scores, their current hand of cards, and which ability score they’ll be able to use. players will be able to pay attention to which cards came up in the city deck, and plan accordingly for future item pickups, police encounters, and otherwise.

 

the game will not be as easy as it has been in the past. again, there are more meaningful choices in the new mechanic, and so players will have to think more to be more successful.

 

the game will be longer. i’m not so pleased with this (predicted) development. but the hope is that the added gameplay afforded through the new mechanics will balance out the need for a longer game. along with this is a future plan to reduce the number of movement spaces on the board overall, so more action can take place in each round. although i enjoy the “sprawl” of the city at the moment, it can definitely be reined in a bit before things are too claustrophobic.

 

the chance cards will become more valuable. these randomly-selected pickups will be the only cost-free way to increase one’s chances in beating any target numbers. i imagine players will want to pick up as many cards as they can, so as to maximize their performance when the opportunity comes along. I’m also planning on instituting a “shop” mechanism to allow players to trade in the less-powerful chance cards, and/or purchase better ones.

 

ultimately, player performance will be more linked to player choice. this is what i’ve wanted all along, and so hopefully things will work out smoothly after all the changes are integrated.

 

playtesting is your friend. perhaps i can convince the players to jump into one more game of this before the design class sessions are completed…

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