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Evaluating Randomness in Game Play

What makes a game fair? Cards are random. Dice are random. Sometimes even the choices other players make are random. How do I know if the win/loss scenario at the end of the game is appropriate for random outcomes along the way?

Well, I could play test many, many times and see if a ‘win’ happens a desirable percentage of the time. But even then, can I be certain the draw of the cards and roll of the dice are matching the outcome?

A 12 sided die with 11 unfavourable events, and one smiley face.

Random Events

The game is a two-player cooperative set-matching game. However, I’ll be playing the solo variant to simplify assessing the favourability of random outcomes that happen each round. My goal is to balance the game’s ‘bite-back’ against players trying to achieve a win.

I wanted to relate the randomness during gameplay to the final win/loss outcome. To do this I made a list of all of the random events:

  1. draw of cards into hand
  2. how beneficial was that turn’s task for achieving an overall game win
  3. how beneficial was the cards in the market for achieving that turn’s task
  4. how unfavourable was the end-of-round dice roll (an adversarial roll)

I also looked at decisions made by players during the game.

  • what set to try to complete that turn
  • whether to play a card from my hand into a set or into a sequence

It’s not entirely clear that any event is strictly random or completely a ‘player choice’ event. Nonetheless, I wanted to track these six events and particularly track just how favourable the outcome was for each event.

To track the favourability of any outcome, I needed to decide what makes the outcome favourable. The game has 10 rounds and there are six outcomes each round. I chose to assess each outcome with a simple Y/—/N, rather than a 1-5 or 1-10 scale. The main reason was consistency.

Favourable Outcome Thresholds

I wanted to be able to consistently assess the same outcomes from round to round and from game to game. Too many choices for the outcome would make the assessment too subjective. 60 data points and three choices for each data point was enough. I still needed to objectively distinguish a Y (favourable) from an N (unfavourable) outcome, from a ‘—’ (neutral) outcome.

I focused on the random outcomes rather than player choice, which gives me 4 outcomes in each of 10 rounds: 40 data points. Somewhat subjectively, I decided on thresholds for making a distinction between a favourable outcome, an unfavourable outcome, and a neutral outcome. I did this for each of the four random events:

  1. draw of cards into hand
    • Favourable: at least 4 cards in a 7 card hand that can make a ‘set of five’.
    • Neutral: exactly 3 cards
    • Unfavourable: 2 cards
  2. how beneficial was the task’s turn
    • Favourable: gain two red blocks
    • Neutral: gain one red block
    • Unfavourable: gain no red blocks
  3. how beneficial were the market cards
    • Favourable: contains three needed card
    • Neutral: contains one/two needed cards
    • Unfavourable: contains no needed cards
  4. how unfavourable was end-of round dice roll
    • Favourable: gave two adverse conditions
    • Neutral: gave one adverse condition
    • Unfavourable: gave no adverse conditions

Evaluating Randomness

With that level of clarity, I just needed to play. I chose to start off with the solo version of this two-player game. At the end of each game I added up the favourable, neutral, and unfavourable outcomes separately, and then subtracted the unfavourable tally

from the favourable tally, while ignoring the neutral tally. This process gives a single number that represents the favourability of the random events in that particular game.

I then compared the favourability rating to the final win scenario. There are four win scenarios:

  • Climate Warrior (highest win)
  • Climate Emissary (respectable win)
  • Climate Novice (lowest win)
  • Climate Consumer (sorry, not sorry)

I evaluated a few dozen solo games with this technique using ‘optimum strategy.’ What that means is that I eliminated player error, by ‘rewinding’ when necessary, just like you’d do if you played the 7 of hearts on the wrong stack in Solitaire.

I found that under optimal play, more favourable random outcomes consistently resulted higher win conditions. But what was nice to see was that the highest win condition was rarest, and the lowest win condition was the most common of the four possible end game conditions. Which means that with sub-optimal play (most likely for the average player), winning is not likely to happen by luck.

Mid-, Early-, Late- Game

After comparing the final win scenario to an aggregate favourability rating, some new questions surfaced.

  • If a game starts out with unfavourable outcomes is the player doomed to failure?
  • If a player enters the end game with a clear path to victory, is winning a certainty?

In short, I’ve fond the answer to both of these questions to be NO, at least for Climate Change 2030: Running out of Time. But how did I go about that discovery?

I divided the ten rounds into three (for lack of a better word) phases: Early (rounds: 1-3), Mid (rounds: 4-6) and Late (rounds 7-10). Round 10 is primarily a ‘clean up’ round with no adverse effects. It just would not be fun to go through the whole game, get to a very nice win scenario, and lose because of a single unfortunate dice roll.

I went back and re-evaluated all of three dozen plus games played so far. I added the favourable, neutral, and unfavorable outcomes during each phase separately. I calculated a single number that represents the favourability of the random events in each phase, by subtracting the unfavourable phase tally form the favourable phase tally.

So there are three favourability ratings for each game: Early, Mid, and Late. Those three numbers gave decisive answers. You’re neither doomed to failure, nor are you home free. Exactly what I’d want in the solo version of this two-player game about climate change peril.

A big challenge ahead at the start of the sixth round

This Week’s Take-Aways

By making subjective, yet consistent decisions, about what makes any outcome favourable, or not favourable, I was able to

  • correlate the favourability of each game’s randomness to that game’s win scenario.
  • determine if a ‘slow start’ would doom a game.
  • Determine if a ‘run-away’ winner can get slopping in the end game.

The balancing within the game was sufficient so that with optimal play

  • the win scenario is consistent with the favourability of the cards and dice
  • you’re NOT doomed because of a slow start
  • you’re NOT coasting to an easy victory simply by riding on your laurels.

Of course with sub-optimal strategy and play, there’s plenty of room for improvement, but that’s where all of the fun is. How do you tell if the randomness in your game is fair and balanced?

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