CMON Feature Friday: What Are the Odds?
Never tell me the odds - Han Solo
If you’re a strategic game player, then you know that board games are usually made up of a series of big and small decisions. The best games find creative ways to make those decisions interesting and challenging. Almost always, you have to decide on a path you want to take: Do I collect wood or go after coal? What you’re really doing, in an abstract way, is calculating the odds of a situation. You’re deciding what actions are more likely to help you generate points, or gold, or whatever the victory conditions are in the game. Knowing the odds is not always a good thing. Sometimes the most fun decisions we make in a game are the ones when we follow our gut. But no matter what leads us to take the actions we do, the odds stay the same.
There is a well know psychological idea called the Gambler’s Fallacy. It’s the belief that the likelihood of something with fixed odds will become higher or lower the more often you do it. Take one of the most common components for randomization in games: dice. The odds of rolling any number on a single six-sided die is exactly one in six. But what if you’ve already rolled three fives in a row? Surely it’s less likely that you’d roll one again. Well, that’s what the gambler’s fallacy would have you believe. But, in fact, the odds remain exactly the same: one in six. It’s when we start to apply emotion and past history to outcomes that they start to become clouded in our minds and we’re more likely to make choices that don’t reflect the best odds in a certain situation.
When dealing with two dice, the odds become a bit more interesting to calculate. There are 36 different potential outcomes, but the odds vary greatly depending on the outcome we’re talking about. A result of two or twelve only has a one in thirty-six chance of coming up, because there’s only one combination of results for each of those numbers. However, a seven has a six in thirty-six chance of coming up. Both the six and the eight have a five in thirty-six chance of being rolled. When you picture a Can’t Stop board or the initial layout of a Catan game, you can see why there’s such fierce competition for certain spaces. The interesting thing is that while having a position that is favored by the odds is helpful and advantageous, it’s not a guarantee of victory. In games with random elements you can do your best to be in a good statistical situation, but ultimately randomness and chaos will determine the outcome.
A lot of games don’t use dice to figure out situations. Cards are another common element in board games. Since each game is different, we’re going to look at some odds from a standard 52-card deck. The likelihood of drawing any single card is one in fifty-two (not particularly good). Now let’s say you need that Ace to complete your straight. The odds seem a bit better, and they are, but only slightly. There are four Aces in the deck (assuming none have been taken out yet). That gives you a four in X chance if finding that Ace (where X is the remaining cards in the deck). When you consider that the odds of getting something other than an Ace from a 52 card deck can be expressed like this: 52/52 – 4/52 = 48/52, all of a sudden, getting that Ace seems very unlikely. That doesn’t stop us from getting up from our chairs and watching with hope against hope that our card might be the next one flipped, but knowing these odds might make you a little more hesitant to back yourself into the corner of needing a specific card to turn up.
Many modern games that use cards recognize this statistical challenge, and build in ways of mitigating it a bit. Some rules will allow you to draw a certain amount of cards and only keep one or two of them, or you’ll have the option of drawing cards from a face-up display. Little tweaks like this increase your pool of options and shifts the balance to being more about the decisions you make and less about the luck of the draw.
Random elements are just that: random. You can look at the odds of a given situation and put yourself in the best statistical position for victory, but nothing is guaranteed. That’s why we play the games, because we don’t know what’s going to happen and it’s a heck of a lot of fun to find out!
Here are a few other facts that board game scientists have come up with:
• The most landed upon Monopoly spot (aside from jail) is Illinois Ave.
• Ms. Peacock starts a game of Clue one space closer to a room than any other character.
• The probability of getting a Yahtzee in a single roll is 1/1296
• Getting a 29 point hand in Cribbage is a 1/216,580 shot.
