Logical Fallacies and Gaming: Neglect of Probability
What even is "Neglect of Probability," and how does it affect your decision-making process when playing a dice-based board game?
There are a lot of things we as humans, with our incredibly complex and confusing brains do not naturally understand. One of those things is probability and it affects all aspects of life, in both awesome and terrible ways. However, this blog is not about life, it is about board gaming and awesome things, so let us discuss what “Neglect of Probability” is, and how it affects your decision-making process when playing a board game involving dice.
Wikipedia defines neglect of probability as:
“ The neglect of probability, a type of cognitive bias, is the tendency to completely disregard probability when making a decision under uncertainty and is one simple way in which people regularly violate the normative rules for decision making. Small risks are typically either neglected entirely or hugely overrated, the continuum between the extremes is ignored.“ –Wikipedia
In laymen’s terms, this is stating that very often, humans, when making decisions, base their choice on anecdotal evidence or a few personal experiences, rather than mathematical probability, simply because the concept of probability is very challenging for the human mind to intuitively understand.
You’ve probably had a conversation with someone before who is incredibly worried about a statistically implausible event – such as being bit by a shark( 1 in 3,748,067 chance) or killed by a plane crash( one in 11 million chance).
No matter what you say about the odds, the person typically remains terrified and won’t set foot near either of the locations where each of those things MIGHT occur, simply because they have heard a story about someone who was eaten by a shark or died in a plane crash.
This is because, for the majority of history, probability really did not exist, and evolutionarily, it has been a lot more important to remember that “Bears can eat us” than that the chance of being eaten by a bear is 1 in 2.1 million, while you are visiting Yellowstone Park, the place which you may remember as – a place with a lot of bears.
So, once while logic has evolved so that we can sit down, in an office and make an informed decision based on comparative probability(”Investing in Stock A is better than Stock B”, etc), it is very challenging to make an informed decision on anything that is emotionally important to us.
So, how does this effect gaming?
Any gamer can tell you that most games are full of emotional situations, charged with excitement, tension and reliance on luck. Most games rely on probability in some form, and offer a chance for comparative probability – however, most gamers make decisions based on intuition, rather than actually looking at the numbers and comparatively.
Allow me to illustrate this point with a short anecdote:
When I was playing Lord of the Rings Miniatures with my friends Donald, Michael, and Jeff, I intuitively thought that using a catapult to knock down a wall would be relatively simple and feasible – after all, isn’t that what they are made for? However, Donald explained to me the game mechanics, and the fact that probability was relatively low than my shots would even hit the wall, since I had to essentially make three dice rolls to A. Fire the Catapult B. Hit the Wall. C. Damage it. And I would have to do this every time I fired. Despite him showing me these numbers, I still figured that it would not be that hard, based on my anecdotal experience of playing other games. But, I decided to use a different siege weapon, ballistas, and focus on attacking objects instead.
Later in the game, I attempted to shoot through a door, which would be a much easier target, but both my shots, with my ballistas, didn’t fire. It was clear that, despite my anecdotal assumption that I would hit, I did not properly calculate the probability, and the results were disastrous.
This is just one example of a situation where someone playing a game makes a decision based on emotion rather than math – and let’s face it, it’s easier to make a quick decision off the cuff, but having a decent understanding of probability will greatly increase your chance of being “good’ at any and all board games involving dice or cards.
The Best Way to Understand Probability is to Translate the Numbers into Percentages and Compare
The reason we have percentages is so that we can reasonably compare fractions without having to guestimate and deal with vague numbers, so I highly recommend getting a basic knowledge of what different fractions translate into in order to compare probability chances mathematically.
Here are the basic steps to get the first level of probability, that can be calculated easily with a smart phone or calculator.
1. Recognize the fractional chance of getting the roll or card you need.
If you need to get a 6 on a 6 sided dice, the probability is 1/6.
2. Translate to Percent
Punch that in a calculator and you get .1666666, which you can translate to a percentage by simply multiplying by 100 or moving the decimal point. Than, you know that the chance of getting a 6 on a 6 sided dice roll is a 1/6 or a 16.6% chance.
3. Do this for other numbers and compare them
Let’s say the game you are playing offers you the choice of either rolling a 6 sided dice and hoping or a 6 or rolling a 20 sided dice and hoping for an 18, 19, 20. The easiest way to do this is simply count up the possible winning numbers here(18, 19, 20), and divide that number by 20. 3/20 = .15, or 15%. So, comparing 15% to 16.6%, it is clear that 16.6% is more likely to occur, you would choose the 6 sided option.
But – I don’t have a calculator on me at all times! I don’t want to do this much math!
Well, I have calculated some common dice rolls and “DC”s for your convenience.
The probability of getting any specific number on Different Dice(rounded)
Probability of Commonly Sought Dice Rolls:
Doubles with 2 Dice – 16.6%
Critical Hit in D&D, Pathfinder (19-20) – 10%
Beating a Dice Check of 10(with no modifiers) – 10%
Beating a Dice Check of 15(with no modifiers) – 25%
Yahtzee on First Roll – 0.0077%
A more complex look at this can be found here:
Generally speaking – the point is this – the human mind does not intuitively understand probability – if you can get a good mastery and understanding of it, you will find yourself enjoying and winning board games more often than your peers.
Please comment with your thoughts about this fallacy and post other fallacies or questions about probability in regards to gaming!
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Originally published by Ed