Great Expectations

  1. What you expect to happen, Vs what does happen

For some reason, I conditioned myself to believe that events that have a 2/3 chance of occurring will never happen, and events with a 1/6 chance of not happening will always happen.

In Blood Bowl, most things that a baseline human player will do (picking up a ball, catching a ball, dodging away from an opponent) will succeed on a 3+ roll on a six-sided die. An elf, on the other hand, being more graceful and agile, will do those same actions as long as they can roll a 2+.

Strangely, I ended up playing games as though it was impossible for an elf to fail to catch the ball, and as though it was a foregone conclusion that a human would never manage to pick the ball up. Thus when my elves fell over their own feet or failed twice in a row to pick up the ball, or when my opponent’s human managed to pick up the ball, dodge away and score, both things seemed manifestly unfair, God playing dice with the universe and always favouring the other side.

Which, given this would imply it would be impossible to occasionally roll a 6 on a 6-sided die, is pretty daft, and makes me realise I need to retrain myself.

I’ve gone some way to doing so, realising that actually, a basic human is better than an elf at many tasks: take a human thrower as an example. As standard, he can pick the ball up by rolling a 3+ on a D6. An elf will do so on a 2+. But throwers come with the Sure Hands skill by default, giving them the ability to reroll a failed pick up, so a regular human thrower only fails a pick up 1 in 9 times, better than an elf who fails once in 6.

Likewise, human catchers fail to dodge only a ninth of the time, rather than a sixth (but they’re less good at picking up the ball, so unskiled elves are the generalist PPE students of the Blood Bowl world, vs the gnarled specialists of real world occupations, I guess).

Perhaps this is all an exercise in stoicism, to make you more resilient as you realise certain successes and certain failures are anything but. Just as it is when a coach complains their Mighty Blow + Claw murder machine doesn’t injure five players every match, when the chances of him doing that many is really quite unlikely.

Related to expecting any dice roll to do exactly what you think it should is the related concept of…

  1. Statistical Expectation
    E(X) is the amount of times, given enough trials, that you’d expect a certain event, X, to occur, given a certain probability, p(X) of it happening. That is, if you have a fair coin and toss it 10 times, then as the probability of getting a head on any single toss is 50%, if you performed that trial (tossing a coin ten times) enough, the average number of heads per trial should converge to 5.

What expectation does not say is that every time you toss a coin ten times, you should expect exactly 5 heads. (The chances of getting that are … consults the binomial distribution for p=0.5 … well, it’s (10! / (5! x 5!) / 2^10, which is just under 25%.) When random results don’t match with statistical expectation, we should understand that is just because we’re looking at one trial, and so we should have no expectation (pun intended) that the results will be the same as those we’d expect convergence to over the long term.

But mostly we don’t, because we’re human and therefore generally not very good at statistics, and probably think that the chance of rolling 4 consecutive 1s is astronomically small, when if it was, then we’d stand a 1 in 1,296 chance of being hit by a meteorite every day, and it’s not like we hear about 2.5 million meteorite-related fatalities in the US every week, is it?

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