I promised (threatened?) earlier in the week that I was going to talk about Chaos Theory again on here, and I'm going to follow through on it because that's just the kind of guy I am.
Regular readers (don't you have anything better to do? On second thoughts don't answer that.) might recall me talking about Chaos Theory before with regards to time-travel plots and how it makes most of them not really work, but today, in a shocking departure from established convention I'm going to link it directly to 40k! And no, I don't mean by math-hammering how many Obliterators it takes to kill a Knight Castellan in one turn.*
Here's a scenario most 40k players, or indeed players of most games with dice in them might recognise. A player fails a clutch roll during a game, and realises after the fact that they could have done something about it. For example, they could have used a command re-roll, or used a one-time rule that gives +1 to a roll, etc. Maybe then they look at the dice and say "Damn***, a 2. If I'd used my +1 to hit ability I'd have succeeded!". Another classic is failing an unlikely roll, say a 6+ hit or save, and saying "It's not worth using my re-roll on that, but let's see what would have happened if I had." Of course, by the law of dramatic inevitability this 'virtual' re-roll then succeeds, leading to much wailing and gnashing of teeth.
Well here's the thing, my fellow disciples of the Great Cuboid Deciders- it doesn't matter. Don't worry, be happy, because none of these scenarios actually means what our grumpy, pattern-obsessed little minds think they do. For the reason why, we need to look to our old friend Chaos Theory, in a development that you might just possibly have seen coming.
To understand why, there's a simple experiment you can conduct. Pick up a dice, a D6 is best and a D4, for reasons I'll explain later, is best avoided. Hold it in your best rolling grip, taking note of exactly where it is relevant to your dice-rolling surface, and let fly. Note the result. Now pick up that dice again, and try to roll it in the exact same way, with the exact same amount of force. You'll find that almost exactly 5/6**** of the time, you'll get a different score, assuming the roll is 'fair'. (i.e. that the dice actually rolls, which is why I discouraged the D4, since those things skid like a rookie F1 driver on the wrong tires in a monsoon.)
Counter-intuitively to what our brains like to think about things like science and physics, even a precision built device that always imparts the exact same amount of force to the dice and throws it from the exact same position will tend to end up with a seemingly random result. This is because there are so many tiny little variables that are impossible to take fully into account- small electromagnetic, seismic or gravitational fluctuations, tiny air currents, accumulating damage to the corners of the dice and the surface it lands on, etc.
So what does this all mean? Simply put, if you were able to go back in time and use that +1 ability you decided not to use the first time, the tiny difference in exactly when and how you rolled that dice would mean the result would be different. You might well still succeed, but you still might not. Likewise, re-rolling a dice to see what would have happened (or looking at the result of the next dice you roll and imagining what would have happened if it were the re-roll) actually tells you nothing, because if you actually had used the re-roll the result would most likely have been different.
Before the geek brigade (of which I am a proud member, let's be clear) turns up to point it out in the comments (ahahaha) we should note that there's an important exception to this rule, which is when your dice rolling takes place on a computer. Since random numbers on computers aren't in fact random, but are instead based on a 'seed' value that's then chewed up by a complicated formula, some implementations will always give the same sequence of results, as can be seen in some of the XCOM games where re-loading a save to retry a missed shot will always result in another miss unless you do something different first to alter the sequence. (I suspect this is why the official GW 'dice app' uses the accelerometer to roll the dice, though there are other ways around the problem). Random number generation is a fun topic if you feel like losing yourself in the labyrinths of Wikipedia for an evening, but probably not something we need to talk about right now.
To get back to the point, what I'm trying to explain here is basically that dice are evil little contrary beasts and one should never, ever assume they they're going to behave the way you'd expect. So the next time you decide not to use a re-roll and regret it, or use one and get another damn 1 again, just remember that whatever you think you would have, should have or could have done instead, it still might not have worked out. It all evens out in the end.*****
*The answer is seven.**
**That's a blatant lie, but I'm hoping no-one reads double footnotes.
***Or most likely, something with a little more spice to it.
**** Or 9/10, if you tried with a D10 like some sort of wise-acre.
***** Though with one of my regular opponents and his hyper-jammy 4++ saves, not yet.
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