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Hey, game geeks!
Want to talk about my favorite hexahedron here, the D3-1, or as most of you probably know it, "that strange die from Betrayal at House on the Hill". Still in search of a better name for it, but as far as die naming conventions go, "D3-1" is still technically accurate, so we'll go with that.
What is the D3-1? It's a six-sided die, the "standard" D6, with two blank faces, two faces with one pip, and two faces with two pips. In short, it creates an even distribution of 0, 1, and 2. This is not the same as the die from Small World, which has 3 blanks, 2 ones, and 1 two. The math on that is very different, so we're discarding it from this particular discussion.
Why do I claim it's the greatest die? Why not the standard D6, or the classic RPG favorite, the D20? While the D6 is indeed a known classic, and the D20 provides a huge variety of outcomes with nice round probabilities in increments of 5%, the D3-1's magic lies in its expected value.
What is expected value? It's the average value that you'd roll on the die if you rolled it a lot. Like, a lot a lot. Technically, infinite. For a standard die with an even distribution of sides ranging from lowest to highest, the expected value is simply (highest value + lowest value) / 2. So for the standard D6, the value is (6+1) /2 = 3.5. For a d20, the value is (20+1) / 2, which is 10.5 (On a tangential note, if you were wondering why base Armor Class and Difficulty Class, or AC and DC, values in D&D was 10, this is why). For the D3-1, this value is (2 + 0) / 2 = 2/2 = 1.
Ok, so the die will roll an average of 1 over the long term. That's cool, I guess, but the D3 does the same with 2. Fudge Dice (which mathematically are just D3-2) have the expected value of 0. Why is the D3-1 so special?
Because, with an expected value of 1, that means you can substitute the D3-1 for a stat to introduce some uncertainty while not messing with your math. If you roll 8 D3-1s, you'll get an average roll of 8. You might have 7 or 9 or 11 or even 0, but on average you get 8. This is precisely what Betrayal at House on the Hill does to great effect, and it uses the unique distribution range to do something very cool.
In Betrayal at House on the Hill, you play as a character with stats. These stats are used to make checks against various challenges in the eponymous House. You might have a Speed stat of 5, and have to make a Speed check of 4. So you roll 5 dice, and hope your total is greater than or equal to 4. Simple enough, right?
Well, the beauty of using the D3-1 for these kinds of rolls in this particular game lies with the theme of the game: it's a horror game. You are not a heroic protagonist of a power-fantasy RPG; you're a horror protagonist who might die at any moment the haunting string music gets a bit too loud. Because rolling a zero on any die is always a possibility, you are never safe. You can ALWAYS fail a check if you're just that unlucky (ask me how I know!). By that same token, if you're lucky, you might succeed where you have no real business succeeding. This uncertainty helps to play into the theme of the game; you have to push your luck to escape the house, and you can always, always fail. The zero faces on the die ensure this. You could roll 10,000 dice, and there is always the possibility, no matter how remote, that you roll all zeros. You can't do that with D6s or D20s.
"Well," you might say, if you are mathematically inclined, "Fudge Dice do something similar, but their expected value is 0, so you can still get that feeling of uncertainty!" And you are absolutely correct, but I hold that the D3-1 is superior for one specific reason: you are never penalized for rolling more D3-1s. No matter how unlucky you are, the worst that can happen is that you add zero. By contrast, rolling more Fudge Dice can punish you if you're unlucky (and I typically am), because two of its faces are -1. So in short, rolling more D3-1s will result in larger numbers with more probability to cluster around the expected value, while rolling more Fudge Dice actuallyincreases uncertainty around a specific value. Fudge Dice cannot substitute for a stat number, though they can "fudge" it a bit, thus the name. D3-1, on the other hand, absolutely can substitute for a stat number, because the expected value of X dice rolled is X.
So how can you use this knowledge? Well, you can throw these dice (pun intended) into any game that has small static bonuses. For example, in D&D, if you get a +1 longsword, you could substitute the static +1 for a single D3-1 die roll, giving some variation in how much the weapon benefits you. I feel this is best left as an option for those who feel lucky (punk), but you do you. Me and my friend/business partner go into this in depth in a long-form discussion on our Youtube channel here: https://www.youtube.com/watch?v=tqiIRjMxpXk.
What about you? What other games (if any) use this die? Why do you think so few games seem to use this die? What problems do you have with the D3-1?
The D3-1: the perfect hexahedron?
Discussing that strange little die from Betrayal at House on the Hill: the D3-1.
- [+] Dice rolls
