Which die is the most honest?

There's a great Goblin Punch article about core resolution mechanics and the pros and cons of each. If you're even the slightest bit interested in RPG mechanics or game design I'd recommend giving it a read, but the general idea can be gleaned from the table at the bottom directly comparing a bunch of core mechanics qualitatively. I won't copy-paste it here, just go look.

What I want to talk about today is one specific aspect of this: transparency. Which die do people understand the odds of most accurately? Which one acts the most like people think it does?

Arnold lists the d100 roll-under mechanic as "perfect" visibility and the d20 roll-under mechanic as "high" visibility. I'm going to make the admittedly weird argument that the d20 in its 5% steps is actually clearer to the average player than the d100.

People do not intuit probability well at all. 65% doesn't feel very high despite the fact that you have almost double the chance of succeeding than you do of failing. Yet somehow, a coin flip feels like pretty good odds to most people. I mean, it's mathematically fair isn't it? Well, until you do flip it and it doesn't go your way. Or you've already flipped once and lost - surely it'll come up your way this time.

Famously, the video game XCOM tried to remedy this by having the displayed hit percentages lie (in a good way!) to the players, telling you that you have a 95% chance to hit but then applying a bunch of modifiers which give you a much greater true chance of hitting. Basically, they wanted people not to feel like the game was cheating them, so they made it cheat in their favour instead. The result? There were still memes about always missing at 95%. The odds are better than what's displayed and people still feel like the game is cheating them.

Human comprehension of probabilities is atrocious.

Finally getting to the point:

Let's map this to the initial examples: 65% and a coin-flip, but in the roll-under d20 system.

• To succeed you need to roll below 10.
• To succeed you need to roll below 13.

How do those statements feel? I don't know if I am an outlier or in the majority here, but the discrete steps of the d20 seem more intuitively comprehensible compared to the mathematical honesty of the d100. I have even seen convincing arguments from some real grognards that the "x-in-d6" of yore is clearer again, and I find it hard to disagree. Who knows, six might actually be a sweet spot between granularity and comprehension, even though it seems backwards that 16.67% steps would be intuitive.