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Have you been under the impression this entire time that I was claiming that 1d20 was similar to 3d6? I've never claimed that. The claim is that 1d20 is similar to 2*3d6-10. Of course 3d6 and 2*3d6-10 yield different results vs the same DCs. The scaling and shifting were never part of the...

No. The set of DCs is the same. I am looking at trying to meet DCs in the range -5 to 27, and comparing apples to apples. If I'm a rogue with a +12 to stealth and I need to beat a passive perception of 11, then my target on a d20 is 0. That's the minimum value I could roll and succeed. I can't...

I posted the hypothetical for the purposes of removing complexity and isolating one aspect of the comparison at a time. Discovering that you are fine with that hypothetical, where we've rescaled DCs and rolls, helps us narrow down the source of your discomfort, by ruling out the unequal spacing...

Fighter 1 gives you some nice features: CON saves, weapon proficiencies, a fighting style (dueling or defense, presumably). I would start fighter 1 / bladesinger 6, for 3rd level spells and extra attack, and then see how it feels from there. Action surge is really powerful, especially if you are...

Do u even map, bro

Make sure you spend as much table time as needed to have a dialogue with that one rules-lawyer player to reach an agreeable compromise for each and every point of disagreement. Don't assume that this is something that can wait until after the session; it's critical that the game not continue...

@Ovinomancer, here's an analogy for you. I'm curious what your intuitions are. Suppose all this time 5e had used a percentile system to resolve checks, instead of the d20, and you had to roll at or under the DC to succeed. A medium difficulty task was DC 60, a really hard task was DC 10, etc...

Not sure what you mean here. The properties of the model follow directly from the basic assumption that we have fair independent dice. That's the connection between model and reality. If that holds, then the model is the reality, because everything else is derived using mathematical laws. This...

There is no statistics going on here; just probability. That's because there is no data; just calculations. Statistics is trying to find a good model to describe a set of observations from the world (the data). Probability is examining the properties of models in and of themselves. This is the...

Ok, we evidently need a little primer on probability. I'm going to put it in a spoiler, because it got a little long:

No, it doesn't look like that. It wouldn't look like that even if I weren't using the confirmation correction mechanism (which you don't seem to ever acknowledge), since we're only ever interested in the probability of getting at least some result. And so even if you can only ever get even...

There is if you use the confirmation die. Rolling a 6 on the 3d6 yields a 2 after the transformation. You then have a 50% chance of that turning into a 1. Outside of critical fumbles or whatever, the distinction between rolling a 1 and rolling a 2 only matters if the number you need to succeed...

Ok, since you continue to be hung up on the fact that my graph ends before the 3d6 curve gets to the top and bottom, here: And for good measure, here's a graph of the differences in success probabilities at each adjusted DC (think of the x-axis of all of these graphs as the DC of the check...

The column headings are aligned in my browser, but apologies if they aren't in yours. Likely a difference in browser/font settings. Glad you were able to sort it out. You are simply not listening. Yes, we all realize that 2*3d6-10 has a wider range than 1d20 does. I've accounted for the...

And yet, you have yet to give any justification for that claim, other than repeatedly harping on the fact (a fact that everyone acknowledges) that the range of 3d6 is not identical to the range of 1d20, and so for extreme DCs in either direction, you have one method giving a small chance of...

EDIT: Fixed @Ovinomancer, for the sake of transparency, here are some tables showing the various quantities that go into my graphs, so you can more easily check my results against AnyDice or whatever. I hadn't shown this before because I was doing my calculations in R code rather than in a...

The OP's point was that you don't need to use 3d6 to achieve the goals that people have in mind when using 3d6 (namely, making bonuses matter more, and randomness matter less). You can just scale bonuses and adjust DCs, and stick with a d20 roll, to achieve nearly the same success rates that 3d6...

I'm nearing the end of my patience with you, because you're so quick to fire insults and shoot down straw men without actually taking time to consider what anyone else is saying. You keep fixating on the fact that the probabilities don't actually match, and, no of course they don't match...

The issue was that 2*3d6-11 has a mean of 10, whereas 1d20 has a mean of 10.5. By introducing a "confirmation" mechanic, we're effectively reducing every roll by 1/2 (if it's easier to see, you can imagine rolling the 1d2 confirmation die after every roll and subtracting 1 on a 1, and leaving...

It occurs to me that one reason the centering and scaling doesn't match probabilities even better than it does is that the discrete nature of die rolls prevents us from actually matching the moments. But this could be dealt with by expanding the DCs in the modified d20 system around 11 instead...