Curves and coin-tosses

[Polycarp]

I like the idea of curved dice probabilities, but something that bothers me about Fudge/FATE dice (4dF, effectively 4d3-8) is that they can't produce a "coin toss."  There's no situation in which you can have a 50% chance to succeed or fail, because there are an odd number of outcomes with zero being the most likely.  Let's assume your "skill" (whatever number you're adding to the dice) is the same as your "target" (the number you want).  If a tie is considered a success, you've got a ~62% chance to succeed (by rolling at least zero); if a tie is considered a failure, then you've got a ~38% chance to succeed (by rolling at least +1).

An even-sided die can give you a 50% shot - in d20, you've got a 50% chance to make an unmodified DC 11 check - but this, of course, is a flat distribution.

So I'm trying to come up with ways to make a curved dice system in which, if your "skill" is the same as your "target," you have exactly a 50% chance to succeed or fail.

One thing that I thought of is median dice.  If you take the median of three even-sided dice (3d6, for instance) you have an even number of possibilities arranged in a curve.  The more sides the dice have, the flatter the curve.  To fulfill my goal above, though - of having a 50% shot when your skill is the same as your target - you'd have to subtract some amount to "center" the curve on zero.  In the case of 3d6, that number is 4 (assuming a tie is counted as a success).

That's not terribly difficult - roll 3d6, take the median, subtract 4 - but it does seem a bit inelegant.  So I was wondering if anyone else had any ideas.

[sparkletwist]

If you roll an odd number of even-sided dice (for example, 3d6) you'll end up with a curved distribution where you can have a 50% chance. In the case of 3d6, you'll have a 50% chance to succeed with a target number of 11, just like a d20. So, if that's all you care about, that may be the simplest approach, without having to mess around with the median and whatever, and you get a longer range of values.

Of course, that also means you'd have to subtract 11 to "normalize" your result when rolling a skill of 0 against a target of 0. There's really no way around this, because the only way to not have to subtract a constant when making a roll is to split it up and subtract (e.g., instead of rolling 4d6, you roll 2d6-2d6) and you can't do this with an odd number of dice.

For what it's worth, here's how I solved the issue in Asura, which uses opposed 2d6: a 0 is always considered by the system to be either +0 or -0, a success or a failure. The exact way Asura makes the determination is a little convoluted, but the simplest approach is to rely on something else in the roll that has a 50/50 chance, like whether the actual number rolled is odd or even. Of course, you could always just roll a tie-breaker die, too. Players might like the added tension, or they might find it a tedious extra step.

[Ghostman]

If you really want a 50/50 chance, why not just toss an actual coin?

[Steerpike]

If you really want a 50/50 chance, why not just toss an actual coin?

I think because Polycarp specifically wants the 50/50 to be when two opponents are evenly matched, when your "skill" is the same as your "target." An actual coin-flip can only provide an exact 50/50 chance.

[sparkletwist]

What Steerpike said.

Not that coin tossing is a bad answer in the case of a tie on curves where you don't have a clean 50/50 split-- like, you could roll 2d6 and toss a coin on a 7, for example.