Let's Talk About Core Game Mechanics

[Staffan]

Um....ok. What do you think the odds are of rolling doubles (but not triples) if you need 14+?

Not sure about the 14+ qualifier, but overall the chance of rolling doubles or triples on 3d6 are close to 50%.

 

[Bill Zebub]

Not sure about the 14+ qualifier, but overall the chance of rolling doubles or triples on 3d6 are close to 50%.

As a fraction of successful combinations, yes. It ranges from under 40% to as high as 60%, up through TN 15, then it spikes for TNs 16, 17, and 18.

But, as I said, I was using a method comparable to saying "You have a 5% chance of rolling a 20". That is, what is your percentage chance of critting before you determine whether or not you hit.

(I'm not defending this as a good game mechanic. Just defending my math.)

 

[...m...]

...but double-or-triple-six crits will show up 1/54 rolls, likewise double or triple-ones, for overall critical shenanigans 1/27 rolls...

(for d4s you're looking at crits either way 1/8 rolls; for d8s 1/64)

 

[JohnSnow]

Um....ok. What do you think the odds are of rolling doubles (but not triples) if you need 14+? I think there are exactly 21 different ways, out of 216 (6^3) total ways to roll 3 dice:

6 6 2
6 2 6
2 6 6
6 6 3
6 3 6
3 6 6
6 6 4
6 4 6
4 6 6
6 6 5
6 5 6
5 6 6
5 5 4
5 4 5
4 5 5
5 5 6
5 6 5
6 5 5
4 4 6
4 6 4
6 4 4

EDIT: Note that I'm calculating the the chance to crit equivalent to saying that in D&D you have a 5% chance to crit. That is, not your chance to crit if you hit, but your chance to crit before you even roll the dice. The chance to crit assuming you hit is much higher.

I’m not questioning your math, but the difference is that on a d20, the chance for a crit remains 5% whatever the target number is.

By contrast, the chance for doubles on 3d6 is ~7.4%/number. The chance of getting double 4s, 5s, or 6s is about 22%.

Let’s say a character has a total check bonus of +5, so any of those rolls is 14+. A double 3 will give 9+ 2/3 of the time (~5%). Double 2s will yield 9+ 1/3 of the time (~2.5%). That means the chance of critting if your dice roll needs to be a 9+ is ~30%.

That’s the THING with dice pools: they make bonuses matter a LOT.

It’s worth noting that the chances of rolling 16+ on the dice is 4.63% - around the same chance as a Nat 20.

There’s a much easier solution if you want to make crits more common on 3d6: 16+ is a “critical hit.”

If that’s too frequent, you can make it 17+ (~2%) or even 18 (~0.5%).

 

[Reynard]

I’m not questioning your math, but the difference is that on a d20, the chance for a crit remains 5% whatever the target number is.

By contrast, the chance for doubles on 3d6 is ~7.4%/number. The chance of getting double 4s, 5s, or 6s is about 22%.

Let’s say a character has a total check bonus of +5, so any of those rolls is 14+. A double 3 will give 9+ 2/3 of the time (~5%). Double 2s will yield 9+ 1/3 of the time (~2.5%). That means the chance of critting if your dice roll needs to be a 9+ is ~30%.

That’s the THING with dice pools: they make bonuses matter a LOT.

It’s worth noting that the chances of rolling 16+ on the dice is 4.63% - around the same chance as a Nat 20.

There’s a much easier solution if you want to make crits more common on 3d6: 16+ is a “critical hit.”

If that’s too frequent, you can make it 17+ (~2%) or even 18 (~0.5%).

Dammit, Jim, I'm an engineer, not a statistician!

(And a civil engineer at that...)

 

[TwoSix]

Not sure about the 14+ qualifier, but overall the chance of rolling doubles or triples on 3d6 are close to 50%.

Chance of 3 different values: 120/216 (55.6%)
Chance of exactly 2 values matching: 90/216 (41.7%)
Chance of 3 values matching: 6/216: (2.8%)

Assuming only roles of 14+ on 3d6:

Chance of 3 different values: 12/35 (34.3%)
Chance of exactly 2 values matching: 21/35 (60%)
Chance of 3 values matching: 2/35: (5.7%)

 

[Bill Zebub]

I’m not questioning your math, but the difference is that on a d20, the chance for a crit remains 5% whatever the target number is.

By contrast, the chance for doubles on 3d6 is ~7.4%/number. The chance of getting double 4s, 5s, or 6s is about 22%.

Let’s say a character has a total check bonus of +5, so any of those rolls is 14+. A double 3 will give 9+ 2/3 of the time (~5%). Double 2s will yield 9+ 1/3 of the time (~2.5%). That means the chance of critting if your dice roll needs to be a 9+ is ~30%.

That’s the THING with dice pools: they make bonuses matter a LOT.

It’s worth noting that the chances of rolling 16+ on the dice is 4.63% - around the same chance as a Nat 20.

There’s a much easier solution if you want to make crits more common on 3d6: 16+ is a “critical hit.”

If that’s too frequent, you can make it 17+ (~2%) or even 18 (~0.5%).

Yeah, again, I'm not arguing this is a great way to do crits, just getting my hackles up about accusations that my math was wrong.

 

[Bill Zebub]

Chance of 3 values matching: 6/216: (2.8%)

Just pulling this one out to illustrate the point about the TN: if the TN is 14, then all 1's, 2's, or 3's will be misses, so the odds of getting a triple that counts is half of that. (Whereas by the D&D rule a crit is, by definition, also a hit.)

 

[TwoSix]

I’m not questioning your math, but the difference is that on a d20, the chance for a crit remains 5% whatever the target number is.

By contrast, the chance for doubles on 3d6 is ~7.4%/number. The chance of getting double 4s, 5s, or 6s is about 22%.

Let’s say a character has a total check bonus of +5, so any of those rolls is 14+. A double 3 will give 9+ 2/3 of the time (~5%). Double 2s will yield 9+ 1/3 of the time (~2.5%). That means the chance of critting if your dice roll needs to be a 9+ is ~30%.

That’s the THING with dice pools: they make bonuses matter a LOT.

It’s worth noting that the chances of rolling 16+ on the dice is 4.63% - around the same chance as a Nat 20.

There’s a much easier solution if you want to make crits more common on 3d6: 16+ is a “critical hit.”

If that’s too frequent, you can make it 17+ (~2%) or even 18 (~0.5%).

This isn't really about the difference between a dice pool and a linear die. This is about the difference between a crit only being rolls at the top of the result range (only a 20 on a d20, or only a 16+ on a 3d6), and thus all crits will be hits, versus having crit results scattered through the result range, and thus making a crit be a combination of "correct roll result" plus "the roll was high enough to meet the target number.

A rough parallel might be if rolling a prime number (excluding 1) was a crit on 1d20. That's also a case where 40% of the total rolls are possible crits, but the actual crit range would vary depending on the exact target number needed to hit.

 

[Barner Cobblewood]

That's interesting. How have you seen that manifest?

The games I play in are biased in favour of the players at the table (as I think they should be), but sometimes I have played with players who, when facing a choice between accepting a unrolled small failure with humiliating outcome (e.g. they miscalculated their PC's capacity, and now should abandon their current strategy / tactic, withdraw, regroup, and improve the PC), they count on the possibility of a crit, combined with the reluctance to give them a greater failure (e.g. roll a new PC), to carry their PC through.

My intuition, based on my limited experience, is that if 1 of every 20 rolls make averages unimportant, a game becomes more about chance than skill. I prefer games of that reward skilled playing over chance.

Basically, the players treat the game outcomes as unimportant, and their PCs become carefree gamblers rather than careful decision makers. Nothing against gambling with friends, but there are better games for that. I play TTRPGs to pretend to be more skilled than I am, not luckier than I am.