How many people need to succeed in a group check with three people?

Question

In the comments of this answer it came up that the section on "Group Checks" states:

To make a group ability check, everyone in the group makes the ability check. If at least half the group succeeds, the whole group succeeds. Otherwise, the group fails...

It came up what does "half the group" mean when there also exists a rule on "Round Down":

There’s one more general rule you need to know at the outset. Whenever you divide a number in the game, round down if you end up with a fraction, even if the fraction is one-half or greater.

There are two possibilities brought up in those comments:

1. At least 1.5 people must succeed, and since you can't have half-people 2 or more people must succeed on the check.

2. The 1.5 people required rounds down to 1 person, so 1 or more people must succeed on the check.

Which of these interpretations is correct?

Answer 1

Which of these interpretations is correct?

Surely this one:

1. At least 1.5 people must succeed, and since you can't have half-people 2 or more people must succeed on the check.

The rounding rule applies when the rules require that "you divide a number in the game". It is not necessary to divide a number in the game to know whether you have more than half the people in the group succeed.

This is similar to a democratic election. We don't expect if there are 3 voters, that "success" is defined by anything other than exceeding half of the total.

For further reinforcement of this idea, I consider some other aspects:

1. The degenerate case of a "group of one", as a variation of "proof by induction". If rounding down is the correct approach, then zero members of this group need to succeed. Clearly, that's not the intent of the rule. And it doesn't make sense that we would have to special-case "group of one" as a completely different set of rules from "group of more than one" (since we intuitively understand that in the "group of one", we need "at least" one person to succeed).
2. In every other case I am aware of, the "round down" rule has the consequence of making it harder for the actor involved. It is not logical that in this one scenario, we would then apply the "round down" rule in a way that makes it easier for them.

Bottom line: I find many logical points in favor of the group having to succeed in excess of half the number of the group, and no logic in thinking that fewer than half can succeed and still have the group be successful overall.

Addendum:

Some, such as the person who posted the original claim that prompted this question, argue that because the group-success rules involve a comparison against "half the group", that necessarily invokes the "you divide a number in the game". However, I don't find this line of argument compelling. There are lots of times that halving or other divisions come up, without requiring rounding down.

For example, if my party decides that 25 gold should be split four ways by giving three members 6 and a fourth member 7, is that contrary to the rules? We did "divide a number", after all. Such a strict reading of the round-down rule that requires me to literally round-down every single division result I might ever do in the context of playing the game is excessive and IMHO absurd.

Furthermore, the scenarios where the rules envision "dividing a number" involve situations where that number is then mathematically applied to some other number. Effects of ability scores, or damage resistance, for example. Since numeric results in the game require integer values, some rounding must be done, so the rules spell out that the rounding is always downward.

But no rounding at all is required to understand whether you have had fewer or more than half of a group succeed.

And since there appears to be some confusion as well on why I only consider "fewer than" and "more than", let me make it plainly clear: the only scenario that is in question is the one where the group has an odd number of members. And half a person cannot succeed or fail, so clearly the number of members that succeed can only be strictly less than or more than half the number of the group. That my language above does not include the possibility of "equal to" is solely because that possibility does not exist in this scenario.

Answer 2

At least 2 people.

Keep the fraction, fractions are cool!

To make a group ability check, everyone in the group makes the ability check. If at least half the group succeeds, the whole group succeeds.

If you have 3 people, then the amount of people \$X\$ that must succeed is given by $$X \geq \frac{3}{2}$$ Because \$X\$ is an integer with possible values \$\{0, 1, 2, 3\}\$, then the answer is that at least 2 people must succeed the group check.

Answer 3

You have quoted all the necessary rules for this. You put them together like this:

To make a group ability check, everyone in the group makes the ability check. If at least half the group succeeds, the whole group succeeds. Otherwise, the group fails...

Okay, we need 'half' the group to succeed. What does 'half' mean? In 5e we use normal language unless the book tells us to do something weird instead. In this case, as you quoted, the book does tell us to do something weird instead! It says:

Whenever you divide a number in the game, round down if you end up with a fraction, even if the fraction is one-half or greater.

So, whereas half of 5 would usually be 2.5, in this game it's 2. Similarly, when one applies these rules to the number '3' one can see that, because '3' is an odd number, halving it makes you end up with a fraction. That means you round down and end up with the next integer number down, in this case '1'. Similarly, if you halved 1, you'd end up with 0.

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Note, however, that in doing this we are making up what 'round down' means. In common parlance, you usually can't 'round down' without reference to something-- you 'round down to the nearest whole number' or 'round down to the nearest ten' or something like that. Used on its own, the phrase is somewhat unclear-- it might mean 'to the nearest whole number' or 'to the nearest integer' or 'to the nearest non-fraction', and not all of these are meanings that result in a reasonable game (though they all, except 'non-fraction' because that is an incoherent idea in its usual expression, mean 3/2 rounds to 1). Because rounding down to the nearest integer is the least completely terrible as a rule, when using this rounding rule it should be assumed you do that.