A question for all DMs out there. So, part of the fun of D&D derives from the randomness of the dice, and to interpret their results in a sensible way -even within the broad boundaries of a make-believe world- is the DM's main job.

The party's wizard may roll horribly on an history check to remember the deeds of the past, but the dumb barbarian may roll so improbably high that, to make peace with his limited relevant skill, the DM could rule that "he remembers that exact anecdote heard during the pub brawl he had the previous night" or such. You could follow the same reasoning from pretty much every other skill: despite having low core stats, one could clumsily dodge, unexpectedly resist, unforeseeably find/solve, incredibly remember/understand, weirdly convince. After all randomness does happen in real life, and it can very well happen under the tyranny of the RNG.

But what about strength checks? Try as I might, I have a hard time imagine how a mage with -1 strength could overpower the +6 orc in arm wrestling without the intervention of external forces if the former beat the latter dice-wise. I guess the orc could be distracted or just let the spellcaster win, but these all seem pretty weak ways to force a result considering that strength is such an objective value. I don't think it's random that its flat value is linked to fixed capabilities like the height and length of one's jumps or one's carrying capacity: a strong character may be tired or ill, but he'll always be able to accomplish physical endeavors that a weak character simply couldn't match without aid.

How would you rule on an unlikely strength check without breaking the players' suspension of disbelief?


13 Answers 13


If failure/success doesn't make sense, don't let them roll in the first place

Let's see what the rules say about ability checks (emphasis mine):


You said you have a hard time imagining how the mage could possibly win in arm wrestling against the orc. That sounds to me like you already determined that the outcome is certain. If the outcome is certain (and it's not an attack), don't ask for a roll.

The DM decides when dice are rolled, not the players. If your players say they want to arm wrestle, and you feel that roleplay-wise there is no way PC 1 could win over PC 2, you simply tell them the outcome.

If you can figure out a way to RP either outcome, then go ahead and ask for the roll! But that's a determination you need to make before you ask for the roll. Don't ask for the roll, and then despair at not being able to narrate the outcome.

How far you want to stretch the imagination is up to you

... and your players' tastes. Some players will enjoy a laugh about "The orc choked on a fly", others will roll their eyes at it. You have to feel that out. Also don't neglect your own preferences, since the game should be enjoyable for you too.

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    \$\begingroup\$ I would add to this - use the character's background as well as their class and abilities. A barbarian with the sage background should get a chance to roll the history check; a barbarian outlander probably no chance. \$\endgroup\$ – Greenstone Walker May 11 at 2:10
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    \$\begingroup\$ @GreenstoneWalker Ch7 disagrees with you. you can try any ability check, but if you don't have proficiency you'll have a lower chance of success, and you may have to roll with disadvantage if the DM sees a factor that lowers success chances. \$\endgroup\$ – KorvinStarmast May 11 at 14:41
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    \$\begingroup\$ @KorvinStarmast I am not aware of any rules stating a GM must provide a static DC for ability checks, only that "the DM decides... the difficulty of the task" (Ch7). Were there any additional rulings that said this decision must be character agnostic? \$\endgroup\$ – Drunut May 11 at 16:19
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    \$\begingroup\$ @KorvinStarmast I misunderstood your comment. When you said, "[Y]ou can try any ability check ...," I disagreed because it sounded like you were disagreeing with RHS's main point, "If failure/success doesn't make sense, don't let them roll in the first place." I see now you were replying to a comment about backgrounds. \$\endgroup\$ – Chris Bouchard May 12 at 2:30
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    \$\begingroup\$ @ChrisBouchard we seem to be in violent agreement. 🤣 \$\endgroup\$ – KorvinStarmast May 12 at 2:31

With feats of strength, there are good days and bad days.

From a rules perspective, it is abundantly clear that a contested Strength (Athletics) check is called for here:

Sometimes one character's or monster's efforts are directly opposed to another's. This can occur when both of them are trying to do the same thing and only one can succeed, such as attempting to snatch up a magic ring that has fallen on the floor. This situation also applies when one of them is trying to prevent the other one from accomplishing a goal — for example, when a monster tries to force open a door that an adventurer is holding closed. In situations like these, the outcome is determined by a special form of ability check, called a contest.


But, sometimes, it can help to rationalize an application of the rules to satisfy our desire for simulation in the game.

Weird flex, but I can deadlift 375 pounds. Sometimes. On any given day, there is no guarantee that I can actually deadlift 375 pounds that day. There is a long list of variables that contribute to my ability to perform this specific feat of strength, including, but not limited to:

  • Did I sleep well last night?
  • Did I sleep well three nights ago?
  • Did I eat more than or less than 200 grams of protein today?
  • Is it morning or afternoon?
  • Have I consumed any alcohol this week?
  • Was my caffeine dose taken 1 hour ago or 1 minute ago?
  • When did I last attempt to deadlift 375 pounds?
  • How long has it been since my last chiropractic adjustment?
  • Did I remember to do my foam rolling and stretching last night?
  • Did I have a bath last night, or was it just a shower?

All of these things affect my ability to perform any feat of strength, including arm wrestling. There are so many confounding variables baked into the bonuses and dice roll. It is entirely conceivable for a character with a strength of 8 to still beat a character with a strength of 20 in an arm wrestle, even if it is unlikely.

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    \$\begingroup\$ Are there any cases where you would fail to deadlift 50 pounds? \$\endgroup\$ – Harper - Reinstate Monica May 10 at 22:14
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    \$\begingroup\$ @Harper-ReinstateMonica Funny you should ask, when I was first trying out a different starting position on my deadlift, it wasn’t quite right and I fell backwards lifting 65 pounds. Besides that, there have been times where I worked so hard that I aggravated an old injury that prevented me from doing even really light deadlifts. In my mind, these things are baked into the die roll and bonuses. \$\endgroup\$ – Thomas Markov May 10 at 22:29
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    \$\begingroup\$ @ThomasMarkov thanks for your contribution, expert insight is always welcome and from now on I'd feel less uncomfortable ruling that the orc is struck by a cramp, slips on the table or feels a sudden torpor. I guess it's hard to imagine abstractly, but even expert athletes can slip om the fundamentals every once in a while \$\endgroup\$ – OmniVictor May 11 at 10:59
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    \$\begingroup\$ I like this answer, and it works both ways. The orc had a bad day, and the wizard had a good day plus a lucky intuition of leverage. This was an opposed roll. With two dice rolled, you get two stories that lead to the given outcome. \$\endgroup\$ – aherocalledFrog May 11 at 21:21
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    \$\begingroup\$ I can attest to old wounds. In my teens I twisted my knee playing softball. Many decades later, I can still feel a twinge of pain just walking down the street. Just apply that to the orc. Some flex surfaced an old axe wound that made them wince and lose the wrestling match. \$\endgroup\$ – MivaScott May 13 at 5:47

As a GM, I generally try to put the onus on my players to explain why something worked.

The wizard might explain that they realized that the surface of the table was uneven, so they picked a spot where they knew the orc wouldn't have a stable place to put their elbow. The wizard might have turned their hand and squeezed their thumb to hit nerve endings in the orc's hand that caused them to have a lapse in concentration. Maybe he summoned up memories of a time when he got beaten and stripped by a half-orc bully in his childhood and his surge of adrenalin got him to surge into a win.

Given the disparity in values, the odds are that it wouldn't happen a second time, but this time it did, and the player explaining why it worked might give you new story hooks to work with (if the wizard won by a "trick", it might generate ill will. If he won by sheer anger over past events, you have a bit of backstory and maybe the orc respects them for managing to make use of their innate savagery).

The key trick I've found is, when the player provides an explanation of why they might have won that time, to not let that become a reason they will win the next time without checking, although you might let them have a +2 circumstance bonus the next time for clever tactics, as long as it's not against the same opponent.

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    \$\begingroup\$ Nice answer. However, a "+2 circumstance bonus" does not sound very 5e-like. Granting advantage seems more natural to me (even though statistically it corresponds to a higher bonus). \$\endgroup\$ – Mars Plastic May 11 at 19:26
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    \$\begingroup\$ @MarsPlastic You're right. :) Prior system biases in effect. \$\endgroup\$ – Sean Duggan May 11 at 19:32

Model the contest as multiple steps, e.g. win by two

This greatly amplifies a statistical advantage, making the final odds of winning the round much more in favour of the stronger (and proficient-in-Athletics) contestant.

Having the math odds be very unlikely opens the door to weirder narrative explanations, like a fluke muscle cramp, on top of brilliant technique by the weaker arm wrestler. You can say that multiple factors conspired to produce the result.

Some contests, like shot put, involve significant technique so there's room for having a good vs. bad throw, i.e. chance. (Although if this isn't the Olympics, and the trained shot-putter knows they only have to beat a puny mage, not try to come out on top of their peers, their consistent throw may be farther than the mage's best possible throw.)

Other contests, like a foot race or arm wrestling, are almost always going to be won by the stronger contestant. i.e. a significant difference in ability will swing the outcome statistics very strongly in one direction. (Some games of mental skill are like that, too, notably chess where a grand master can simultaneously beat a room full of amateur opponents.)

A single roll in 5e's bounded-accuracy design doesn't model the latter kind of contest at all well. This is what creates the disconnect between what you'd estimate the -1 Wizard's chances would be against the +6 Orc: we can't rule out the wizard winning, but we know it's very unlikely.

@RHS calculated the chances of a -1 vs. +6 contested check at 22.75%. (I didn't check the math, but seems reasonable). That's far too high a chance for the wizard to win an arm-wrestling contest.

On Critical Role, Matt Mercer has run arm wrestling as a series of opposed Athletics checks, moving the arm position by one step (or two with a big success margin or a nat 20). The starting point is like Deuce in tennis, with the first win creating "game point", within one more success of overall victory. Or returning from that point to neutral. This appears to work well for creating fun, if the DM and players can get into the spirit of excitement over the give and take of the contest. (CR 2x17 "Harvest Close", from 1:22:10 through about 1:38:38 shows this in action, including the whole party getting really into cheering on one player in an exciting match.)

Mathematically, the chance of the mage winning two or three consecutive rolls is quite a lot lower, low enough to not be totally silly. In fact, 0.2275 squared is 0.052; about 5% or 1 in 20. (I'm ignoring the chance of coming back to even, then eventually winning. I think that's not a huge problem for lopsided contests, but 0.5 squared = 0.25 is obviously not right for an evenly-matched contest. That's just your chance of winning without any setbacks.)

Doing something outrageous with the same odds as a nat-20 sounds just about right for D&D. If you model it as even more small steps, odds swing even more strongly towards the side with even a minor advantage. (But that's not fun to roll; in most games there's a win-by-2 condition, like tennis's deuce / advantage.)

Of course, don't allow a roll at all when there's no plausible narrative explanation. It's up to the table where you draw the line; some groups like outrageous things to be possible when someone rolls a natural 20. But picking up a boulder 10 times your own weight isn't something you should get to roll for at all. It's harder to justify not allowing a role for a contested check, but if you limit yourself to modelling it as only deuce / advantage (win by 2) then the odds may still be too high if a weak human wants to arm-wrestle an ogre.

Food for thought: perhaps in the world of 5e, long jump is the most popular event, because everyone's success is linearly correlated with their Strength score, no randomness involved.


(with a DC10 Strength (Athletics) check to clear a low obstacle on the way, so that part is random.)

Does that mean you shouldn't roll contested anything for long-jump competitions? Well, what it really means is that 5e is not a sports simulator; if you want to focus more attention on contests, you'll have to put some work into modeling them (i.e. turning them into a fun dice game).

I don't know if arm wrestling is really an example of a contest that's almost always won by the same person, if two people have multiple matches.

Other sports certainly are like that, though, especially racing.

For example, in short track speed skating, a personal best of 47 seconds over 500m is a lot better than say 52 seconds. A skater with a personal best multiple seconds faster will win almost every time over that distance, even if they don't win the start and do have to set up a pass on one of the straightaways. (OTOH, it takes a lot more effort to go a bit faster; air drag is approximately quadratic with speed. Similarly for foot race sprints. Still, in 5e terms, someone that much faster might have Str and Con 16 vs. 12, only a +2 difference. And maybe Expertise in Athletics or that specific event for a technique sport, for maybe another +2 or 3 advantage. So in 5e terms, things might only work out if you model each lap as a separate roll where you can gain some separation or close the gap some.)

  • \$\begingroup\$ Are you sure about arm wrestling being purely about strength? Did some quick searching and that doesn't seem to be the case. \$\endgroup\$ – NautArch May 11 at 1:46
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    \$\begingroup\$ @NautArch: No, I'm not. Between two people of similar strength, there's certainly some technique. But that's what proficiency in Athletics models. Is there much chance, though? Am I wrong that if two people arm wrestle repeatedly, one of them will win fairly consistently if there's much difference between them? In a tournament to decide an overall winner, do you do best of 3 or 5, or just one? (And that's for contestants that are presumed to be at a similar level of ability, like a tennis match of 5 sets of multiple games each.) \$\endgroup\$ – Peter Cordes May 11 at 2:02
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    \$\begingroup\$ @NautArch: I added "foot race" as an example where people perform pretty consistently, so the stronger contestant will almost always win. \$\endgroup\$ – Peter Cordes May 11 at 2:18
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    \$\begingroup\$ @PeterCordes this question came to me specifically watching CR Harvest close's episode. As Fjord lost three consecutive games at trebuchet (a 1 in 8000 chance if I'm not wrond),I imagined Yasha rolling 3 consecutive nat 1 in arm wrestling against Nott; unlikely but possible, and as ridiculous. I guess the players could retcon these rolls with Caleb distracting Yasha or Molly maledicting her or something like that, but you can never be sure the the players on a table are willing to bend their characters' actions to make sense of these rolls \$\endgroup\$ – OmniVictor May 11 at 9:58
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    \$\begingroup\$ @OmniVictor: heh, I see. The motivation for this answer is that making the dice odds more unlikely allows narrative explanations that are more of a fluke, for the rare times when they still actually happen. At some point, if you want to allow a roll at all, you have to realize that extraordinary things happen to D&D heroes. (Semi-related Terry Pratchett quote: "million-to-one chances crop up nine times out of ten." wiki.lspace.org/mediawiki/Million-to-one_chance) \$\endgroup\$ – Peter Cordes May 11 at 10:07

Use passive checks for peaceful situations

Rolling d20 for every side and adding modifiers is called a contest.

The rules suggest using contests in the context of combat:

Battle often involves pitting your prowess against that of your foe. Such a challenge is represented by a contest.

Player's Handbook p. 195 Contests in Combat

Sometimes one character's or monster's efforts are directly opposed to another's [...] In situations like these, the outcome is determined by a special form of ability check, called a contest.

Player's Handbook p. 174 Contests

This is important, because context matters:

In any piece of writing, context matters. If a rule has multiple sentences, they're meant to be read together.

Using a d20 roll is understandable for a risky situation, but it is ill-suited for adjudicating peaceful cases like an arm wrestling match. The rules give us another tool called passive checks.

A passive check is a special kind of ability check that doesn't involve any die rolls. Such a check can represent the average result for a task done repeatedly (see PHB p. 175), or any mundane task with zero risk, which can't be plausibly spoiled by accident.

This is perfectly fine rules as written, since the rules explicitly allow not using dice outside of the combat:

One approach is to use dice as rarely as possible. Some DMs use them only during combat, and determine success or failure as they like in other situations.

With this approach, the DM decides whether an action or a plan succeeds or fails based on how well the players make their case, how thorough or creative they are, or other factors.

DMG p. 236 The Role of Dice


Going over the top

The gates for being successful are already created by the stats of the two entities and the dice and modifiers help tell that tale. If you're looking for reasons why an outcome happened, just get creative! Maybe they sneezed, were distracted, or something purely incredible happened with the PC to have gone over the top and won. Heck, if you're unsure, let the player narrate it! I often let players narrate kills and crits and that gives them a way to get more into the scene as well.

This is all about story telling and fun, and upsets are always great stories.

Don't limit contested ability checks because you're unsure how to narrate success or failure

The action requested by your player is completely reasonable. These are adventurer-heroes we're talking about and amazing things can happen to them and done by them. There really isn't a solid reason to limit any PCs ability to arm wrestle, push, or even attack someone.

While there is guidance to not call for rolls when the outcome is certain, that determination shouldn't be made often. This is a game of chance, storytelling, and fun. If the story very much doesn't call for a check here, then don't call for one, but don't limit because of being unsure how to narrate.

You did the right thing by allowing for the check, and I respect your request for more information as to then how to narrate a success. It's tricky, but this is where you can really have some fun.

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    \$\begingroup\$ To give a better space for a back and forth discussion; this conversation has been moved to chat. \$\endgroup\$ – Someone_Evil May 12 at 0:21

Only ask for rolls, if you don't know the actual outcome from the start!

For example: A halfling wants to arm wrestle an ogre. Don't let them roll in the first place; the ogre just automatically wins. Don't forget: The player describes what they want to do. The DM tells the outcome and calls for rolls if needed.

If needed the DM sets a DC (most oftenly hidden)... so to avoid strange action outcomes, the DM can set the DC just very very high. A nat 20 is BTW not an automatic success. So the wizard in your example can beat a DC of 19 at max. It's impossible for that wizard to beat a DC of 20 or higher. The stats of the orc (at least if it's an NPC) are not relevant at this point. The DM gives that particular situation a DC, that's it.

If you have a situation, where success/fail is possible but highly unlikely...

... the DM is free to give you advantage or disadvantage. And that's in fact absolutely RAW as written in Player's Handbook p.173:

You usually gain advantage or disadvantage through the use of special abilities, actions, or spells. Inspiration (see chapter 4) can also give a character advantage on checks related to the character's personality, ideals, or bonds. The DM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result.

Although some players don't like the fact, that the DM can pretty much control everything, it happens to be a real thing. The Dungeon/Game Master is (the title gives actually a broad hint) the master after all.

A quick Game Design Insight

In Game Design we talk about different kinds of information (this might seem a little off-topic at first, but read to the end, I promise this makes sense), that are described by Jesse Schell in his book The Art of Game Design p.137f. In there Schell distinguishes between 5 secrecy levels:

Information that is known...

  1. ...by everyone

  2. ...to some players, but not known by others

  3. ...only by one player

  4. ...by the game

  5. ...by only the gods; the dice god especially

Let's translate Schell's list to DMing:

  1. The story the DM describes, NPC dialogue, environmental descriptions, the outcome of the players' actions etc.
  2. Secret letters between the DM and a player.
  3. The DM's mind, their decisions and improvisation
  4. The DM's preparations, all predetermined results... ie. "Quantum Ogres" but also the order of card decks.
  5. Dice rolls

The DM's control is between level 3 and 4, but how does that help to answer your question? Well, you are not the dice god. Everytime a DM calls for a roll they hand over responsibility to that strange deity. The Dice God is chaotic neutral with emphasis on the chaotic part. If you don't want chaotic randomness, don't call for rolls, because you don't know the outcome. That's also the reason why (at least from a game design perspective) it's okay for a DM to fudge rolls. That's actually a pretty common thing in video games (you just don't realize that, because you don't know when the system rolls or not), but that's another story.

If this answer needs clarification, write me in the comments. I tried to keep it short with this one, but I can explain more if needed.


There are lots of options, but remember in a DnD world even more than the real world strange things happen.

First as others have pointed out don't make it a single role, make it a series of rolls. Also if it is impossible don't even let them roll, but this is not impossible just improbably, if the wizard was asleep it would be impossible.

How to deal with improbably rolls, that's easy, you get creative, add an outside influence, a strange occurrence, elements of luck, or even just the mysterious, "yeah that was weird wasn't it."

"the orc and the wizard square off, the orc grins barely taking the wizard seriously there is little tension in his arm, flies buzz around as the the referee starts counting down, THREE, TWO, the orc chuckles at the wizard but as he does so he inhales a fly up his nose and the orc starts gagging and sneezing, ONE, the wizard ---"

If you made it a single roll, "----slams the distracted orc's arms down on the table, and the crowd goes wild. The orc looks furious."

If you made it multiple rolls, "---yanks the distracted orc's arm down mere inches form the table... Make another athletics check!"

I just recently had to deal with contests, and I always make them multiple checks. it increases the drama, the suspense and makes for a more exciting event. I set it up as you needed at least 2 successes in row to win. the first roll got you part way there the second finished them off, this put some suspense in it because the contest went back and forth.

Don't be afraid to have fun with it:

There are a thousand things that can happen that can give you unexpected outcomes

  1. A drop of seagull poops drops on a contestant.

  2. As the orc strains her abused belt tears dropping her pants around her ankles, embarrassment wins against pride as she is distracted.

  3. You watch in horrid fascination as the much abused muscle tears in the orc arm, the muscle slithering under the skin like some evil thing.

  4. An inebriated leprechaun shouts "Oy ye bastard ye winna be taken me ale again" at the orc and the your arm suddenly stronger than it has ever felt.

  5. A female Orc in the crowd screams, "Borky! Have you been gambling again! Why ain't you at work!" and your opponent suddenly goes pale and cowers.

Remember the story of the tortoise and the hare, the tortoise wins not through superior skill but because they had the balls to try and the hare got to cocky.


If a task is specific to the dice, then you should set a target amount to hit. People think "nat 20's" let you do anything, but they don't. A task may be "impossibly high" to do, but a person with great skill & a nat 20 may pull it off. But, the high skill check would keep that task out-of-reach of normal folks just trying.

However, this is where you need to stop roll-playing, and start role-playing.

Ok, fine.. a strength check is impossibly high. But, maybe a wizard can logic a way out of a strength problem. Maybe a bard can charismatically shmooze their way around it.

The bars on the jail won't bend themselves.

  • The barbarian of the group could possibly achieve a massively high skill check to do so.

  • The magician might have an acid spell to dissolve the bars, or find a tool they could use as a file to start cutting away at them slowly.

  • the bard could ask the jail keep to show up, and try to seduce them.

When you own a hammer, all your problems look like nails. But, each character owns a different hammer, so how they try to nail a problem is different. Give the player's options.

But, if you're wanting the "one in a million" chance for a nobody to succeed at something that some rockstar would normally only be able to do...you can track a random "luck" factor.

D&D doesn't really do this, but some campaigns I've played in and DM'ed, I've used it.

"Luck" can be whatever you want it to be...karma, fate, whatever. You rack it up based on whatever you think would bring or lose "luck" in the game. Maybe your players are doing deeds that the diety likes. So, the diety looks favorably on them. Maybe they're helping folks out. Whatever floats your boat.

Luck can get tracked either secretly by you, or by the players.

If you let players track it, you give them rules to spend it.

EG: I had a campaign where I let the players do the following...

  • use a point of luck to change a skill role into another skill (EG: a bard could change a strength feat into a seduce.. this would be the "I'm gonna woo the jail keep to get us past these bars"). It's up to them to role-play why this is possible. You can get players making up some great tall tales to justify it.

  • use a point of luck to double a roll. That nat 20 turns into a nat 40.. then skill is added. This is the proverbial nobody that just did some rockstar feat that nobody thought they could do. The party weakling intimidated a troll. The wizard bent the bars. Again, have the players make up the role-playing to justify this.

  • spend all their luck to automatically succeed at a task, like an impossible skill check, a saving throw, etc... often b/c it's life or death. (Yes, even if they had 1 luck point, they could blow it to do this. But, they built up luck so slowly, that it let them pick-n-choose if they wanted to smart and bank their luck or keep playing stupid and zero it out all the time).

As they spent luck, it would go down. But, as they did things I, as the DM, liked them doing, like not murder hobo'ing the townsfolks, and actually following the quest lines, I'd hand out a point of luck to them all occasionally.

The cleric would justify their luck as their diety favoring them. The bard would say it's just part of her charismatic coolness. The wizard would say luck favors the prepared and role-play pulling some stupid trick out of their hat (literally).

The point of D&D is to role-play & have fun. We often get too side-tracked in roll-play & rules-lawyering, where we just rely on the dice to tell us everything and/or argue over the game mechanics.

The dice can be used as impartial tools in mediating outcomes, but in good story-telling, you often need to fudge things or give the players an edge they can decide to use.

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    \$\begingroup\$ welcome to stacks, and thanks for your contribution. I feel like you wandered a little off-topic from the main question, or at least forgot a coda to get to the nitty gritty. If I understand correctly, in the arm wrestling scenario you would use the straight dice to determine the result BUT you would allow the players to use a buffed, homebrew version of hero points to alter the nature or/and the outcome of the contest? \$\endgroup\$ – OmniVictor May 12 at 7:35

There are a number of options

  • Don't roll when the result isn't in question.

This option is supported by the rules and is often overlooked. The DM chooses when to ask for rolls in 5e D&D. The players state what they are trying to do, the DM determines if a roll is needed, describes what the roll is, and the player rolls it.

Here, the DM simply doesn't have to call for a roll, and states the wizard loses the arm wrestling match, unless something comes up that could change it.

  • Use an extended contest

The issue you have addresses is that the +5 strength vs -1 strength is much smaller than the 1d20 range. Repeatedly rolling dice lowers the standard deviation compared to the average.

1d20-1d20 has an average of 0 and a variance of 798/12 (66.5) and a standard deviation of 8.15. Beat-by-6 is only 6/8.15 = 0.74 z away from mean, or about a 27% chance of pulling it off.

If you take that contest and repeat it, say best-of-X, you get 0.27 - (1-.27) = -0.46 X average and a Variance of .27*(1-.27)=0.73 X, or a SD of 0.85 sqrt(X).

The z-score of the wizard not losing is then -0.46X / (0.85 sqrt(X)) is 0.54 sqrt(X).

As X goes up, the chance of the wizard winning drops. And as a side effect, you can generate a narrative besides "the wizard won".

  • Yes, but...

A standard way to handle contests in many RPGs is to either include stakes, or offer choices.

Stakes here would be to tell the player before the contest "If you lose, your arm is broken. If you win the contest, you fail without injury".

Choices would be to offer the player "You won the roll. If you can come up with a way to cheat, you'll win the arm wrestling contest; otherwise, you fail without injury. How do you cheat?"

On a failed roll, you might offer a harsher choice "You failed. Your arm is going to be broken unless you come up with a way to cheat. Do you cheat? How do you cheat?"

  • Retroactive justification

Treat the dice as the random chance they are, instead of them being variation in competence.

When the dice come up with something surprising, they mean you have to explain how the failure occurred.

Another bar patron gets in a fight, and they smash into the wizard's opponent. This causes the opponent's arm to fall over as the opponent falls to the floor, and the wizard ends up winning for a second.

The dice roll here doesn't represent "how strong the wizard is" but the total effects of "random" (undescribed) elements in the situation.


Magic, if a Wizard is doing it

This might depend on the specifics of who is the one performing the check and winning, but in this case, you're mentioning a wizard, who might be limited in the spells they can cast normally.

That said, you could always have them succeed on their strength check (Say, natural 20 versus a roll of 12 by the Orc), and use it as a way to give them an..."fairer" advantage, by having them focusing so hard on the task they temporarily forget the action they're doing would have them cast a spell.

For Wizards in this example

Spells, like Levitate could lift the Orc's elbow off the table, and as a result, the wizard now essentially just has a weightless lever to push over.

Potentially a house-rule'd version of Blade Ward would grant resistance to physical damage by weapon attacks, but also against bludgeoning strength from an arm, or Haste for having them act faster.

If you're going for consequences out of trying , you could also cast Stoneskin - if you turn them to stone, they can't fight back if you just lift them and basically lightly let them down.

In general

So this can help if your wizard specifically has some of those spells prepared that day, as you can ask them to burn a spell slot, but if the person doesn't have it, this could also be a point to either grant them an additional spell of those types as they learn it on the fly, essentially, and have them effectively had learned it through a trial by fire.

You could also have it be a one-time thing of a spell slot of one of the ones available; one iconic event my DM created in a session a while back involved a warlock trying to spook a captain by pretending to cast a curse on them in front of a bunch of their sailors - the Intimidate Check did work on the sailors, but not the captain - and then the warlock was told to expend a spell slot. We've yet to see what the results of those consequences yet, and as I recall, the spell used wasn't specified, but...all we know is the warlock knew that their fake magic performance act actually involved their usual spellcasting abilities.

  • \$\begingroup\$ Hi Alexander The 1st, and welcome to Stacks. So, you suggest to use a lot of flavor, even at the point of gifting spell slots. It certainly works and makes sense, but it's quite a hassle for the DM. Moreover, I feel l like the aforementioned wizard player should have asked to use these incantations beforehand if he didn't want a fair fight. If he didn't, he either didn't think about or didn't want to after all. I would also add the spells have components, and the Orc would have seen him casting stuff: I I think this should have sparked a reaction. In a contest, cheating seems a weird solution \$\endgroup\$ – OmniVictor May 13 at 8:16
  • \$\begingroup\$ It's certainly possible for them to have intended to cast the spell themselves, but in a case where they manage to attempt a strength check that's unlikely, and manage to successfully pass it, having unexpected magical talents show up during the check would be the way I would recommend the DM resolve how it worked out - unintentional cheating might leave the Orc to have noticed the casting itself, but that gives a way to have additional aspects show up later. \$\endgroup\$ – Alexander The 1st Jun 5 at 1:33
  • \$\begingroup\$ As for it being cheating - to some extent, the Orc barbarian succeeding a history check by remembering that exact anecdote of someone else talking about it effectively cheating as well - it's not their intelligence they're using, but someone else's they overheard - or almost using their perception check to pass a history check. \$\endgroup\$ – Alexander The 1st Jun 5 at 1:39

I'd say in the case of the wizard vs the barbarian, I'd allow the wizard to roll. A 20 would mean that the wizard managed to get the jump on the barbarian and actually push the barbarian's arm down, about 3/4 of an inch. At which point the barbarian would simply push the wizard’s arm down. However, the fact that the wizard got the jump on him, if just for a fraction of a second, might cause the barbarian to get mad, calling the wizard a "cheat" and insist the wizard buy him a drink, where the barbarian shares a valuable piece of information that you possibly needed.

But yeah, no roll is necessary.

  • \$\begingroup\$ welcome to stack, and thanks for your contribution. I was actually thinking something on the same line: not a regular athletics contest, but perhaps the mage could roll a performace/deception/insight check with a high DC; in case of success, he comes up with a distraction and wins a strength challenge with his wits. Of course, the wizard player need to come up with a plan, or it's gonna be a straight loss for him. Alternatively, the wizard could roll a d100: for results above 95, an unexpected event helps him win (like a bird falling on the orc, the orc sneezing etc) \$\endgroup\$ – OmniVictor May 11 at 10:07

It's not a contest. See the PHB p. 174

Sometimes one character's or monster's efforts are directly opposed to another's... In situations like these, the outcome is determined by a special form of ability check, called a contest.

The players aren't free by the normal rules to directly oppose the other person, merely use strength. If it was a true contest then they could do things like kicking them in the balls, or hitting their arm with a stick and then pulling it down.

Contests are meant to represent especially random events, where lots of things could be done. A straight arm wrestle I would represent with a straight skill check with the DC set by the strength of the other person since you can't freely contest the other person.

Here's an example used by the PHB.

This situation also applies when one of them is trying to prevent the other one from accomplishing a goal— for example, when a monster tries to force open a door that an adventurer is holding closed. In situations like these, the outcome is determined by a Special form of ability check, called a contest.

Against a monster, a PC is allowed to use any tactics, including dirty tactics like punching the monster, opening the door and then slamming it on the monster, or a host of things that would be subsumed in the roll to keep the door closed. They are not limited to just strength vs strength.

If they wanted a contest they would either need to cheat radically or do something else like deceive the orc into believing they are wrestling a god and so should lose. Any 'contest' where you are not free to do whatever isn't a proper contest.

  • 3
    \$\begingroup\$ One of the given examples of a contest is "when a monster tries to force open a door that an adventurer is holding closed." I find that extremely similar to the scenario of an arm wrestle. I downvoted simply because I believe the definition you are using for "contest" is wrong \$\endgroup\$ – Medix2 May 11 at 16:42
  • \$\begingroup\$ @Medix2 Holding a door closed is very different than a formal arm wrestle. Arm wrestling is arranged so that as little besides strength matters. For a door, there are going to be piles of confounding factors. \$\endgroup\$ – Yakk May 11 at 17:52
  • \$\begingroup\$ If you agree to not stop the monster from busting through the door with anything but muscular strength, sure, but generally when that is happening you are free to do whatever you want to win the contest. It's not like a bar wrestle, where dirty tactics are forbidden. \$\endgroup\$ – Nepene Nep May 11 at 19:13

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