17
\$\begingroup\$

When DMing and randomly determining a character to take damage or an effect, it's easy to roll a die if you have an even number of characters. But what about if you have an odd number of characters?

What is the simplest method for randomly choosing 1 out of an odd number of characters, while ensuring that each character's probability of getting chosen is equal or very close to equal?

\$\endgroup\$
52
\$\begingroup\$

Dice work just fine for the most common numbers of players

I work with probabilities a lot. Dice allow you to represent many common probabilities, but when you want to roll to pick from options, I've discovered the following "law": it stops making sense to people when you have to roll more than a single die at once. Luckily, the most common numbers of players can be chosen from using just a single die roll, or a single die roll that occasionally gets re-rolled when its result is invalid.

If you have a single player, no need to roll.

If you have three players, a d6 will do --- one player gets results 1-2, another 3-4 and the third one 5-6.

Five players, roll a d10. One player gets 1-2, the next 3-4, then 5-6, then 7-8, and the final one 9-10.

There is just a bit of math behind these two options: they work neatly because three and five are factors of six and ten, respectively. That means we can "partition" each dice's possible outcomes into that many equally probable sets, similar to how we can use "odd" and "even" to select from two options using a d6.

Seven players is the first tricky one because it's the least prime number that's not a factor of any of the common die sizes of 4, 6, 8, 10, 12 or 20. This means you cannot resolve a choice between seven players with any bounded number of these die rolls with complete fairness. You can, however, use a d8 with numbers 1-7 corresponding to each of the players and 8 indicating a reroll. The chances of having to roll the die impractically many times for a single decision are minimal.

Nine players or eleven players, similar to seven except use a d10 or d12, respectively. Since nine is divisible by three, you can also use two rolls of a d6: first divide the player into three groups of three, let the first roll decide which group you pick and the second roll which particular player from that group. The d10 method is simpler, though.

You can of course use arbitrarily large dice to cover any amount of players using the "reroll if too high" strategy, but it can get unwieldy for larger numbers.

Drawing from a deck of cards works for many sizes of groups

Using a deck of cards provides a simple solution for groups small and large, without having to remember any complex roll rules. Have each player draw a card from a standard deck of 52 cards. The player who gets the highest card (or lowest, if you prefer) is chosen. Remember to have a set convention on the ordering used (aces high or low and precedence of suits).

There's 52 cards in a normal French-style deck of cards, and each is unique, so you can choose a random player with everyone drawing a single card for groups up to 52 players. That's probably more than enough.

Draw from a bag

Yet another classic method: have each player write their name on a slip of paper. Put them in a box or bag, and resolve the decision by drawing one without looking. My experience is that this is quite awkward especially when table space is limited --- I appreciate the other methods' compactness. However, this method works quite well regardless of the size of the game, assuming you have a big enough box for the name slips and shuffle it well.

Random number list, if you want to keep it secret

If you know the amount of players you'll have in advance, you can create a list of random numbers and bring that to the game with you. When consulting the list, cross over the topmost number on it and select the player based on that number.

This solution is, for most games, over-engineered, but it has an advantage in that unlike die rolls and draws from the deck of cards, it is very subtle and allows invoking the randomness without signaling it to your players. My experience has been, though, that it's best to let the players know when you're actually choosing one of them at random in most cases --- otherwise, they can assume the choice is you being arbitrary.

\$\endgroup\$
  • 2
    \$\begingroup\$ Re dice: If you have four or fewer players, I suppose you could use these. Just be very sure you don't accidentally mix them in with the regular d12s, or the DM will not be happy with you ("What do you mean, you rolled a 47 on 1d12?"). \$\endgroup\$ – Kevin Apr 8 at 3:18
  • \$\begingroup\$ If you go with drawing from a bag, I would recommend physical items. Differently-coloured tiddlywinks (or dice of the same size) if exact fairness is more important than immersion; cheap unpainted miniatures if the reverse. \$\endgroup\$ – Tim Lymington supports Monica Apr 8 at 8:23
  • 1
    \$\begingroup\$ Yeah, I think this is best. It's not perfect, but this works well, is fair, and rarely makes arguments. Maybe also mention apps or websites as an alternative, if "just getting a number" outweighs "being able to see how" for some people. \$\endgroup\$ – Jack V. Apr 8 at 12:17
32
\$\begingroup\$

If you have 5 players, roll a d6. If you get a 6, re-roll until you get a number other than 6. And so on, for other odd numbers. Yes, this is completely fair, if the die you're rolling is a fair die.

\$\endgroup\$
9
\$\begingroup\$

How I have done this over the years:

It makes for even probabilities.

  1. For three players: roll 1d6, divide result by 2, round up.

  2. For five players: roll 1d10, divide result by 2, round up

  3. For seven players: roll 1d8, re roll any 8.

  4. For nine players: Roll 2d6 of different colors. (Let's say red and green, since that is what my bag is filled with)

    • Green die indicates which range of three: 1 or 2 =1-3, 3 or 4 = 4-6, 5 or 6 = 7-9.
    • You now have a "three players" situation
    • Red die indicates who in that group is chosen by using the "for three players" above.
  5. For 11 players; roll a d12, re roll 12's.

It's really fast and intuitive once you start doing this (it's easy to do the comparison in your head). It takes longer to describe it than to do it.

Notes:

  1. While I don't do this, @BenR suggests out that for 9 you could do it as you do for 7; roll a d10 and re roll 0's/10's. Since I prefer to roll just once; the 2d6 is one roll and the result is right there).

  2. While I have not done this, @Yakk suggests this for a d13 if you have 13 players.

    • For 1d13, roll a red, green and blue d12. If all 3 match, use the value. If red and green match, but not blue, use 13. Otherwise, use red. Accurate within a fraction of a percent to 1/13 for each value.
\$\endgroup\$
4
\$\begingroup\$

The existing answers all presuppose that the GM is the one rolling for the determination, but this is not necessary. Another approach is to have each player roll a d20 and the lowest (or highest) roll is selected. In the event of a tie, the tied players roll again until a single low/high roll is achieved.

The primary flaw in this method is that it reveals to players that you are making a random selection among them, which may or may not be an issue depending on your group conventions and the reason for the selection.

The primary advantage of this method is that it works for any size group of players. (With an exceptionally-large group, frequent ties could become an issue, but that can be resolved by using a d100 instead of d20.)

If you are running a system with a "luck" stat of some sort, this method can also be enhanced to take that stat into account. e.g., everyone makes opposed luck rolls, roll d20+luck if it's a numeric stat, roll (luck)d20 and take the best (or worst, if you have negative luck) if luck is bought in "levels", etc.

\$\endgroup\$
1
\$\begingroup\$

This answer assumes sandbox play where changing encounter difficulty is not really an issue. If you prefer a game with precisely balanced encounters, you will need to take this into account when doing the balancing.


As demonstrated in other answers, you have an exact solution when there are at most six players.

I am going to consider the example of seven players, for concreteness.

You will roll a d8, but before rolling, think of a consequence to rolling 8, so that it adds variability and spice to the game, rather than being a distraction and a flaw in the mechanics. Some possibilities:

  • On 8, the monster runs away, smashes the pillar, tries to grab an opponent (reroll whom), or does some other plausible and effective, but less likely, action.
  • On 8, the monster attacks a familiar, a horse, or a hireling.
  • On 8, the trap is stuck and the shot delayed by a bit, or the trap breaks down in a barrage of flying gears, springs and bolts, and a very loud noise (make a random encounter check and maybe people take 1 damage if they are nearby), etc.

If you can not come up with anything, just do a simple reroll to see whom the monster attacks, but add strange positioning, the monster yelling or growling a lot or thumping its feet, yelling for its mommy, swearing it will kill you all and your families will be cursed for three generations, or some other bit of interesting and colourful description.

Essentially, take rolling too big a number as a creative prompt.


I have used this a couple of times, but more generally, when resolving something randomly, I often add about 1/6 chance for an unexpected or less likely outcome. It works fine and makes the game more interesting. What I suggest here is a simple special case of the general practice.

\$\endgroup\$
  • 1
    \$\begingroup\$ Have you tried it at your table? How it affected encounter difficulty? It looks like it would remove ⅛ of monster damage dealing opportunities, possibly more in standard 3 rounds encounter. Didn't it make encounters easier than intended by game authors? Et cetera. \$\endgroup\$ – Mołot May 26 at 7:00
  • \$\begingroup\$ @Mołot Clarified the answer. Encounter balance is only a concern for specific styles of play of specific editions, so I did not think to discuss that, but I added a warning to that effect. \$\endgroup\$ – Thanuir May 26 at 8:08
0
\$\begingroup\$

For me it depends on the creatures intelligence first and foremost. If the creature is smart, fairness goes out the window.

I.E. that lich is definitely looking at that wizard like he's lunch. In the case of really stupid creatures, its usually whoever's the closest, or being the most annoying to the creature.

But in fair encounters I usually just roll a d(whatever) and count around the table till I hit that person. Granted, If I roll a number greater than the number of seats I reroll to keep it fair.

\$\endgroup\$
  • 1
    \$\begingroup\$ Question asks for a random way to do it if there are no storytelling reasons for one character to be singled out. Frame challenge is ok, but needs to be done right. \$\endgroup\$ – Mołot May 26 at 7:23
0
\$\begingroup\$

A simple solution with equal probabilities has to be a single die roll.

For 5 characters, roll a D6. When a 6 is rolled, that can be DM choice or hit multiple characters or monster fumbles and hits its party or it can be an automatic miss. It can add a whole new dimension of random excitement.

DM judgement is especially useful. For example, all members of a party have taken damage. Most are within one hit of death, but one fighter still has armor and hitpoints to survive the hit. The DM assigns the 6 roll to the character that would survive.

Another example is to correct playing out of class. A cleric that attempts to get behind the monsters, away from the party exposes him/her and the party to great risk. A cleric should stay in the rear ready to heal. The extra chance of getting hit reinforces proper roles.

An automatic miss is useful when the party is fleeing or when cover / concealment modify a portion of the melee.

A fumble generates an dropped weapon, hit on own party with a new roll to hit, a fall, a stun or other mishap. Fumbles were sometimes funny and prevented powerful characters from taking everything for granted. There is always some risk.

\$\endgroup\$
  • \$\begingroup\$ Have you tried this house-rule (for when a 6 is rolled, for instance)? How has it worked in your experience? \$\endgroup\$ – V2Blast May 26 at 3:06
  • 2
    \$\begingroup\$ Yes, the DM sets the expectation up front that the extra die slots will be up to DM judgement or one of those choices. It applied to both party and monster. Then it is perceived as fair. \$\endgroup\$ – ExcessOperatorHeadspace May 26 at 3:16
  • 1
    \$\begingroup\$ You should edit this information about your experience into your answer to support it. \$\endgroup\$ – V2Blast May 26 at 3:32

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.