balderdash!—a game

balderdash! is a game that I came up with in 2020. I recently revisited it and fleshed it out with my friend vorboyvo. It’s an oral¹ game to pass time for two² people.

In balderdash!, players count up. There are rules, determined by the players as explained below, that modify what is said. In a turn, a player applies the rules to the original number of that turn, and says the result. Play begins with the first player at original number 1. The next player then takes their turn with original number 2, and so on. For example, if the only rule is “multiply even numbers by two” and a player’s original number is 2, they say 4, but if their original number is 5, they say 5.

Before the game starts, a coin toss determines who goes first. Then, opposite the order of play, the players take turns making rules for two rounds. It’s recommended that each player makes one rule affecting the creation of rules and one rule modifying what numbers are said.

When a player takes their turn, the other players can call them out if they made a mistake—that is, if they said something that is not the output of the rules applied to their original number. If the group determines that there was a mistake, the next player first makes a new rule, and then says the result of the rules (including the new one) applied to the mistaken player’s original number.

Example game

Two players, Meow and Woof, play balderdash!

Meow tosses a coin, calling heads. The coin comes up tails, so Meow goes second, but makes a rule first.

Meow makes the rule “If you have an power of 2, take its log base 2.”
Woof makes the rule “If your original number has two consecutive 6s, rescind or amend a rule.”
Meow makes the rule “If what you have is at least 10 and its digits are consecutive descending numbers, you may amend a rule by limiting the conditions where it applies.”
Woof makes the rule “If you have a multiple of 6, add 7.”

Woof goes first, and from original number 1, says 1, thinking that no rules apply. Meow, however, notices that 1 is a power of 2, and calls out Woof, who should have said 0. Meow makes the rule “If you have a multiple of 11, say balderdash!” Play proceeds with Meow at original number 1.

Meow: 0
Woof: 1
Meow: 3
Woof: 2
Meow: 5
Woof: 13
Meow: 7
Woof: 3
Meow: 9
Woof: 10

Woof has a number that is at least 10 and its digits are consecutive descending numbers, so by the third initial rule they choose to amend a rule by limiting the conditions where it applies. Woof chooses to amend the third initial rule by requiring that none of the digits in the number are 0. Play proceeds with Meow at original number 11.

Meow: balderdash!

Play proceeds with Woof at original number 12, but this example ends here.

Technicalities

• In a rule, original number or similar refers to the number before application of the rules, and your number or what you have or similar refers to the number after application of preceding rules.
• A rule must be able to be evaluated using only the original number and the other rules. Rules like “If it’s after 10:30, add three to your number” and “If you are Meow, multiply your number by 5” are not allowed.
• Where a rule provides for a player to modify the rules, this modification happens after their turn.
• If a player after making a rule realizes that it is ambiguous, then they must bring this up to the group, which must make a decision as to the interpretation of the rule.
• If a rule would have a player say nothing (for example, the rule “do not say multiples of 5” at original number 15), then play proceeds with that player at the next original number (in the example, 16). This way, a player always says something on their turn.

Style in rules

If the rules get complicated, it’s useful to write them down. Here are some tips for doing so.

• Number the rules in the order they’re made.
• Record the name of the player who makes a rule.
• Record, if applicable, the original number of the last mistake-free turn made when a rule is made.
• Record the mechanism by which a rule is being made.
• Record amendments to rules and rules being rescinded as you would record any other rule.
• Try to word rules as simply as possible.

For example, in the example game above, the rules could be recorded as

1. Meow: If you have an power of 2, take its log base 2.
2. Woof: If your original number has two consecutive 6s, rescind or amend a rule.
3. Meow: If what you have is at least 10 and its digits are consecutive descending numbers, you may amend a rule by limiting the conditions where it applies.
4. Woof: If you have a multiple of 6, add 7.
5. Meow: If you have a multiple of 11, say balderdash! (at 0, B messed up)
6. Woof: Amend rule 3 by requiring that no digits of what you have are 0. (at 10, by rule 3).

Another example

Here’s a complete ruleset for a game between Meow and Woof:

1. Meow: If your original number and what you have are larger than 10, and every digit of what you have is the same, amend a rule germanely.
2. Woof: If you have a perfect square with root at least five, you may make the condition for any rule stricter.
3. Meow. If the first digit of your number is 1, remove it.
4. Woof: If your number ends in 5, at your choice, either add or subtract 5.
5. Meow: Amend rule 2 by adding “If you do so, take the square root of your number.” (at 11, by rule 1)
6. Woof: Amend rule 3 by replacing “it” with “all digits 1”. (at 22, by rule 1)
7. Meow: Amend rule 1 by adding “or make a new rule”. (at 33, by rule 1)
8. Woof: Amend rule 1 by requiring that every digit of your number is even. (at 36, by rule 2)
9. Woof: If your number is a power of 2, take its log base 2. (at 44, by rule 1)
10. Woof: If your number is a multiple of 4, divide it by 2. (at 66, by rule 1)
11. Woof: If your number ends with 3, skip it. (at 88, by rule 1)
12. Meow: Amend rule 11 by requiring that your number only has one digit 3. (at 121, by rule 2)
13. Meow: Repeat every rule, not including this one, in order, until you reach a fixed point; if a fixed point is never reached, say balderdash! (at 122, by rule 1)
14. Woof: Amend rule 4 by only requiring that your number end in 5 or 0. (at 144, by rule 1).
15. Woof: Amend rule 13 by requiring that your original number be even. (at 149, by rule 2).

Play ended by mutual agreement with the last turn being taken by Meow at 174.