Blackbox Decoder

"Just win, ez gg." -Spadez

Overview

In this DM, players will be attempting to decode a sequence of blackboxes created by the other player.

Setup

This DM will consist of 9 rounds. In each round, there are two phases: the preparation phase, and the decoding phase. The preparation phase will happen first, followed by the decoding phase. In the construction phase, players will be using blackboxes to construct a bigger blackbox, called a superbox. In the decoding phase, players will be attempting to guess their opponent's superbox.

Blackboxes

A blackbox consists of an input and an output. The blackbox takes some input and produces an output based on the input.

The input and output can be in one of a few formats:

An n-tuple of integers, where n is any positive integer. A 1-tuple is trivially defined as one integer.

A string, which is a concatenation of characters in a sequence. These characters only consist of lowercase English letters from a to z, inclusive. Any string that is used as input will be automatically lowercase.

In every round, players will be given a list of blackboxes, labelled by letter. For each blackbox, you will be given its input format, output format, and the operation it performs on the input to produce an output.

Superboxes

A superbox consists of a sequence of not necessarily distinct blackboxes. For every blackbox in the superbox, the output of the previous blockbox (if any), must match the format of the input of the current blackbox.

The input format of the superbox is the input format of the first blackbox in its sequence, and the output format of the superbox is the output format of the last blackbox in its sequence.

The superbox's output is just the final output of the chain of blackboxes. In more formal terms, the output of a blackbox is what the blackbox outputs given the previous blackbox's output as input, where the previous blackbox of the first blackbox is defined as the input to the superbox. The superbox's output will then be defined as the output of the final blackbox.

Superboxes will be written as a sequence of letters, where the first blackbox in the superbox is the leftmost letter in the sequence. So ABC would be a superbox that uses blackbox A first, then B, then C.

Construction Phase

In the construction phase, players will be given the list of blackboxes (this list will have a maximum size of 26), and will privately construct a superbox. In every round, the maximum number of blackboxes that can be in a superbox is restricted, though this number is at least 2 and at most 10.

Decoding Phase

In the decoding phase, players will be attempting to decode the other player's superbox. For an action, players may do one of two things:

Submit an input to their opponent's superbox. They will receive the output.

Guess a sequence of blackboxes that is equivalent to their opponent's superbox.

After doing an action, there is an action cooldown of 30 seconds before you can do another action.

If a player guesses, the timers and cooldowns are paused. The non-guesser will then have a chance to rebuke the guess by providing an input that gives a different output for their own superbox and the guessed superbox. If this input does indeed produce different outputs, the guesser is penalized. Otherwise, the guesser wins the round.

The penalty for an incorrect guess is that you cannot submit another guess for 1 minute. In addition, your opponent is given 3 free actions. A free action is automatically used when you want to use an action but you are still on the action cooldown. This will allow you to do an action anyways and ignore the cooldown. Note that the cooldown timer is not changed; think of this action just giving you an action without affecting the normal action timer.

After 6 minutes, the action cooldown becomes 20 seconds. After 10 minutes, the action cooldown becomes 10 seconds. At these times, the current action cooldown timer is not affected; it only affects new actions done at or after the specified time.

If after 12 minutes there are no correct guesses, both players will be given one final chance to guess, starting with the player who has less time remaining on their guess cooldown. If both players have no guess cooldown, then it will start with the player who least recently did a non-free action (i.e. the player who has less time left on their cooldown timer). Incorrect guesses will not have a penalty. If both guesses are wrong, the round is a tie.

Winning

The player with more round wins at the end of the DM wins the DM. If this is a tie, the player with less incorrect guesses (excluding the final chance guesses) throughout all rounds wins the DM. If this is also a tie, the player with a lower combined time for all their correct guesses wins the DM. If this is also a tie, screw you I flip a coin.

Submissions

In the construction phase, players will submit a sequence of blackboxes that forms their superbox in private. In the decoding phase, all actions and action results will be public. In addition, the input and output format of each players' superboxes will be public.

Timing

In the construction phase, players will be given 3 minutes to read the provided blackboxes and construct a superbox.

In the decoding phase, players can make an action once every 30 seconds. This timer reduces to 20 seconds after 6 minutes, and to 10 seconds after 10 minutes. This timer is paused when a player guesses. When a player guesses, the other player has 2 minutes to come up with a counterexample.

Whenever a player guesses, all timers are paused. This includes all cooldown timers, as well as the 12 minute decoding phase timer.

Restrictions

You may take notes during the DM; however, the use of external tools such as calculators, programs, or spreadsheet formulas is prohibited.

Addendum: The input and output format of each players' superboxes will be public.

Addendum: The maximum number of blackboxes in a round is 26.

Clarification: Your action cooldown starts when you submit your action.

Clarification: Each blackbox will have exactly one format for its input and one format for its output.

Clarification: Strings are 0 indexed from the left.

Clarification: The empty string is valid input for a string.

Clarification: No blackbox will require outside knowledge outside of basic things (such as primes). If more advanced terms are used, it will be defined explicitly during the DM.