Palindrome Construction

TBD

Designer(s): elara Match Type: MM (for 7/9 players)
Featured in: The Genius Puzzler, Genius Recharged

Main Match 8: Palindrome Construction

In Palindrome Construction, players bid on digits to form digit strings. Each string scores points based on its qualities, but non-palindromes automatically score zero points.


RULES

This game takes place over seven rounds, each of which has two phases: a bidding phase and a construction phase. For the first six rounds, the construction phase overlaps with the next round's bidding phase, so there are eight rounds of gameplay in total.


Each bidding phase, all players receive bidding cards numbered 0-9, that they use to bid on digit packs.

Each digit pack contains 3 digits, and there are 10 digit packs per round. These digit packs are generated randomly, with the additional restriction that each digit from 0-9 must appear at least twice among all packs in each round.

Players assign cards to the digit packs they'd like to receive. After the bidding phase, the player who bid the highest unique card on each digit pack receives that pack. (If such a player does not exist, nobody receives the pack.)

In addition to the digit packs, each bidding phase also provides a single item. These items allow you to modify your numbers. The rule for bidding on items is slightly different--you may spend any number of cards on it, and the player who bids the highest unique sum of all cards receives the item. Furthermore, you may spend garnets to increase your sum, at the rate of 1 Garnet = +5 to your sum.

After the bidding phase, it is revealed who received each digit pack as well as the item for that round, but not the exact card assignment distributions for each player.


For the construction phase, players use the digits from the packs they received and append them to their digit strings. Players are given three digit strings to work with, all of which start out empty. You may discard digits that you receive, but you cannot use them afterwards, they are gone forever.

In addition, any items you have received in the past can be used. Items are one-time use, which means that once one is used, it is gone.

As an example, if you currently have the digit strings 123, 456, and 789, and just received the digit pack 235, you may form the new digit strings 12332, 4565, and 789.

If you also had the item Duplicate: You may duplicate a single digit that you received this round, you could form the digit strings 123332, 4565, and 789.

(This item may or may not appear in the actual game, it's just used as an example here.)


After all rounds have ended, each player's strings are revealed, and you earn points according to the final digit strings you formed. First, if a string is empty or is not a palindrome (i.e. it is not the same when read in reverse), then the string scores zero points automatically. The string will still affect "Normality" and "Maximal" of other strings.

Otherwise, the following criteria are used to determine number of points:

Primality: If this digit string forms a prime number in base 10, it scores 2 points.

Accumulation: A digit string with the sum of its digits equal to A receives log_2(A) points, rounded down.

Length: A digit string with length L scores L/2 points, rounded down.

Identical: If your string is the same as one that a different player created, gain 2 points.

Normality: If your three digit strings all contain the same number of digits, gain 1 point (for each one).

Differences: A digit string with D unique digits for D>2 scores D-2 points.

Repetition: If your string consists only of a single digit repeated at least four times, it scores 2 points.

O's: Digit strings score 1 point for every zero in the string.

Maximal: If this digit string is the numerical largest out of all players, it scores 3 points.

Exodia: If this digit string is 20 characters long consisting of two of each digit, it scores 8 points. This is in addition to the point reward of Differences.


Afterwards, each player's string scores are summed up for their overall score. The player with the highest sum wins the Main Match and receives two Tokens of Life. If multiple people have the same highest score, they all receive one ToL each.

The Elimination Candidate is the player with the lowest overall score.

Garnets will be given out proportionally in this Main Match. The winning player(s) will receive 5 Garnets. Any player whose total score is 80% or higher of the winner's receives 4 Garnets. Any player whose total score is 60% or higher receives 3, 40% will receive 2, and 20% will receive 1.


ADMINISTRATION

Timing

This game will have a single pregame phase, lasting 24 hours. (You will not receive the Round 1 item and digit packs during this phase.) Afterwards, we will have:

  • Round 1 bidding
  • Round 2 bidding + Round 1 construction
  • Round 3 bidding + Round 2 construction

...

  • Round 7 bidding + Round 6 construction
  • Round 7 construction

Each of the above phases will last 24 hours each.


Submissions

For bidding phases, submit an assignment of each card to a digit pack or item, and optionally how many Garnets you'd like to spend on the item.

For construction phases, submit where you would like each of your digits from digit packs you received this round will go, and in what order. You may also use an item if you have one.

Failure to submit in bidding phases means you bid on no digit packs. Failure to submit in construction phases means you do no actions, which means you will lose your digit packs from the round.


Information

Publicly announced, at the start of each bidding phase:

  • The digit packs for the round
  • The item for the round

Publicly announced, at the end of each bidding phase:

  • Which player received each digit pack and item

Publicly announced, at the end of the game:

  • The final digit strings of each player
  • The final scores (and therefore winners/losers)

Known only to you:

  • Your distribution of cards during each bidding phase

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Main Match 5: Palindrome Construction — originally designed by @elara


SUMMARY

In this Main Match, players bid on digits to form digit strings. Each string scores points based on its qualities, but non-palindromes automatically score zero points.


This game takes place over five rounds, each of which has two phases: a bidding phase and a construction phase. For the first four rounds, the construction phase overlaps with the next round's bidding phase, so there are six rounds of gameplay total.


BIDDING PHASE

Each bidding phase, all players receive bidding cards numbered 0-9, that they use to bid on digit packs.


Each digit packs contains 5 digits,, and there are 10 digit packs per round. These digit packs are generated randomly, with the additional restriction that each digit from 0-9 must appear at least three times among all packs in each round.


Players assign cards to the digit packs they'd like to receive. After the bidding phase, the player who bid the highest unique card on each digit pack receives that pack. (If such a player does not exist, nobody receives the pack.)


In addition to the digit packs, each bidding phase also provides 2 items. These items provide advantages. The rule for bidding on items is slightly different--you may spend any number of cards on it, and the player who bids the highest unique sum of all cards receives the item.


After the bidding phase, it is revealed who received each digit pack as well as the item for that round, but not the exact card assignment distributions for each player.


CONSTRUCTION PHASE

For the construction phase, players use the digits from the packs they received and append them to the end of their digit strings. Players are given three digit strings to work with, all of which start out empty. You may discard digits that you receive, but you cannot use them afterwards: they are gone forever.

In addition, any items you have received in the past can be used. Items are one-time use, which means that once one is used, it is gone.


  • As an example, if you currently have the digit strings 123, 456, and 789, and just received the digit pack 235, you may form the new digit strings 12332, 4565, and 789.
  • If you also had the item Duplicate: You may duplicate a single digit that you received this round, you could form the digit strings 123332, 4565, and 789.

(This item may or may not appear in the actual game, it's just used as an example here.)


SCORING

After all rounds have ended, each player's strings are revealed, and you earn points according to the final digit strings you formed. First, if a string is empty or is not a palindrome (i.e. it is not the same when read in reverse), then the string scores zero points automatically. The string will still affect "Normality" and "Maximal" of other strings.

Otherwise, the following criteria are used to determine number of points:

  • Primality: If this digit string forms a prime number, it scores 2 points.
  • Accumulation: A digit string with the sum of its digits equal to A receives log_2(A) points, rounded down. - (https://www.calculator.net/log-calculator.html)
  • Length: A digit string with length L scores L/2 points, rounded down.
  • Identical: If your string is the same as one that a different player created, gain 2 points.
  • Normality: If your three digit strings all contain the same number of digits, gain 1 point (for each one).
  • Differences: A digit string with D unique digits for D>2 scores D-2 points.
  • Repetition: If your string consists only of a single digit repeated at least four times, it scores 2 points.
  • O's: Digit strings score 1 point for every zero in the string.
  • Maximal: If this digit string is the numerical largest out of all players, it scores 3 points.
  • Exodia: If this digit string is 20 characters long consisting of two of each digit, it scores 8 points. This is in addition to the point reward of Differences.

Afterwards, each player's string scores are summed up for their overall score. The player with the highest sum wins the Main Match and receives two Tokens of Life. If multiple people have the same highest score, they all receive one ToL each.

The Elimination Candidate is the player with the lowest overall score.

Garnets will be given out proportionally in this Main Match. The winning player(s) will receive 5 Garnets. Any player whose total score is 80% or higher of the winner's receives 4 Garnets. Any player whose total score is 60% or higher receives 3, 40% will receive 2, and 20% will receive 1.


TIMING

For phases we will have:

Round 1 bidding

Round 2 bidding + Round 1 construction

...

Round 5 bidding + Round 4 construction

Round 5 construction

Each of the above phases will last 24 hours each.


SUBMISSIONS

For bidding phases, submit an assignment of each card to a digit pack or item.

For construction phases, submit where you would like each of your digits from digit packs you received this round will go, and in what order.

Items use timing will depend on the specific item.

Failure to submit in bidding phases means you bid on no digit packs. Failure to submit in construction phases means you do no actions, which means you will lose your digit packs from the round.

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