TaylorBowls

TaylorBowls, also known as Bowls, are the main minigame in the TaylorBowl Discord server. They are started with the command !taylorbowl and last, by default, 11 minutes. Every Bowl has two tracks chosen from a list of matchups which have the letter 'A' or 'B' given to them. They receive votes by users sending their letter alone in a message. At the end of the time, the Bowl will end and the track with more votes gains a score called Elo while the other track loses Elo. If the votes are tied, Extra Time for more voting and/or a Tiebreaker for bribing using Credits happens.

Every TaylorBowl follows the same mechanics of starting, duration, voting, ending, Extra Time, Tiebreaker, and results.

To start a TaylorBowl, the command !taylorbowl is used. Using this command successfully is unofficially known as a "natural start". This starts a Bowl at a random Tier and it will last 11 minutes. This can be changed through forcing or queueing Bowls, which lets users choose a specific Tier, duration, or even matchup. If a bowl is queued, it will take priority and natural starts cannot happen.

Between TaylorBowls, there is a 2 minute "cooldown" period where no new Bowls can be started, but other actions can be done. This was done for "post-discussion" after certain Bowls. The durations for a default TaylorBowl and cooldown were chosen as they add up to 13.

Every TaylorBowl has two song options, chosen from a list of matchups. The song with the higher Elo is assigned the letter A, and the song with lower elo is assigned the letter B. Sending either letter as its own message counts as a vote. Alternatively, sending any message containing [A] or [B] counts as a vote for that option. If a message contains both [A] and [B], it is counted as a vote for A. You can switch votes by simply voting again except during the last minute of each Bowl.

The command !showbowl or its shortened form !sbowl can be used at any point during the Bowl to show the two options and the number of votes each currently has. The command /didivote user can be used at any point during the bowl to privately check if you or a specified user has voted, and for which song. If used after a Bowl ends, the command shows whether you voted in the previous Bowl. Note that there is an edge case where using /didivote during the logging period of a Bowl will not show whether the user voted in the Bowl that just ended, but instead the one before it.

If at the end of a Bowl there is an track with more votes than the other, it is chosen as the winner. BowlBot will then enter a "logging" period, which typically lasts between 15 and 30 seconds. This is counted as part of the bowl cooldown.

At the end of each logging period, BowlBot saves all changes that happened during the Bowl. This is a sort of mini-backup. When Bot Restarts happen, anything that happened since the end of the previous Bowl is not saved. This includes data of the bowl that ended as well as other areas including but not limited to Blooms and Blights, changes in currency, Autovoting status, and transfers.

At the end of the logging period, BowlBot sends a summary message of the bowl. It includes the two songs and their resultant ranks, total votes acquired by both, and voters for each side from the server the message is sent in.

If the number of votes is tied, Extra Time happens which lasts 2 minutes. This is known internally as the 'Lydia Rule'. Switching votes is re-enabled for the first minute and disabled for the last minute. Bribing is enabled but will not have any effect unless Tiebreaker happens.

If at the end of Extra Time the number of votes is still tied, the Tiebreaker happens. Votes cannot be cast or changed and the only way to influence the outcome is through bribing. The command !tiebreak amount or its shorter alternative !bribe amount bribes the specified number of Credits for the track you voted for. This means users who did not vote in a Bowl cannot bribe. At the end of the Tiebreaker, the winner of the Bowl is decided based on the number of Credits used to bribe. If one track has twice the number of bribed Credits than the other, it is twice as likely to win the Bowl, or a 2 in 3 chance. This holds true for all ratios of bribed Credits. If any one song has no credits used to bribe for it, it has a 0% probability of winning. If both songs have no credits used to bribe for them, they both have a 50% probability of winning.

At the end of every TaylorBowl, BowlBot sends a summary message of the Bowl, which includes the number of votes for both options and the votes of each member in the server; the change in Elo of both tracks; and the TaylorBowl number and time to log.

Command	Description
!bribe amount	Bribes the specified number of credits for the user's choice. amount is a mandatory parameter that refers to the number of credits bribed. Alternative forms: !tiebreak amount
/didivote user	Checks whether a user voted and for which track. If used with no ongoing Bowl, confirms whether the user voted in the previous Bowl. user is an optional parameter that refers to the user whose vote is being checked. Defaults to command user.
!sbowl	Shows the current TaylorBowl. Alternative forms: !showbowl
!taylorbowl	Starts a TaylorBowl.

1.1 Probability that Track $A$ wins the Tiebreaker:

$$P(A\text{ wins})=\cfrac{\text{Credits bribed for }A}{\text{Total credits bribed}}$$

1.2 Ratio of the probability that Track $A$ wins to that of Track $B$:

$$P(A\text{ wins}):P(B\text{ wins})=\text{Credits bribed for } A:\text{Credits bribed for } B$$

List of Terms

Term	Definition
Lydia Rule	Internal name for Extra Time.
Natural Start	Starting a TaylorBowl without forcing or queueing it.
Logging	BowlBot saving information about what happened since the last Bowl ended.