The Kingmaker

Main Match 11: The Kingmaker

In The Kingmaker, players must crown the right people, but without upsetting the masses.

Overview

This game is nine rounds long. In each round, one player is a designated kingmaker. This rotates every three rounds, so Rounds 1, 4, and 7 each have the same kingmaker.

If you are the kingmaker for the round, your goal is to influence the round so that one of the other two players gains at least two more points than the other one, but no more than four points more. If the absolute difference between the points that the other two players earn in that round is between 2 and 4, you earn bonus points equal to the higher point count of the two players. If the absolute difference is more than four points, the round is denoted clearly rigged; no player will earn points, and the kingmaker will lose two points as a penalty.

Bots

In addition to the three players, there are 9 Bots in this game, designated the letters A-I. In each round, one of the bots is the King, depending on the round number (A is the king in Round 1, etc.)

Bots, by default, will make predetermined moves. These moves (finger choice and king's distribution) will be revealed in each round.

It is possible for bots to be bribed to make a different action. This will cost garnets.

Gameplay

Each player in the game controls four "accounts". Each account will submit a separate action, and are denoted as P.1 P.2 P.3 P.4 where P is the player (e.g. Summit.1 Summit.2 Summit.3 Summit.4).

On each round, each player account and non-king bot will choose a finger to show, either thumb, pointer, or pinky. As such, there will be 20 finger submissions. These submissions must be divided into three groups, labeled groups Alpha, Beta, and Gamma. There is no restriction on how many submissions need to be partitioned into each group; they could be all in a single group, for instance. The king bot's submission includes where each bot will go, but the players will individually decide where their accounts will go.

Points

Players earn points as follows:

Within each group, we calculate which fingers appeared the most, which fingers appeared the median amount, and which fingers appeared the least. If multiple fingers appeared the same number, they each count for the higher value.

For instance, if thumb, pointer, and pinky each appeared twice, they all count as most.

If thumb and pointer each appeared twice but pinky appeared three times, then pinky counts as the most, but thumb and pointer are tied for median.

Any account submission that is median in its group gains one point for that player. Any account submission that is least in its group gains three points for that player.

Bot Helping

Each player is given three bots they want to help. Every time that bot would have earned a point on a turn in which that player was kingmaker, the player earns the point instead. The bots that each player wants to help are generated randomly at the beginning of Round 1, such that a player is not a kingmaker on a turn in which their bot is king. A single bot may be helped by multiple players.

Points earned this way are not revealed publicly.

Endgame

At the end of nine rounds, all player point counts are revealed. The player with the highest number of points is the winner of Main Match 11 and moves on to the Finals. If there is a tie for most points, the player who earned fewer points via Bot Helping is the winner; a further tie is broken by the Gamewide Tiebreaker.

The player with the fewest points is the Elimination Candidate; the player with second fewest points is the Death Match Opponent. (This only matters for the purpose of DM selection.) A tie for fewest points is broken in the same way as a tie for most points.

Twists

Group Decision: The Group Decision decides the mechanics of bribing. There are three possibilities:

1) In a single bribe, a player may choose one non-king bot and change their finger choice and/or location.

2) In a single bribe, a player may move up to two bots' locations. For instance, you could move bot A from Alpha to Gamma and bot D from Beta to Alpha.

3) In a single bribe, the kingmaker may choose up to two non-king bots and change their finger choices and/or locations.

In any case, two conflicting bribes automatically cancel each other out. In the first two options, players may not make more than two bribes per round.

Submit one of the three options. In the case of a 1:1:1 tie, the player who is neither the MM Winner nor the DM Winner has the final decision.

MM Winner Decision: The MM Winner decides the amount of Garnets per bribe. Submit a number between 3 and 7 Garnets.

DM Winner Decision: The DM Winner decides the ordering of the three players amongst the rounds. Submit a distribution of players to rounds 1-3; each player will be a kingmaker on that round and the rounds 3 and 6 after it.

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Clarification: The final decisions of all bots are revealed. So if a bot has been bribed, you'd know because their decision has changed, but you wouldn't know who did it.

Amendment:

Typo fix in Bot Helping:

Every time that bot would have earned a point on a turn in which that player was king kingmaker,

Relatively Major Typo Fix:

Any account submission that is largest least in its group gains three points for that player.

Dunno how I managed to mess this up. Sorry.

Clarlfication: Player account decisions are revealed too, so you'll know if a round was clearly rigged.

Clarification: If the round is clearly rigged, the kingmaker can still earn points from bot helping.