Boundary of Few and Many

DM5 / DM9: Boundary of Few and Many

**Players are not allowed to search up information when the DM begins, or use any tools (programs, search engines, books). Players can only use their brains, writing tools, and public server channels. To enforce this, players will have their roles taken away for the duration of the DM.

Players can take notes during this DM, but cannot bring pre-written notes into this DM.**

This Death Match has 15 rounds. The first player to win 8 rounds wins the DM.

In each round, players will receive a question that has a numerical answer. Players have 3 minutes to privately give an upper bound and a lower bound. (Bounds can be in integer, decimal, or scientific notation form, but must be positive and nonzero.) Players can change their answer until the 3 minutes are up, but only the final answer will be taken.

Final submissions should be in the form [a, b]. If a player does not submit in time, they score infinity points.

After the 3 minutes are up, the correct answer will be revealed. If the correct answer is within a player’s bounds (or literally on one of the two bounds), that player’s succeeds. Their score is equal to their upper bound divided by their lower bound. Otherwise, that player fails, and their score is set to infinity. The player with the lower score wins the round; otherwise, no player wins the round.

Each round will also have three possible hints, with descriptions of the hints being given. Players can privately request any set of the hints in the first 90 seconds; they will privately get the requested hints at the 90 second mark. Players cannot request hints after the 90 seconds have expired. Players will not know what hints their opponent requested.

Each hint also comes with a multiplier. For each hint you use, your score for that round will be multiplied by the multiplier. Multipliers multiply multiplicatively; that is, a 2x and a 3x multiplier become a 6x multiplier.

All correct answers to questions and hints with a value that is impossible to precisely determine will be based on Wikipedia’s best estimates, as of December 21, 2023. I will be using the metric system, and your answers should always use the metric system as well. If it makes things easier, remember 1 inch = 2.54 cm.

An example question and hints are as follows:

What is the number of floors in the (rebuilt) One World Trade Center?

Hint 1 - 1.15x - The height of the One World Trade Center

(Answer: 541 meters)

Hint 2 - 1.3x - A two-sentence description of the One World Trade Center regarding the building's relative height

(Answer: “On November 3, 2014, One World Trade Center became the tallest building in the Western Hemisphere. It is the 7th-tallest building in the world.”)

Hint 3 - 1.5x - The largest number of floors in any US building, and the height of said building

(Answer: 108 floors, 442 meters)

Final Answer: 104 floors

If 15 rounds are reached and no player has won 8 rounds, the player who won more rounds wins the DM. If there is a further tie, the player with a lower product of scores (not counting scores equal to infinity) wins the DM. If there is somehow a further tie, the DMO wins.

Anomalies

Boundary Theft: Instead of submitting both bounds, players have the option to submit the word 'steal' in place of one of the two bounds. Choosing to steal a boundary multiplies your score by 1.25x. In scoring calculations, players will take the specified boundary of their opponent as their own. If both players steal the same bound, both fail and score infinity points.

Esrever: All questions and hints descriptions will have have everything (text, etc.) reversed. Hint answers will read normally.

Information War: Hint multipliers all begin at cost 1x. When players request hints, they must also give their own hint multiplier greater than or equal to 1. (Multipliers must be in decimal and can have at most two decimal places.) At the 90 second mark, players only receive a hint if their multiplier exceeds or ties their opponent's.

Placebo: Players get twenty needles (numbered 1-20) and ten poison vials. Before game start, players place all ten poison vials in different needles. During the 90 seconds used for hinting, players can inject their opponent with any number of needles they haven't used yet. The needles used will be publicized when hints are released, but which needles were poisoned will only be revealed post-round. Players will have their score at the end of the round multiplied by 2 for each poisoned needle used on them.

Retry: Players receive six retry clocks. At the end of each round, only player scores will be revealed (but not the correct answer). Revealed scores include adjustments from other Anomalies except Placebo.

Players have one minute to use a retry clock, if they wish. When doing so, players must also privately submit a new set of bounds. Their new final submission will be the score they've achieved with their new set of bounds. Only one retry clock can be used each round.

Smooth Scoring: Players no longer win or lose rounds. If both players fail a round, both score 1. If one player fails and the other player succeeds, the failing player scores 5 times the score of the succeeding player. If both players succeed, but one player has a score above 5 times the other, that player instead scores 5 times the other's score. The winner of the DM is the player with a lower product of all scores; the DMO wins ties.

You First!: The first round proceeds as normal. If a player won the last round, that player must submit their bounds within 150 seconds instead of 180. The submitted bounds will be revealed to the other player (who can use the remaining 30 seconds to submit an answer). As usual, players will only know what Hints were bought and which bounds were valid at the end of the 180 second interval.

If Steal is in play, the submitted bound will appear with 'Steal' in it. For example, [200, Steal] or [Steal, 10000].