Ocean Zero

aka "Guess 2/3 of the average" on blockchain.

Ocean Zero is a game that explores how a player’s strategic reasoning process takes into account the mental process of others in the game.

Ocean Zero is a game in which participants choose an Ocean numbered between 0 and 10 (inclusive), with the goal of guessing as close to 2/3 the average as possible.

Example:

Player 1	Ocean 2
Player 2	Ocean 9
Player 3	Ocean 6
Player 4	Ocean 3
Average	(2+9+6+3) / 4 = 5
2/3 average	5 * 2/3 = 3.33
Winning Ocean	3 (rounded from 3.33)
Winner	Player 4

Ocean Zero is truly a game where players have to think about what other players are thinking about what other players are thinking about...

Level-K Thinking

K stands for the number of times a cycle of reasoning is repeated.

A player playing at k-level 0 doesn't even understand the rules, might even pick Ocean 10 (even though Oceans 8, 9 and 10 can NEVER win).

A person playing at k-level 1 would assume that every other player is level-0. In their logic, level-0 players will be picking random numbers, resulting in the average of 5. So level-1 players will pick Ocean 3 (rounded 2/3 of 5).

A player playing at k-level 2 would assume that everyone else was playing at k-level 1, resulting in the average of 3. Thus, level-2 players will pick Ocean 2 (rounded 2/3 of 3).

Players' Level	Think others will pick	So they pick	Notes
Level-0	Incapable of thinking	Random number	A Level-0 player is literary a zero IQ degen choosing a random shiny number from 0 to 10. Most likely hasn't ever saved their seed phrase.
Level-1	Random number	3	Level-1 players would assume that every other player is level-0, so they would guess the average to be around 5, leading them to choose 3 as their number.
Level-2	3	2	A Level-2 player would assume that every other player is level-1, who would choose 3. So they choose 2 as their number.
Level-3	2	1	A Level-3 player would assume that every other player is level-2, who would choose 2. So they choose 1 as their number.
Level-4	0-1	0	Level-4 players expect all other participants to be rational and pick 0, leading them to pick 0 as well.

TEETH fees/payouts

To enter the Ocean Zero game, players pay a fee in $TEETH. The fee amount is calculated based on the size of the sharks entering the game (the bigger the shark, the more TEETH its owner needs to pay).

The winner(s) gets all the fees + 50,000 TEETH bonus from the Ecosystem fund.

If there are multiple winning Sharks, the payouts are divided based on their sizes (the bigger the shark, the bigger the TEETH payout). That's why you need to max-lock your Shark if you want to earn more TEETH.

Example:

Shark	Shark Size	% of TEETH
Shark 1	10T	10%
Shark 2	40T	40%
Shark 3	50T	50%

Duration, Commit-and-Reveal scheme

An epoch lasts 7 days (Monday 00:00:00 UTC - Sunday 23:59:59 UTC).

There are two steps players need to do in order to play:

1. From Monday through Friday players commit their picks to the blockchain.

2. On Saturday and Sunday players reveal their picks to the blockchain.

This scheme is known as commit-and-reveal. Why is it needed? Since all data on blockchain is public, without this scheme people would be able cheat by watching the blockchain and being able to see which Oceans other players are picking and then adjusting their own picks.

With this scheme, what happens is Monday-Friday players save encrypted picks on the blockchain (no way to see which player picked which ocean), Saturday-Sunday people decrypt their picks (now its possible to see the picks but its impossible to cheat because the commit period is over).