There are several high-earning crypto games that allow you to participate and earn rewards without needing an initial investment. These games typically operate on the play-to-earn (P2E) model, where players can earn cryptocurrency or non-fungible tokens (NFTs) by participating in gameplay or completing tasks. However, while these games may not require a direct financial investment, they often involve time, effort, and sometimes a learning curve. Here are some of the top high-earning crypto games that require zero investment:

1. Splinterlands
How It Works: Splinterlands is a collectible card game where players battle using cards representing different creatures. You can earn Dark Energy Crystals (DEC), the game's native token, by winning battles. These tokens can be traded for other cryptocurrencies.

Earning Potential: You can earn DEC tokens through battles, quests, and tournaments. Players can also sell cards or participate in the game's marketplace.

Zero Investment Opportunity: The game offers a free starter deck to new players, allowing them to start earning without any upfront costs.

2. Gods Unchained
How It Works: Gods Unchained is a blockchain-based card game similar to Hearthstone. Players earn cards by competing in matches, and cards can be traded or sold on the marketplace.

Earning Potential: Players can earn $GODS (the game's token) and NFTs, which can be sold or traded for profit.

Zero Investment Opportunity: Gods Unchained offers a free starter pack for new players, allowing them to start without an initial financial commitment.

3. Axie Infinity (Free-to-Play Version)
How It Works: Axie Infinity is one of the most popular play-to-earn games, where players breed, collect, and battle creatures called Axies. The in-game currency, Smooth Love Potion (SLP), can be earned by battling and completing quests.

Earning Potential: Axie Infinity's ecosystem is built around earning and selling NFTs, such as Axies and land, along with SLP tokens.

Zero Investment Opportunity: Although Axie Infinity traditionally requires an upfront investment for buying Axies, there are scholarship programs that allow you to play without purchasing the creatures upfront. Some players lend their Axies to others in exchange for a percentage of the profits earned.

4. The Sandbox (Free Land & Play-to-Earn Opportunities)
How It Works: The Sandbox is a virtual world where users can create, own, and trade virtual assets using NFTs. It's a massive multiplayer online world that allows players to create experiences, games, and virtual land, which can then be monetized.

Earning Potential: Players can earn SAND tokens (the native cryptocurrency) by creating assets, land, or experiences and selling them in the game's marketplace.

Zero Investment Opportunity: The Sandbox allows users to participate in its free land giveaways or take part in user-generated experiences that reward players with SAND tokens for specific activities or competitions.

5. Alien Worlds
How It Works: Alien Worlds is a decentralized metaverse where players mine resources on different planets. You can stake your assets, battle, and explore in this game, earning the game's native tokens, such as Trilium (TLM).

Earning Potential: By mining or staking assets, you earn TLM, which can be traded or used in the game for further rewards. Players can also earn NFTs.

Zero Investment Opportunity: Alien Worlds offers a free mining option that allows players to participate without spending money upfront. Players earn TLM simply by staking NFTs and performing in-game tasks.

6. Lost Relics
How It Works: Lost Relics is an action-adventure game where players explore dungeons, fight monsters, and collect loot. The game operates with blockchain technology, meaning that rare items and weapons can be tokenized as NFTs.

Earning Potential: Players can earn NFTs by defeating enemies and completing quests. These NFTs can be sold in the marketplace for real money or traded for other cryptocurrencies.

Zero Investment Opportunity: Lost Relics allows players to play for free and earn NFTs through gameplay. Some items found in the game can be very valuable if you are lucky enough to discover rare drops.

7. My DeFi Pet
How It Works: My DeFi Pet combines pet raising, battle mechanics, and DeFi features. Players collect and raise pets, which can be used in battles or traded in the game's marketplace.

Earning Potential: You can earn DPET tokens (the native token) by completing quests, raising pets, and battling.

Zero Investment Opportunity: My DeFi Pet offers free-to-play options where you can earn in-game tokens without the need to buy pets upfront. Players can start earning by participating in battles and events.

8. Zed Run
How It Works: Zed Run is a digital horse racing game that uses blockchain technology to allow players to buy, breed, and race virtual horses. The game allows players to earn through betting on races or by breeding and selling horses.

Earning Potential: Players can earn ETH (Ethereum) by winning races or selling high-performance horses in the marketplace.

Zero Investment Opportunity: Zed Run offers a free starter horse, which allows new players to begin racing and earning without any upfront investment.

9. CryptoKitties
How It Works: CryptoKitties is one of the first blockchain-based games where players breed, collect, and trade virtual cats. These cats are NFTs and can be bought or sold in the game's marketplace.

Earning Potential: Players can earn cryptocurrency by breeding rare CryptoKitties and selling them on the marketplace.

Zero Investment Opportunity: While CryptoKitties usually requires buying cats to start breeding, the game occasionally offers free giveaways or promotions where players can earn NFTs without investing money.

10. TownStar
How It Works: TownStar is a city-building game where players can create and manage their own towns. Players earn TOWN tokens by completing challenges and building efficient towns.

Earning Potential: Players can earn tokens based on the performance of their towns in various competitions and events.

Zero Investment Opportunity: TownStar offers a free-to-play version, where players can participate in weekly competitions and earn rewards without having to spend money.

Conclusion
While many crypto games require an initial investment for full participation, there are several opportunities to play and earn rewards without spending any money upfront. The games mentioned above offer free-to-play options or give out starter packs, NFTs, or other rewards for consistent gameplay and participation. Although these games offer an entry point without financial investment, time and effort are often required to earn substantial rewards. Always ensure you read the terms and conditions of each game to understand how you can earn without breaking any rules.