SURVIVE: THE A.I. is a digital collectible card game where games and mathematics intersect, offering a unique blend of strategic gameplay and mathematical optimization. Set in a post-apocalyptic world ruled by AI, players must use mathematical thinking to manage resources, calculate probabilities, and optimize card combinations to achieve victory. In this game, the core mechanics revolve around resource management. Players earn resources such as Compute, Energy, and Creativity by controlling locations on the board. These resources are generated mathematically based on the player's control of specific areas, requiring careful planning and optimization. For example, each location generates one resource per turn, and controlling multiple locations can exponentially increase resource production. This mathematical model ensures that players must strategically prioritize which locations to capture and maintain. The card system also relies heavily on mathematical principles. Each card has a specific mana cost, and players must calculate their mana pool to determine which cards they can play each turn. The mana pool increases by one point each turn, adding a layer of mathematical progression to the gameplay. Additionally, some cards possess unique abilities that trigger mathematical effects, such as doubling resource production or modifying the mana cost of subsequent cards. Deck building is another aspect where games and mathematics converge. Players can gather cards from humans, AI, and hybrids, and build their team with different Archetype strategies. For instance, the "Copy Field" archetype gives all cards +1 power, creating a mathematical advantage as the player's deck grows stronger with each card played. Similarly, the "AI Race Power" archetype rewards players for playing multiple AI tribe cards, with the team's power increasing exponentially as more AI cards are deployed. The game also features a Resource System that requires players to mathematically balance their resource generation and consumption. For example, activating a card's Awakening ability consumes a specific amount of resources, and players must calculate whether the benefit of activating the ability outweighs the cost. This balance of resource management and mathematical optimization is a key component of the game's strategic depth. Moreover, the game's PVP mode introduces competitive elements where players must mathematically analyze their opponents' strategies and adapt their own deck to counter them. Each victory in PVP mode rewards players with Gems and Card Shards, which can be used to enhance their deck. The Rank System further adds a layer of mathematical progression, as players climb ranks based on their win-loss ratios and total points earned. In the PVE mode, players must use mathematical reasoning to counter the mechanics of each boss. For example, when facing AI opponents, players may opt to use energy-heavy HAI cards to maximize damage output. This requires calculating the optimal card combinations and resource allocations to ensure victory. The game's timeline also reflects the intersection of games and mathematics. From the birth of the first AI Superintelligence in 2045 to the global war in 2053, the progression of events is driven by mathematical certainties and strategic calculations. Players must piece together the dark secrets of the Zero Event and Irene Nova's disappearance while navigating a world governed by logical systems and mathematical probabilities. In summary, SURVIVE: THE A.I. is a game where games and mathematics are deeply intertwined. Players must use mathematical thinking to manage resources, optimize card combinations, and outwit opponents in a world ruled by AI. Whether it's the strategic calculation of resource allocation or the mathematical optimization of deck building, this game offers a unique experience for fans of both games and mathematics.