Again, this question is usually impossible to answer exactly, but because any strategy’s win rate is a lower bound for the optimal win rate, we can develop intuition about the answer by analyzing the win rate of players. We can go even further, and refine our answer to question 1, by asking how often a perfect player is expected to win. “Can a perfect player win every game?” No.To summarize, for Minesweeper, the answer to our two questions would be: Therefore, each seed is winnable by simply learning which squares do not contain mines. For Minesweeper, this means all the mines are in the same location each time you play a seed. Now, I’ve used the word seed twice, but what does it mean? In a computer game with randomness, a seed is a sequence of letters or numbers which determines all of the randomness in a playthrough. Because such positions are guaranteed to arise in some seeds, not every game of Minesweeper can be won, even following an optimal strategy. For example, in the Minesweeper game below, the two remaining mines can either be in the squares marked “A” or the squares marked “B”, and a guess must be made. However, even without knowing how to play perfectly, we can still prove that a perfect player cannot win every game. Despite having simple rules, perfect play is still very difficult to achieve. Minesweeper is a puzzle game where the objective is to find the hidden locations of mines, using the number of surrounding mines as clues. As an example for how to answer these types of questions, however, we may look at another game with heavy randomness: Minesweeper. However, in many respects, it is the more useful question to a player looking to maximize their own win rate, as it shows how close they are to playing optimally. Generally, there is no computationally feasible way to actually play optimally, so this question is very difficult to answer. The first question concerns the performance of a player that makes the theoretically optimal decisions at every point in the game to maximize its win rate, given the information available.
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