The statement "It can potentially lead to suboptimal solutions compared to mini-max search without any pruning" is false. Alpha-beta pruning does not affect the outcome of the mini-max search algorithm. It only reduces the number of nodes that the algorithm needs to evaluate, thus making it more efficient. The final decision of the mini-max algorithm remains the same with or without alpha-beta pruning.

The statement "It is guaranteed to improve the running time in-comparison to the mini-max search without any pruning" is also false. While alpha-beta pruning can significantly improve the efficiency of the mini-max algorithm in many cases, it is not guaranteed to do so in all cases. The efficiency gain depends on the order in which nodes are evaluated. In the worst-case scenario, where nodes are evaluated in the least favorable order, alpha-beta pruning does not provide any efficiency gain.

The statement "The order in which nodes are visited affects the amount of pruning" is true. The efficiency of alpha-beta pruning depends on the order in which nodes are evaluated. If the nodes are evaluated in the most favorable order, alpha-beta pruning can cut down the number of nodes to be evaluated to the square root of the total number of nodes.

The statement "If the successors of a node are chosen randomly, the time complexity (on average) is O(b3m/4)" is false. The average time complexity of the mini-max algorithm with alpha-beta pruning, when successors of a node are chosen randomly, is O(b^(m/2)), where b is the branching factor and m is the maximum depth of the tree.

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The statement "It can potentially lead to suboptimal solutions compared to mini-max search without any pruning" is false. Alpha-beta pruning does not affect the outcome of the mini-max search algorithm. It only reduces the number of nodes that the algorithm needs to evaluate, thus making it more efficient. The final decision of the mini-max algorithm remains the same with or without alpha-beta pruning.

The statement "It is guaranteed to improve the running time in-comparison to the mini-max search without any pruning" is also false. While alpha-beta pruning can significantly improve the efficiency of the mini-max algorithm in many cases, it is not guaranteed to do so in all cases. The efficiency gain depends on the order in which nodes are evaluated. In the worst-case scenario, where nodes are evaluated in the least favorable order, alpha-beta pruning does not provide any efficiency gain.

The statement "The order in which nodes are visited affects the amount of pruning" is true. The efficiency of alpha-beta pruning depends on the order in which nodes are evaluated. If the nodes are evaluated in the most favorable order, alpha-beta pruning can cut down the number of nodes to be evaluated to the square root of the total number of nodes.

The statement "If the successors of a node are chosen randomly, the time complexity (on average) is O(b3m/4)" is false. The average time complexity of the mini-max algorithm with alpha-beta pruning, when successors of a node are chosen randomly, is O(b^(m/2)), where b is the branching factor and m is the maximum depth of the tree.

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The statement "It can potentially lead to suboptimal solutions compared to mini-max search without any pruning" is false. Alpha-beta pruning does not affect the outcome of the mini-max search algorithm. It only reduces the number of nodes that the algorithm needs to evaluate, thus making it more efficient. The final decision of the mini-max algorithm remains the same with or without alpha-beta pruning.

The statement "It is guaranteed to improve the running time in-comparison to the mini-max search without any pruning" is also false. While alpha-beta pruning can significantly improve the efficiency of the mini-max algorithm in many cases, it is not guaranteed to do so in all cases. The efficiency gain depends on the order in which nodes are evaluated. In the worst-case scenario, where nodes are evaluated in the least favorable order, alpha-beta pruning does not provide any efficiency gain.

The statement "The order in which nodes are visited affects the amount of pruning" is true. The efficiency of alpha-beta pruning depends on the order in which nodes are evaluated. If the nodes are evaluated in the most favorable order, alpha-beta pruning can cut down the number of nodes to be evaluated to the square root of the total number of nodes.

The statement "If the successors of a node are chosen randomly, the time complexity (on average) is O(b3m/4)" is false. The average time complexity of the mini-max algorithm with alpha-beta pruning, when successors of a node are chosen randomly, is O(b^(m/2)), where b is the branching factor and m is the maximum depth of the tree.

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