Question 1
1.1 A utility function serves as a means to quantify the perceived numerical worth of a state, be it
a final outcome or an intermediate stage, for a given player. Its primary purpose is to determine
the optimal move that a player can make based on the available options.
1.2 Even without complete information, agents can still achieve the optimal strategy while
playing. This implies that the optimal strategy takes into account the concept of limited
information. However, it is highly probable that an agent with perfect information will outperform
an agent with limited or imperfect information when facing the same problem
1.3 Forward pruning involves discarding certain nodes without even examining them. In contrast,
when using beam search (among other methods), only a subset of the most promising moves is
considered at each level. However, there is a risk that the best move could be discarded during
this process
1.4 Minimax becomes an exhaustive search, considering all possible outcomes, only if pruning is
not employed. In such cases, the specific configuration parameters, such as depth or plys,
dictate the extent of the search, and the order of nodes does not affect the results
Question 2
2.1 A = -7, B = -7, C = -8, D = -7, E = 0,
F = 5, G = -8, H = -3, I = 3
2.2 Move B has a higher utility value for MAX compared to move C.
2.3 A=(-1, ∞), B=(-∞, -7), C=(-7, ∞), D=(-7, ∞), E=(-∞, -7), F=(-∞, -7), G=(-7, ∞)
2.4 The nodes below C, H, and I are pruned in A-cut, and the nodes below F and M are
pruned in B-cut, thus preventing their expansion.
Question 3
3.1 a) Every AI search algorithm incorporates an evaluation function, which has the ability to
provide either a true utility or an expected value as its output. Utility represents an optimal
assessment of the state, offering a quantitative measure of its desirability. Typically, this
evaluation process involves playing the game until reaching a terminal state and then
propagating the utility values back up to the internal nodes. However, when there is a large
number of possible actions from a state and the depth required to reach a terminal state is
significant, this approach becomes impractical. In such cases, an expected utility is
employed, aiming to evaluate a state by considering its features in order to estimate the
utility that can be expected from that state. In many scenarios, the expected utility can simply
be the probability of winning from a specific state.
1.1 A utility function serves as a means to quantify the perceived numerical worth of a state, be it
a final outcome or an intermediate stage, for a given player. Its primary purpose is to determine
the optimal move that a player can make based on the available options.
1.2 Even without complete information, agents can still achieve the optimal strategy while
playing. This implies that the optimal strategy takes into account the concept of limited
information. However, it is highly probable that an agent with perfect information will outperform
an agent with limited or imperfect information when facing the same problem
1.3 Forward pruning involves discarding certain nodes without even examining them. In contrast,
when using beam search (among other methods), only a subset of the most promising moves is
considered at each level. However, there is a risk that the best move could be discarded during
this process
1.4 Minimax becomes an exhaustive search, considering all possible outcomes, only if pruning is
not employed. In such cases, the specific configuration parameters, such as depth or plys,
dictate the extent of the search, and the order of nodes does not affect the results
Question 2
2.1 A = -7, B = -7, C = -8, D = -7, E = 0,
F = 5, G = -8, H = -3, I = 3
2.2 Move B has a higher utility value for MAX compared to move C.
2.3 A=(-1, ∞), B=(-∞, -7), C=(-7, ∞), D=(-7, ∞), E=(-∞, -7), F=(-∞, -7), G=(-7, ∞)
2.4 The nodes below C, H, and I are pruned in A-cut, and the nodes below F and M are
pruned in B-cut, thus preventing their expansion.
Question 3
3.1 a) Every AI search algorithm incorporates an evaluation function, which has the ability to
provide either a true utility or an expected value as its output. Utility represents an optimal
assessment of the state, offering a quantitative measure of its desirability. Typically, this
evaluation process involves playing the game until reaching a terminal state and then
propagating the utility values back up to the internal nodes. However, when there is a large
number of possible actions from a state and the depth required to reach a terminal state is
significant, this approach becomes impractical. In such cases, an expected utility is
employed, aiming to evaluate a state by considering its features in order to estimate the
utility that can be expected from that state. In many scenarios, the expected utility can simply
be the probability of winning from a specific state.
