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A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly.This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance.
Here there are two variables a and b but one equation. The solution is constrained by the fact that a and b can take only values 0 or 1. There is only one solution here, both a = 0, and b = 0. Another simple example is given below: a + b = 2. The solution is straightforward: a and b must be 1 to make a + b equal to 2. Another interesting case ...
The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player switch from door 1 to door 2. The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall.
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The game can be represented by an undirected graph, the nodes representing distributions of disks and the edges representing moves. For one disk, the graph is a triangle: The graph for two disks is three triangles connected to form the corners of a larger triangle. A second letter is added to represent the larger disk.
Subgames that would not be chosen by Player 2 in the previous step are no longer considered because they are ruled out by the assumption of rational play. For example, in the first subgame, the choice "go to movie" offers a payoff of 9 since the decision tree terminates at the reward (9, 11), considering Player 2's previously established choice.
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