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They consider a scenario where the host chooses between revealing two goats with a preference expressed as a probability q, having a value between 0 and 1. If the host picks randomly q would be 1 / 2 and switching wins with probability 2 / 3 regardless of which door the host opens.
Odds and evens is a simple game of chance and hand game, involving two people simultaneously revealing a number of fingers and winning or losing depending on whether they are odd or even, or alternatively involving one person picking up coins or other small objects and hiding them in their closed hand, while another player guesses whether they have an odd or even number.
Two-alternative forced choice (2AFC) is a method for measuring the sensitivity of a person or animal to some particular sensory input, stimulus, through that observer's pattern of choices and response times to two versions of the sensory input. For example, to determine a person's sensitivity to dim light, the observer would be presented with a ...
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Sequential game: A game is sequential if one player performs their actions after another player; otherwise, the game is a simultaneous move game. Perfect information : A game has perfect information if it is a sequential game and every player knows the strategies chosen by the players who preceded them.
One of the two men can reason: "I have the amount A in my wallet. That's the maximum that I could lose. If I win (probability 0.5), the amount that I'll have in my possession at the end of the game will be more than 2A. Therefore the game is favourable to me." The other man can reason in exactly the same way. In fact, by symmetry, the game is fair.
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or "One, two, three, shoot!"). On "shoot", both players hold out either one or two fingers. If the sum of fingers shown by both players is an even number (i.e. two or four) then the "evens" player wins; otherwise the "odds" player is the winner. Since there are two possible ways to add up to three, both players have an equal chance of winning.