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Title / Subject - or probabilities are hard
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<blockquote data-quote="Ovinomancer" data-source="post: 7270176" data-attributes="member: 16814"><p>The paladin is playing a different game, though. Essentially, the paladin (our the die) is overweighting the chance that the first pick is correct and underweighting the others as potentially correct.</p><p></p><p>This is clearer in the extreme example. If there are 10 picks, you have a 1:10 chance initially. That's a 9:10 chance of being wrong. If, of the unpicked 9, I reveal 8 that are wrong and offer you the chance to switch, you have a 90% chance that the switch will be correct compared to 10% for your initial. The paladin walks by and naively picks between 2 available choices, 50/50. He overweights the initial pick too much and underweights the switch pick by too much, but, for his information, this is the best he can do.</p><p></p><p>The Monte problem hinges on the fact that the offer to switch is no longer made under niave conditions. Substituting a new naive choice, even though more constrained, does not accurately reflect the probabities. Even in the original, the d3 roll overestimates the probability of the first pick being correct (1:4 to 1:3), and underestimates the switch pick (3:8 to 1:3). The difference in the switch is slight, which is where some of the confusion can set in. Few look at the change in probabilities of the first pick as relevant, but they very much are.</p></blockquote><p></p>
[QUOTE="Ovinomancer, post: 7270176, member: 16814"] The paladin is playing a different game, though. Essentially, the paladin (our the die) is overweighting the chance that the first pick is correct and underweighting the others as potentially correct. This is clearer in the extreme example. If there are 10 picks, you have a 1:10 chance initially. That's a 9:10 chance of being wrong. If, of the unpicked 9, I reveal 8 that are wrong and offer you the chance to switch, you have a 90% chance that the switch will be correct compared to 10% for your initial. The paladin walks by and naively picks between 2 available choices, 50/50. He overweights the initial pick too much and underweights the switch pick by too much, but, for his information, this is the best he can do. The Monte problem hinges on the fact that the offer to switch is no longer made under niave conditions. Substituting a new naive choice, even though more constrained, does not accurately reflect the probabities. Even in the original, the d3 roll overestimates the probability of the first pick being correct (1:4 to 1:3), and underestimates the switch pick (3:8 to 1:3). The difference in the switch is slight, which is where some of the confusion can set in. Few look at the change in probabilities of the first pick as relevant, but they very much are. [/QUOTE]
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