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Old 07-03-2005, 11:35 PM
capybara capybara is offline
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Default An approximate method for determining the favorite

Sklansky's second paragraph should be enough to give careful readers a hint that 7632 is the favorite. The error in the "common sense" reasoning is the swift conclusion that 5432 is the favorite.

To recap, the reasoning is as follows: there are three cases where 7632 almost always loses: (a) catching a 7 (b) catching a 6 (c) catching the same card as 5432.

There are three cases where 5432 almost always loses: (A) catching a 5 (B) catching a 4 (C) catching a 6

Intuitively, (a) and (A) should roughly cancel, as (b) and (B). But (c) and (C) are not similar events.

The chance of catching a 6 is 3/44, while the chance of getting the same card is about (28/44)x(3/44), since this event is only likely/relevant if the card is one of AKQJT98.

Thus, (C) is more likely than (c) so 5432 should be an underdog.
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