Quote:
Originally Posted by just_grindin
Not exactly. Again the villain only risks 1 unit with his bluffs. His other hands aren't risking they are valuebetting. So the balance is defending enough to prevent villain's bluffs from profiting while not paying off villain's valuebets too often. It's why in the AKQ game the K only defends 50% of the time. It just happens to be the results based on the relative frequency the A/Q bettor shows up with value and air.
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ok i just read the AKQ game section. but the upshot is that the caller defends with 1/3 of his Kings to a 1/2 pot bet.
"Similar reasoning works for X. He wants to call often enough that the opponent is indifferent to
bluffing with his queens. When his opponent bluffs successfully, he wins two bets, while
bluffing unsuccessfully costs just one bet. So X must call twice as often as he folds in order to
make the bluffer indifferent. This fraction is 2/3 (leaving 1/3
of hands to fold). But half of the
time that the opponent is bluffing, X will hold an ace. So he needs to call with an additional
fraction of his hands equal to 2/3 - 1/2, or 1/6 . Since kings make up 1/2
of his hands when the opponent has a queen, he needs to call with 2/6 or 1/3
of kings. " (pg 142, P2)
according to my math, player X should never call with a King to a pot size bet. (he can just call with his Aces and never get exploited).
similarly, if faced with a 10x pot sized bet (or a 1000x pot sized bet), player X should only call with Aces.
SO u dont just call with 1/2 your bluff catchers! you use MDF to find out how much u have to call, then U take: MDF - (% of range is aces) = Z. Then if Z>0 you add Z bluff catchers so that u reach the MDF!