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Old 02-04-2005, 08:38 PM
maurile maurile is offline
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Join Date: Mar 2003
Posts: 95
Default Re: basic triple draw probability questions

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2. I am heads up on the last draw and draw one card and pair up for a final holding of 22357. my opponent drew one card as well and bets 4 dollars into me. basically i can only beat a bluff. how big must the pot be for me to correctly call?

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It depends on your opponent's bluffing frequency. If he never bluffs, you should call 0% of the time. [img]/images/graemlins/wink.gif[/img]

If he draws one card, his chance of pairing up is about 25%.

If he bluffs every time he pairs up on the end (and value bets every time he doesn't), that makes you a 3-1 dog to be ahead whenever he bets (assuming your pair of twos will beat any pair he has). So the pot would only have to be $12 for you to call.

If he bluffs half the time on the end after pairing, that means you can beat him 12.5/(75+12.5) = 14% of the time that he bets, making you a 6-1 dog. So you'd need the pot to be $24 in order to call.

If he bluffs 10% of the time that he pairs up on the end, that means you can beat him 2.5/77.5 = 3.2% of the time that he bets, making you a 30-1 dog. So the pot would have to have $120 in it before you should call.

(These figures naively assume that your opponent would value bet every time he doesn't pair up on the end. If he'd value bet a lesser fraction of the time -- say, only when he draws a jack or better -- the pot doesn't have to be as big to call.)
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