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#1
12-28-2006, 05:27 PM
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4 spades on the river
On the river there are 4 spades on the board. I have 2 opponents. If neither of them have a spade I have the nuts.
What is the percentage that neither of them have a spade. Assume we were all in before the flop. 
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#3
12-28-2006, 07:30 PM
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Re: 4 spades on the river
[ QUOTE ]
There are 9 spades remaining among 46 unknown cards . 1-37C4/46c4=59.5% There is a 59.5% that at least one of them has a spade . [/ QUOTE ] There are 45 unknown cards on the river, and this makes 60.5%, but only if he doesn't hold a spade himself. If he holds 1 spade, the probability that one of his opponents holds a spade is 1 - C(37,4)/C(45,4) =~ 55.7% and if he holds 2 spades, it is 1 - C(38,4)/C(45,4) =~ 50.5%. Of course, he can still win some of these if he has the highest spade. These assume that all hands are equally likely. The calculation should really be done over the range of possible hands with which the opponents would go all in.
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#4
12-28-2006, 08:01 PM
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Re: 4 spades on the river
Op addressed that he doesn't hold a spade in his hand since he would have the nuts if they don't hold a spade .
Actually it is a little less likely that your opponents would hold two spades since they would likely restrict their calling range which means more medium and higher pocket pairs are being played .
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#5
12-28-2006, 08:17 PM
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Re: 4 spades on the river
[ QUOTE ]
Op addressed that he doesn't hold a spade in his hand since <font color="red">he would have the nuts if they don't hold a spade</font> . [/ QUOTE ] The premise in red in no way implies that he does not hold a spade.
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#6
12-29-2006, 07:00 PM
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Re: 4 spades on the river
[ QUOTE ]
[ QUOTE ] Op addressed that he doesn't hold a spade in his hand since <font color="red">he would have the nuts if they don't hold a spade</font> . [/ QUOTE ] The premise in red in no way implies that he does not hold a spade. [/ QUOTE ] That may be true, but "On the river there are 4 spades on the board. I have 2 opponents. If neither of them have a spade I have the nuts." sure is an odd way of saying he has the 2 of spades. Sounds more like he has the best possible hand below a flush.
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#7
12-29-2006, 07:48 PM
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Re: 4 spades on the river
That's most likely what OP meant ... but it makes sense to report all 3 numbers, since we don't know for sure if a) he has a strong non-flush hand, b) one small flush card, or c) something like 65s that was boss on the turn but might have been counterfeited.
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#8
12-29-2006, 08:20 PM
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Re: 4 spades on the river
I'm guessing the back story here, is he pushed all in with AKs (clubs) and flopped the nut straight JcQsTs, turned a 5s, and rivered the 3s, and got beat AGAIN by some yahoo that called with K6o (6 of spades)...
He came here to validate his feeling that he is the unluckiest person on the face of the earth. While I feel his pain, I no longer think I am the unluckiest person. It's clear that GREEN GAMBLER is [img]/images/graemlins/smile.gif[/img]
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