Pot odds for calling a river bet with 4 flush on board

[LockLow34]

Note: while this does involve a specific hand I was in, my question is of a more general nature.

your hand: J/images/graemlins/club.gif T/images/graemlins/spade.gif

board: T/images/graemlins/diamond.gif 3/images/graemlins/diamond.gif 7/images/graemlins/spade.gif A/images/graemlins/diamond.gif J/images/graemlins/diamond.gif

Against a single opponent on the river what pot odds do you need to correctly call a bet from him?

My thinking (feel free to correct me) is that I know where 4 of the diamonds are, so of the 45 remaining unknown cards, 9 of them are diamonds. So it's 4-1 against him having a diamond in his hand. Therefore if the pot is laying me 5-1 a call is correct.

[LetYouDown]

First of all, the size of the bet is incredibly important. Second of all, your opponent has two cards, not one.

You know 7 cards, 4 of which are diamonds. Therefore, there are C(45,2) combinations he can hold. C(36,2) is the number of hands that he can have that don't have a diamond. That comes out to about 36.4% that he has one, or 1.75 to 1. The problem here is that a diamond isn't the only thing that beats you. K-Q, any set, higher two pair.

This is opponent based to a large extent, but 99 times out of 100, I'm folding in that spot to any reasonable bet.

[AaronBrown]

In addition to LetYouDown's excellent reply, I'd add that you have important clues from the betting. He stayed in the first round, then stayed in for a flop that probably didn't help him. Okay, he could have had two diamonds or an 8 9 (either of which will beat you); but more likely he held two high cards, or an Ace and another card that paired on the board, or a pair or suited high cards or connectors. His betting pattern should tell you a lot about the relative probabilities.

Think of all those hands that beat you: KQ, A with J, 10, 3 or 7; JJ, 10 10 (okay, both of those are unlikely), 7 7, 3 3, any hand with a diamond. About the only likely hands that don't beat you are A K, A Q and K J, and none of these are likely to be bet on the river as this hand was.

I would need a good reason to stay in this pot, extraordinary pot odds or a strong indication that he's betting on a pair of Aces and nothing else. It's hard to see any hand you could beat, other than a pure bluff.

[uuDevil]

[ QUOTE ]
Against a single opponent on the river what pot odds do you need to correctly call a bet from him?

[/ QUOTE ]

If you were first to act, maybe you should have bet. (Do a search for "Clarkmeister Theorem" or see this thread (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=2560271&page=0&view=colla psed&sb=5&o=7&fpart=1&vc=1) for example.) If you checked, you may have induced a bluff, so it depends on how your opponent plays. If he ALWAYS bets, then LetYouDown is right and you need pot odds of > 1.75:1.

LetYouDown said:

[ QUOTE ]

This is opponent based to a large extent, but 99 times out of 100, I'm folding in that spot to any reasonable bet.

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However, I'm not so sure about this. Against a player who may bluff or bet a hand I can beat, I'm calling most of the time. To get a number requires solving an EV equation:

P(my hand is best)*Potsize+(1-P(my hand is best))*(-amt of bet I must call)=0

So I have to estimate P(my hand is best) in order to solve for Potsize. If I think my opponent will bet 20% of the time without a diamond and MHIG that same percentage, P(my hand is best)=.2 and I must call 1 BB, then Potsize= 4 BB. To fold very often in a bigger pot, you have to be VERY sure of your opponent, and I don't think you can be that sure of most poker player's tendencies.

[LetYouDown]

I'll admit that 99/100 was a bit of a stretch. If you're up against a complete LAG or know your opponent reasonably well and think he's very capable of a bluff there, it might be worth calling. I was just saying that the only hands you really beat are complete bluffs...and as likely as that board is to be bluffed at, he could be bluffing with the better hand.

[shutupndeal]

I agree with almost everythin said here but the main thing in my play is to keep it up fron that its all one big game which means that yes given the correct pot odds I am calling, I may not like it but Im going to do it, without them Im gonna cry and moan about my rotten luck and how the world hates me and then click fold with my usual deftness!