I probably ripped off the name of a real paradox.

Discussing a hand with Aseem; made me think about an approach one may take while deciding whether or not to call the flop.

Lets say you have QJ Hearts in EP and limp in.
MP3 (a TAG) raises, SB calls, and you call.

Flop comes 8,6,2 1 Heart (7 SB)
SB check, You check, Mp3 bet, SB Fold, You ?

Well, if you're bdfd catching lucky me, you call.
Aseem says, easy fold. I think I agreee now; but the following logic confused me.
Find the flaw.

Aseem and I both agreed that if we did call the flop, we would call the turn bet if it came Q/J/Heart
So we agreed it's +EV to call the turn in those cases. I will assume Aseem would call the river UI in the case of hittng a Q/J on the turn and fold the river UI if we get a heart.
Without much thought about the chances of Q's or J's winnning, we just know we are calling a turn bet if we get one.

So we have 10 hearts and 6 Q/J's for a total of 16 cards that will "let us" see the river.

We are getting 8:1. With 16 "outs" to see the river
We'll be geting 5:1 calling the turn; if we hit one of our cards.


Why is this not an easy flop call?

poor effective odds

(i'm a party pooper, but i just got done writing a problem set for intro econ)

Damn paradox. I don't feel like thinking, so I'll just work out the flop.

1.5 outs for a bd flush. 1 out for Q and J (2.5 total at most). 3.5 outs total.

Fold. You will hit your queen and jack too often and still lose.

Edited.

wow..the overs are that dirty?

Oops.

I meant one for each card.

I think they are dirty against villians range. Too many AA-JJ/AQ/AJ/KQ/KJ type hands. Plus, if you hit one of your cards on the turn, you could get outdrawn by any A/K on the river.

I think the main problem is effective odds as tim said. You are giving yourself 10 good flush cards on the flop, then another 9 good flush cards on the turn. Unlike the queens or jacks, you have to hit these good cards runner-runner.

Another way to look at it would be in terms of how much money you put in depending on what hits:

(10/47) x (9/46) = 4.16% --> BD FLUSH

(6/47) + (10/47) x (6/46) = 15.54% --> PAIR

TOTAL WIN = 11.93%

We use (10/47) instead of (44/47) because you will only continue to hit your pair if you hit a flush on the turn.

(10/47) x (32/46) = 14.80% --> MISS RIVER

(31/47) = 65.96% --> MISS TURN


Now let's calculate the EV assuming you will hit your pair and still lose 50% of the time:

7.77% x (+6BB) + 7.77% x (-2.5BB) + 14.80% x (-1.5BB) + 65.96% x (-0.5BB) =
-0.28BB


Or to look at it another way, you would have to think you would win 71% of the time if you spiked a pair for the EV of calling = 0.

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couldn't resist?

Ya, you guys are too smart to be tricked up.
I wanted people to look first at the turn..and say "If I hit one of these 16 cards..Q/J or Heart...I'd call a bet to see the river...."

"So, since it's 16 outs to see the river, and the pot is laying 8:1 on the flop...I can call profitably"


This completely overlooks conditional probability
And the 8:1 pot odds to catch 1 of 16 cards is not a relevant comparison..at ALL - or extremely misleading at best.

Ever here the one where a man was thrown into the dungeon on Saturday Night and was told he would be executed next Week (Sun-Sat). But that it would be a surprise, as far as which day. The man thought for a bit and said

"No, It won't be. for you can not wait unitl Saturday because I will know that that is the day I'm to be killed. Thus Saturday is out. Therefore yuo must kill me Sun-Friday. But hence, you cannot wait until Friday for once again that would not be a surprise. So you can't kill me on Friday....Thus you must kill me between Sun-Thurs.. and so on. Until So you have to kill me Sun or Mon. but you can't wait until Mon because there's no suprise anymore. Thus U have to kill me tomorrow, Sunday. And as you can clearly see, I'm not suprised." They let him go.

So back to poker. It's sorta analogous to saying: If I were to hit 1 more heart on the turn, I'd call a turn bet. Because I'd be getting 4.5:1 immediate odds. Given that hitting a Heart makes calling the Turn bet profitable ( +EV), then calling the flop getting 8:1 to hit one of 9 ( or 16) outs is correct....and so forth.

I'm afraid I might've let this logic slip into my decisions when I'm feelnig particualrly fishy! I know SSHE says sometimes you can make a loose flop call; but w/o the book in front of me I can't think of the circumstances (not this one, likely.)