Any Two Cards

[Antinomy]

Does anyone know how big the pot odds have to be before one should be willing to call before the flop in hold 'em with any two cards and pray for a miracle? I did some figuring on the back of an envelope, and got 26 to 1. That struck me as a little high.

If this is a perennial question, forgive me.

[meow_meow]

I don't really understand, but what you seem to be asking is "when is it ok to call with complete garbage preflop?".
I guess if you were in SB in a full ring game and everyone limped around to you, you might be close to even completing with a garbage hand, but otherwise...

[mrjim]

In a "rack attack" situation where the house puts an extra $100 in the pot any two are probably good.

[Kurn, son of Mogh]

In a 15/60 game with a 10/15 blind structure, it's almost never correct to fold the SB in an unraised multi-way pot.

Say 3 limpers to you and a passive player in the BB, you're getting 14-1 to call. Pretty hard to fold.

[Antinomy]

I was just figuring it as a theoretical problem. I used 72o as the worst possible hand and defined a miracle to be the following flops:

7 2 X (3/50)(3/49)(44/48) = .003367
7 X 2 (3/50)(44/49)(3/48) = .003367
X 7 2 (44/50)(3/49)(3/48) = .003367
X 2 7 (44/50)(3/49)(3/48) = .003367
2 X 7 (3/50)(44/49)(3/48) = .003367
2 7 X (3/50)(3/49)(44/48) = .003367
7 7 X (3/50)(2/49)(44/48) = .002245
7 X 7 (3/50)(44/49)(2/48) = .002245
X 7 7 (44/50)(3/49)(2/48) = .002245
2 2 X (3/50)(2/49)(44/48) = .002245
2 X 2 (3/50)(44/49)(2/48) = .002245
X 2 2 (44/50)(3/49)(2/48) = .002245
7 7 7 (3/50)(2/49)(1/48) = .000051
2 2 3 (3/50)(2/49)(1/48) = .000051

Add up all the probabilities to get .033776.

Change it to odds: (1 - .033776)/(.033776) = 28.6 to 1 (I made an error last night.)

That assumes I haven't made a conceptual or mathematical mistake. It doesn't count flopping three suited cards that match one in your hand, because with that many people in the pot, you will probably loose to a higher flush if it comes in. I also neglected flopping a straight draw.

I'm not taking into consideration any implied odds, and I should be.