Do you consider the "throwaway factor" in what the BB might have?

[eastbay]

There's lots of calculations like Sklansky/Karlson (search if you didn't catch that one) that assume that the BB's holdings are random when it is folded to you in the SB.

But they're not completely random. You do know that N people ahead of you have thrown away their hands. I think a reasonable argument can be made that this increases the likelihood that the BB is holding a better than average hand.

Do you folks generally consider this a factor, or do you think the effect is so small as to be not worth considering?

I seem to run into awfully big hands from the BB in this spot and I'm wondering if it's selective memory or if this effect is more important than you might think.

Thoughts?

eastbay

[NotMitch]

By that same logic shouldnt the cards you have in the SB be better that average as well? So does it seem like you get a lot of good hands in this spot?

[DrPhysic]

Eastbay,

I have been giving some thought to the same thing in maybe a little different light. The card distribution is not the same for two people playing after 7 (or 8) folds on a full table as it is for two people playing heads up. You have removed 14 cards from the ones in play. While there may be some Kx or Ax cards that have been removed, one has to assume that you are now playing with a high card enriched deck.

So yes, I think you have to assume that the bb's hand is better than a 2 of 52 random. I tend to think that playing into it is a similar thing to the gap theorey. Granted the BB did not open the hand, but you may need a little better hand to call or raise than you would if you were opening the hand without those 14 cards removed.

I don't think it is a huge factor. Certainly not as much as the gap created if the hand had been opened. But it could influence my thinking about calling or raising with a tossup marginal hand.

Just some musings.

Doc

[DrPhysic]

I think you do mitch. Not much different, but consider this: you can deal 23 holdem hands with a deck. If you are sitting on the small blind and 21 hands just folded in front of you, isn't it a pretty good guess that if those guys don't have the cards to open, that your chances just went up? If that happened, I think I'd open in the dark.

Now it isn't as much of a factor at a 9 hand table, but i do think there is a little truth there. Just a small percentage that your hand will be better than a 2 in 52 random because you now know that the 7 hands in front of you folded.

Of course, my other thought is that Bozeman and company will probably have lots of fun educating me on statistics theorey on this one.

Doc

[eastbay]

[ QUOTE ]
I think you do mitch. Not much different, but consider this: you can deal 23 holdem hands with a deck. If you are sitting on the small blind and 21 hands just folded in front of you, isn't it a pretty good guess that if those guys don't have the cards to open, that your chances just went up? If that happened, I think I'd open in the dark.

Now it isn't as much of a factor at a 9 hand table, but i do think there is a little truth there. Just a small percentage that your hand will be better than a 2 in 52 random because you now know that the 7 hands in front of you folded.

Of course, my other thought is that Bozeman and company will probably have lots of fun educating me on statistics theorey on this one.

Doc

[/ QUOTE ]

With an assumed set of hands that would open, the adjusted odds of each hand after N folds seems calculable. Has anyone tried this? Seems worth considering.

eastbay

[PrayingMantis]

I've posted a question in the teory forum ("stealing and position in NL tourneys"), and tried to bring up this subject, as long as others. I think what you say here is generally a valid point, however, you should probably consider these points too:

A. Tightness of the table. Many players will throw hands like Ax, Kx, etc, from early position. If so, the fact that it was folded to you on the SB, can tell you almost nothing about the amount of high cards "left" in the deck. The tighter the table is, the less it will mean.

B. Suppose it was folded to you (on a looser table), and you assume there are more high cards left. But now, say you have even a strong hand like TT and push. BB calls with A9. IF there are relatively more A's left in the deck, he has a better chance than "usual" to hit an A on the board, to bust your TT. In other words, A high hands might be actually stronger than on "normal" conditions, and there could be some other similar effects.

[Al_Capone_Junior]

[ QUOTE ]
But they're not completely random. You do know that N people ahead of you have thrown away their hands. I think a reasonable argument can be made that this increases the likelihood that the BB is holding a better than average hand.

Do you folks generally consider this a factor, or do you think the effect is so small as to be not worth considering?


[/ QUOTE ]

This effect has been discussed before in MM's discussions of the "bunching factor." It's minimal in hold'em, so there's really little more chance that the BB has a good hand just because others have folded.

al

[CrisBrown]

Hi eastbay,

Yes, if everyone has folded to you in the SB, there is a greater likelihood that the BB has a hand. I don't know how significant it is, but T.J. Cloutier talks about (in a very general way) in CHAMPIONSHIP PL-NO HOLD'EM.

How much that likelihood increases will depend on the character of the table. At a very loose table -- where people will play any A-, K-, or Q-high hand -- it's more likely that the BB will have hand, as would be 12 As-Qs left in a 38-card deck (14 having been mucked). At a tighter table -- where people will muck weak Aces, Kings, and Queens -- the difference isn't so great, and I don't think you're quite as likely to run into a monster.

Still, when everyone has folded ahead of you, it is marginally more likely that someone behind you has a hand.

Cris

[M.B.E.]

If you're playing two-handed and you are first to act, and you do not have an ace in your hand, then the probability your opponent holds at least one ace is 190/1275 = 0.149.

Now if you're playing in a nine-handed game where your opponents will all play any hand with an ace but fold everything else, and it is folded to you in the small blind and you do not have an ace in your hand, then the probability your opponent holds at least one ace is 134/630 = 0.213.

If you use more realistic assumptions then of course the effect is not as significant.