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Siegmund
05-04-2005, 10:01 PM
I posted last Friday some simulation results about what hands the BB holds when the whole table folds around to him.

As a followup to that, I repeated the experiment for each seat at the table, to see how the effect grows progressively stronger as more and more people have folded ahead of you.

Couldn't figure out how to make the forum display fixed-width columns for a table, so a full summary is on my website at http://taigabridge.com/poker/bunching_effect.txt

The executive summary is that the effect is measurable even in UTG+1, but pretty tiny until you look at CO-vs-button and button-vs-SB.

To give a for-instance, suppose we define as "premium hands" 88+, suited broadway, and AK/AK/AQ/AJ (130/1326~9.8% of starting hands.) If you are UTG, your chance of holding this hand is exactly 9.8% of course. If it's folded around to you, the chance rises like this (each of these good to ±.03%):

UTG+1: 9.88%
UTG+2: 10.00%
MP1: 10.15%
MP2: 10.32%
MP3: 10.47%
CO: 10.66%
B: 11.00%
SB: 11.35%
BB: 11.89%

Not really any obvious practical application of this, except perhaps to empirically adjust what the definition of "best 50% of hands" for opening from the small blind is. But hope some of you will find it an interesting factoid.

Pokerscott
05-05-2005, 06:23 PM
I would have to say that the 'folded around to the BB' data is the least interesting /images/graemlins/smile.gif

Honestly though, this is pretty nifty. Intuitively, people know that if someone folds in front of you then they are more likely to be folding low cards vs. folding high cards. Given this, the deck gets more and more skewed to higher cards as more and more people fold. To figure it out, you need to assume what hands constitute 'folding hands' by position. Nifty to see some analysis on it!

Pokerscott

Siegmund
05-05-2005, 06:47 PM
[ QUOTE ]
I would have to say that the 'folded around to the BB' data is the least interesting /images/graemlins/smile.gif

[/ QUOTE ]

That was what the OP was asking about last week - and one of the replies in that thread made the same point you did, knowing what the BB has is just trivia but knowing what the button or SB has might be useful.