A weird odds situation - a case for drawing to big overcards

[DcifrThs]

you are overestimating the information gained from your "knowledge."

Barron

[kbfc]

I've got this little voice inside me telling me I'm missing something, but my first instinct is: can't you do this for almost every card in the deck?

Let's say the action preflop indicates nobody could have had a pair > 66. That means that at least one of each player's cards could not be a 7,8,9,T,J,Q,K, or A.

This whole method of reasoning turns into a giant mess. It's much better to just consider actual hand distributions, if you're looking for clumping effects. I think Barry Greenstein wrote a program to calculate this sorta thing.

[Hoi Polloi]

[ QUOTE ]
I talked to Justin A about it and he basically agrees. His calculations led him to believe that it maybe makes a 1 card difference. Maybe I am just a freak that is persuaded by lame clumping theories [img]/images/graemlins/smile.gif[/img]
-James

[/ QUOTE ]

Drawing to 6 against 40. If you say your 7 folding opponents held 7 non-AK cards you ask whether your true draw might be 6 against 33. That would improve you from 15% to 18%. However, by eliminating those 7 cards, you are also implicitly making odds on the other card held by each of your folding opponents. What are those odds? The odds that any of 7 random cards drawn from a 46 card deck containing 6AKs will be an A or K. I can't do the math right now, but I bet they add back most of 3% you gained earlier.

Interesting post.