Preflop drawing dead problem....

[bigpooch]

Suppose a player has 2 [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/heart.gif[/img]. For this player
to have absolutely zero equity, he cannot play the board
with all the other players doing likewise. Thus, the board
cannot be allowed to have any straight flush possibilities.

Clearly, some other player must have 2 [img]/images/graemlins/diamond.gif[/img] 2 [img]/images/graemlins/club.gif[/img]

If the other hands are as below, no straights are possible
and therefore no straight flushes.

7 [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/heart.gif[/img]
7 [img]/images/graemlins/diamond.gif[/img] 7 [img]/images/graemlins/club.gif[/img]
Q [img]/images/graemlins/spade.gif[/img] Q [img]/images/graemlins/heart.gif[/img]
Q [img]/images/graemlins/diamond.gif[/img] Q [img]/images/graemlins/club.gif[/img]

Thus, with a total of five other hands, it is possible for
22 to be drawing dead.

Here's an easy question to answer! What hands in holdem
require the least number of other hands competing to have
exactly zero equity? You should be able to immediately
determine which hands they are and what the least number
of hands will be.

[bigpooch]

Actually, should have 55, 55, TT, TT as other hands.

[clovenhoof]

Sh!t.

I mean, add the other AA's -- that should do it.

'hoof

[johnd192]

ad ah
as kc
ac ks
tc 7s
7c ts
7d 7h
td th
2s 3d
2h 3c
kh kd

http://twodimes.net/h/?z=219517

pokenum -h ad ah - as kc - ac ks - tc 7s - 7c ts - 7d 7h - td th - 2s 3d - 2h 3c - kh kd

Holdem Hi: 201376 enumerated boards
cards win %win lose %lose tie %tie EV
Ad Ah 135708 67.39 64288 31.92 1380 0.69 0.676
As Kc 1626 0.81 198370 98.51 1380 0.69 0.010
Ks Ac 1626 0.81 198370 98.51 1380 0.69 0.010
7s Tc 110 0.05 164974 81.92 36292 18.02 0.081
Ts 7c 83 0.04 165001 81.94 36292 18.02 0.081
7d 7h 137 0.07 194563 96.62 6676 3.32 0.012
Td Th 56 0.03 195992 97.33 5328 2.65 0.009
2s 3d 27 0.01 177045 87.92 24304 12.07 0.060
3c 2h 27 0.01 177045 87.92 24304 12.07 0.060
Kd Kh 0 0.00 201376 100.00 0 0.00 0.000

[Bozeman]

You made the same mistake, all aces need to be out or else A4444 is a chop, for example.

[thylacine]

2222 is dead to 3333!

[bigpooch]

If the last hand is AA, there won't be nine other hands
that give AA an equity of zero.

If the last hand is a smaller pocket pair, say Ks Kh, you
can take out the other KK, the two pocket aces, two pocket
tens and two pocket fives so now the KK has zero equity. If
the pair is say 5s 5h, take out the other fives, the two
pocket aces, two pocket sixes and two pocket tens.

Now if the tenth hand is A [img]/images/graemlins/spade.gif[/img] K [img]/images/graemlins/spade.gif[/img], pick these
hands:

A [img]/images/graemlins/heart.gif[/img] A [img]/images/graemlins/diamond.gif[/img]
K [img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/diamond.gif[/img]
A [img]/images/graemlins/club.gif[/img] K [img]/images/graemlins/club.gif[/img]
Q [img]/images/graemlins/spade.gif[/img] J [img]/images/graemlins/spade.gif[/img]
T [img]/images/graemlins/spade.gif[/img] 9 [img]/images/graemlins/spade.gif[/img]
8 [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/spade.gif[/img]
6 [img]/images/graemlins/spade.gif[/img] 5 [img]/images/graemlins/spade.gif[/img]
T [img]/images/graemlins/heart.gif[/img] T [img]/images/graemlins/diamond.gif[/img]
5 [img]/images/graemlins/heart.gif[/img] 5 [img]/images/graemlins/diamond.gif[/img]
T [img]/images/graemlins/club.gif[/img] 5 [img]/images/graemlins/club.gif[/img]

Now, if a spade flush is possible, the 6s 5s makes the nut
straight flush. Similarly, for AY suited, there will be a
possible straight flush that can be made and so nine hands
can be chosen to give this hand zero equity.

For a smaller suited hand, say K [img]/images/graemlins/spade.gif[/img] Q [img]/images/graemlins/spade.gif[/img], just
pick the following:

A [img]/images/graemlins/spade.gif[/img] T [img]/images/graemlins/spade.gif[/img]
K [img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/diamond.gif[/img]
Q [img]/images/graemlins/heart.gif[/img] Q [img]/images/graemlins/diamond.gif[/img]
A [img]/images/graemlins/club.gif[/img] K [img]/images/graemlins/club.gif[/img]
Q [img]/images/graemlins/club.gif[/img] T [img]/images/graemlins/club.gif[/img]
A [img]/images/graemlins/heart.gif[/img] A [img]/images/graemlins/diamond.gif[/img]
T [img]/images/graemlins/heart.gif[/img] T [img]/images/graemlins/diamond.gif[/img]
5 [img]/images/graemlins/spade.gif[/img] 5 [img]/images/graemlins/heart.gif[/img]
5 [img]/images/graemlins/diamond.gif[/img] 5 [img]/images/graemlins/club.gif[/img]

For nonsuited hands, the task is simpler.

[clovenhoof]

You don't need the two 23 hands. A 6 high straight flush on board doesn't play because one of the 77's beats it.

'hoof

[M.B.E.]

Here are two threads showing how pocket aces could be drawing dead preflop:

November 2002 thread started by JTG51

March 2003 thread started by rharless

[bigpooch]

Good work! Your example gives the minimum number of
opponents for AA to have zero equity.

Here is the argument for at least eleven opponents:

Say our hero has A [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/heart.gif[/img]. The other hands must
have at least 8 spades and 8 hearts because of the flush
possibilities: with only four consecutive spades and four
consecutive hearts outstanding, as long as the top card of
the sequences isn't the rank of a king, then it allows all
four of the cards of the suit to show up and gives one of
the other hands a straight flush. Also, with four missing
in a suit with a gap, as long as the top card is not a king,
if these four appear on board, one of the hands makes a
straight flush.

The A [img]/images/graemlins/diamond.gif[/img] and A [img]/images/graemlins/club.gif[/img] must also be in the other hands
so that our hero can't make trips and win and to avoid a
straight flush in diamonds or clubs on board that everyone
plays, another two diamonds and two clubs must be in the
other hands to make it impossible for a straight flush to
play on board.

Altogether, that is a minimum of 22 cards or eleven hands.