Quiz: Draw dead preflip with AA

Inspired by a discussion on this board, I have a quiz question regarding holdem poker:

What is the minimum number of opponents where you can draw dead preflop with AA?
Which cards should each of these players hold?

By drawing dead, I mean that the player should not be able to win the pot or get a split of it no matter what cards hit the board.

[waffle]

I don't know about the minimum. I tried to create a scenario where AA had 0% preflop equity.

AA
vs..
33
44
55
66
77
88
99
TT
JJ
QQ
KK
KK
A2
A2
22

Hi, thanks for your suggestion.
I guess with your given hands, there is a possibility for the board to show a straight flush for a split between all players. Depending on the suits there is also a possibility for AA to draw the highest flush.
There is a solution where AA draws dead and with less than 15 players on the table.

You have to stop:

- Quads and sets
This requires that both other aces be out

- Board four flushes (includes straight flush)

this requires that 9 out of 13 of each Ace's suit are in other player's hands. (total:18 cards)

- Board three trips (e.g. 77749) which gives a full house.

Requires that every card 2-K is present at least once (total: 12 cards) Having every card out also satisfies the requirement that someone will have at least 2 pair to beat AA no matter what comes.

- 10-A and A-5 straight

Requires that all of (K or Q or J or 10) are out AND a 6 is out

So we can see it cannot be done with less than 9 hands (18/2). Putting this all together gives:

You hold AdAh. Opponent's cards are:

AsAc
KsKc
KhKd
QhJd
Th9d
8h7d
6h5d
4h3d

Now we need a 2, 3 more hearts, 3 more diamonds:

Qd2h
Td5h
4d3h

That's 11 players.

AA is not drawing dead in your scenario.
There is still the possibility of flopping a straight flush for a split between all players.
Can you reaarange for the eleven players to prevent that split also?

EDIT:
There is also the possibility for a lot of split pots between the pocket aces for one pair if I see this correct.

[ QUOTE ]
Can you reaarange for the eleven players to prevent that split also?

[/ QUOTE ]
Oops.

For the straight flush you'll need 5 blockers and T blockers of the other two suits. We can remove the KK as it is no longer needed for straight blocking with four 10s out. So the list becomes:

AsAc
KhQd
Jh9d
8h7d
6h5d
4h3d

TsTc
TdTh
5s5c

Now we need a 2, 3 more hearts, 3 more diamonds:

Qd2h
8d5h
Kd3h

Which is 12.

edit:
[ QUOTE ]
EDIT:
There is also the possibility for a lot of split pots between the pocket aces for one pair if I see this correct.

[/ QUOTE ]
No because every other card is out, so there will always be at least 2 pair and AA will always lose. When the board double pair, somone will have trips, etc. It's mentioned in the conditions above.

edit again: actually hold that thought, some further rearrangement may be required to prevent this on non pairing boards. It should be possible with 12 though [img]/images/graemlins/grin.gif[/img]

Damn, you're right, K7492 is one such possibility for example. This is tougher than I thought [img]/images/graemlins/smile.gif[/img]. Back to the drawing board. I think part of the trick will be to unpair the 5s and 10s and separate the connectors so that a straight becomes inevitable when 2 pairs are missed.

Thanks for trying it out. It seems you have Qd twice in the list. As I have edited into my previous post, I still think that you are missing when the board comes rags like: 2d 4c 6c 9c Qs. Then the Aces will split the pot with top pair.

I have constructed an example where AA is drawing dead that I have verified with http://twodimes.net. I will post the example later today but it might be fun if someone could beat me with the number of opponents I had to use or come up with another combination than I did.

Here's my solution:

You hold Ad Ah. Opponents hold:

As Ac
Kd Qh
Jd Jh
Jc Js
9d Th
8d 8h
6d 6h
Qd 7h
5s 5c
4d 2h
3d 3h

Solution with 11 numbers

+ any remaining diamond-heart couple = 12 hand total.


I'm guessing you did it in 11? If so, I don't know how. You need:

- 9 diamonds + 9 hearts to block a four flush = 9 hands minimum
- One offsuit high pair (e.g. JJ) to block a high straight & straight flush - 1 extra hand
- One offsuit low pair to block the board doing a straight flush split - 1 extra hand
- One offsuit AA to block quads and a set - 1 extra hand

For a total of 12 hands.

Here is my suggested solution to the quiz with 11 opponents.

The reason my solution is one less than Phils solution is that I have taken an extra card out for each suit of the aces. This allows the aces to flop a flush, but if that happens one of the opponents has flopped a straigh flush.

I guess it is impossible to find a solution with less opponents but I could stand corrected.