Gedankenexperiment #3 (My last one)

[PDosterM]

Gedankenexperiment (Thought Experiment) #3

You often hear people complain about low limit games, saying that there are so many callers going to the river that somebody always sucks out on them. During one such discussion, a player wondered whether or not it was possible to be ahead on the turn (that is currently have the best five-card poker hand among up to ten players) and still be drawing dead.

Hypothesize any group of initial two-card holdings with any four-card board from the remaining cards. Can one be ahead at the turn and still be drawing dead among ten players? What is the fewest number of players where this situation could theoretically arise?

[DrSavage]

I can only come up with 10 handed example where 2 hands folded preflop.
you:
AK
others:
AQ
AJ
AT
K9
K8
K7
45
folded preflop:
23
33
board:
2223

[bisonbison]

You: T/images/graemlins/diamond.gif 7/images/graemlins/club.gif

Board 3/images/graemlins/spade.gif 2/images/graemlins/heart.gif 4/images/graemlins/spade.gif T/images/graemlins/heart.gif

other hands:
A/images/graemlins/spade.gif 6/images/graemlins/spade.gif
K/images/graemlins/heart.gif 4/images/graemlins/heart.gif
Q/images/graemlins/club.gif J/images/graemlins/club.gif
2/images/graemlins/club.gif 8/images/graemlins/club.gif
3/images/graemlins/diamond.gif 9/images/graemlins/diamond.gif
T/images/graemlins/club.gif 5/images/graemlins/spade.gif
T/images/graemlins/spade.gif 6/images/graemlins/heart.gif
7/images/graemlins/heart.gif 7/images/graemlins/spade.gif

[DrSavage]

Very nice. I also liked how you changed a5 to a6 as i was typing my response /images/graemlins/smile.gif

[bisonbison]

I accidentally stopped previewing and submitted it. I won't be editing it no more.

[bisonbison]

Actually, there's an inefficiency in mine. I've removed one of the opponent hands and changed another:

You: T/images/graemlins/diamond.gif 7/images/graemlins/club.gif

Board 3/images/graemlins/spade.gif 2/images/graemlins/heart.gif 4/images/graemlins/spade.gif T/images/graemlins/heart.gif

other hands:
T/images/graemlins/spade.gif 6/images/graemlins/spade.gif
K/images/graemlins/heart.gif 4/images/graemlins/heart.gif
Q/images/graemlins/club.gif J/images/graemlins/club.gif
2/images/graemlins/club.gif 8/images/graemlins/club.gif
3/images/graemlins/diamond.gif 9/images/graemlins/diamond.gif
T/images/graemlins/club.gif 5/images/graemlins/spade.gif
7/images/graemlins/heart.gif 7/images/graemlins/spade.gif

[alThor]

[ QUOTE ]
You: T/images/graemlins/diamond.gif 7/images/graemlins/club.gif

Board 3/images/graemlins/spade.gif 2/images/graemlins/heart.gif 4/images/graemlins/spade.gif T/images/graemlins/diamond.gif

other hands:
A/images/graemlins/spade.gif 6/images/graemlins/spade.gif
K/images/graemlins/heart.gif 4/images/graemlins/heart.gif
Q/images/graemlins/club.gif J/images/graemlins/club.gif
2/images/graemlins/club.gif 8/images/graemlins/club.gif
3/images/graemlins/diamond.gif 9/images/graemlins/diamond.gif
T/images/graemlins/club.gif 5/images/graemlins/spade.gif
T/images/graemlins/spade.gif 6/images/graemlins/heart.gif
7/images/graemlins/heart.gif 7/images/graemlins/spade.gif


[/ QUOTE ]

I came up with a very similar example. In fact, I got it down to seven opponents, by making it so that if the hero gets trips then someone else gets a flush. (Whereas you eliminated the trips problem by giving both remaining tens to opponents.) I'll bet you can modify your example to do the same... put one of the tens back in the deck, but make it yield a flush.

My example:
hero holds 5/images/graemlins/spade.gif 7/images/graemlins/spade.gif
board is 2/images/graemlins/heart.gif 3 /images/graemlins/heart.gif 6 /images/graemlins/heart.gif 7/images/graemlins/diamond.gif
Opponents:
4/images/graemlins/heart.gif 7/images/graemlins/club.gif
5/images/graemlins/spade.gif 8/images/graemlins/diamond.gif
A/images/graemlins/spade.gif 6/images/graemlins/spade.gif
8/images/graemlins/spade.gif 9/images/graemlins/spade.gif
3/images/graemlins/spade.gif J/images/graemlins/spade.gif
Q/images/graemlins/spade.gif K/images/graemlins/spade.gif
2/images/graemlins/spade.gif T/images/graemlins/spade.gif

I hope I didn't screw it up while typing it in.

al'Thor

[Ed Miller]

This is exactly why you don't play T7o.

[Bozeman]

I tried to improve on yours and found:

2348

8 7
7 7
k 2
q 3
j t
9 4
8 5
8 6

(suits unimportant, as long as there is no card duplication)

But this showed me that your A6 hand is unnecessary (ace makes wheel, 5 makes 6 high str8). So I haven't really improved on yours /images/graemlins/smile.gif

Craig

[bisonbison]

Here's one with 6 opponents, but you're tied on the turn:

You: T/images/graemlins/diamond.gif 7/images/graemlins/diamond.gif

Board 3/images/graemlins/spade.gif 2/images/graemlins/heart.gif 4/images/graemlins/spade.gif T/images/graemlins/heart.gif

other hands:
T/images/graemlins/spade.gif 5/images/graemlins/spade.gif
K/images/graemlins/heart.gif 4/images/graemlins/heart.gif
Q/images/graemlins/club.gif J/images/graemlins/club.gif
2/images/graemlins/club.gif 8/images/graemlins/club.gif
3/images/graemlins/diamond.gif 9/images/graemlins/diamond.gif
T/images/graemlins/club.gif 7/images/graemlins/club.gif

[Festus22]

Board is A-A-A-2

You have 2-2

Opponents have:
K-Q
J-10
9-8
7-6
5-4
3-2

If you allow "in the lead" to be tied for the lead.

[gigahurts]

5 players... any problems?

Hero: A /images/graemlins/diamond.gif J /images/graemlins/diamond.gif

Board: 2 /images/graemlins/heart.gif 6 /images/graemlins/club.gif J /images/graemlins/spade.gif J /images/graemlins/heart.gif

Others:
J /images/graemlins/club.gif T /images/graemlins/diamond.gif
A /images/graemlins/heart.gif 2 /images/graemlins/diamond.gif
A /images/graemlins/club.gif 6 /images/graemlins/heart.gif
A /images/graemlins/spade.gif K /images/graemlins/diamond.gif

[bisonbison]

The hero isn't drawing dead, though.

Any K, Q, 9, 8, 7, 5, 4, 3 will let Hero win.

[Bozeman]

2s 3s 4h 8h

8d 7c

7d 6s
kh 2h
qs 3c
js ts
9d 4s
8c 5s

Gives 6 opps, with no tie on the turn.

Craig

[Franchise (TTT)]

I think there are plenty of other reasons I don't play T7o. Drawing dead while ahead isn't one of them.

[PDosterM]

Very good!

The best I came up with was seven opponents, although mine had a legitimate starting hand for our hero: A/images/graemlins/spade.gif A/images/graemlins/club.gif

Board: 6/images/graemlins/diamond.gif 5/images/graemlins/diamond.gif Q/images/graemlins/heart.gif J/images/graemlins/heart.gif

A/images/graemlins/spade.gif A/images/graemlins/club.gif

T/images/graemlins/heart.gif 9/images/graemlins/heart.gif
Q/images/graemlins/diamond.gif 8/images/graemlins/diamond.gif
J/images/graemlins/diamond.gif 7/images/graemlins/diamond.gif
8/images/graemlins/spade.gif 9/images/graemlins/club.gif
7/images/graemlins/spade.gif 8/images/graemlins/club.gif
6/images/graemlins/club.gif 3/images/graemlins/diamond.gif
5/images/graemlins/spade.gif 2/images/graemlins/club.gif


So it looks like six opponents works for the minimum. Anyone find a solution for five opponents?

[Bozeman]

However, there is a meaningful point in Ed's post: when you make a hand (like top pair) with T7, there are very few safe cards, most everything either makes a higher pair, a str., or lower trips possible.

Craig

[Bozeman]

I came up with a 6 opp. case for AA:

5h 6h jd qd

As Ac is drawing dead to:

9h td eliminates k,8
3d 4h 2,7
qh 3h 3,q,ah
9d 5d 9,5,ad
jh th j,t
6d 4d 6,4

In general, you need to eliminate 13 ranks, flushes can get rid of 1 (against a pp), each hand can eliminate 2 others. Proper arrangement of str8's is necessary for it work. 4 hands need to eliminate all 2 pair wins, and any rank can be picked for their other elimination, except on represented on the board. To eliminate the other 4 ranks, 2 OE str8 draws (that don't counterfeit each other) must be there.

Another possibility is to have the OE str8 draws overlap a card, thus eliminating this rank if the only remaining ones make flushes. Then one of the paired hands doesn't need to eliminate another rank:

6h 7h jd qd

As Ac

9c t -k,8 (9c)
9s 8 -t,5 (9s)
qh 2h -q,2,Ah,9h
7d 3d -7,3,Ad,9d
j 4 -j,4
6 x -6

For the pp at least, I don't think this can be improved upon.


Craig

[Bozeman]

Ack, I keep doing better:

2c 3c 4s 7s

8d 8h

4c 5c -A,4,5,6,8c
ks 2s -k,2,8s
q 3 -q,3
j 7 -j,7
t 9 -t,9

I will go out on a limb and say this cannot be beat, though it can be tied. I think an overpair is the easiest hand to be drawing dead when ahead, since top pair needs to have insurance against hitting it's 2 pair. Better hands will be harder since hands drawing against them will have fewer outs. No pair needs its nonflushing pairing outs gone. Pair below top is impossible unless there are dead cards, since pairing top card will keep it in the lead (unless a flush is made, and only 2/3 cards can do this).

Fun problem,
Craig

[PDosterM]

Very nice.

This last one is going to be hard to top.

[Leo Bello]

[ QUOTE ]
Actually, there's an inefficiency in mine. I've removed one of the opponent hands and changed another:

You: T/images/graemlins/diamond.gif 7/images/graemlins/club.gif

Board 3/images/graemlins/spade.gif 2/images/graemlins/heart.gif 4/images/graemlins/spade.gif T/images/graemlins/heart.gif

other hands:
T/images/graemlins/spade.gif 6/images/graemlins/spade.gif
K/images/graemlins/heart.gif 4/images/graemlins/heart.gif
Q/images/graemlins/club.gif J/images/graemlins/club.gif
2/images/graemlins/club.gif 8/images/graemlins/club.gif
3/images/graemlins/diamond.gif 9/images/graemlins/diamond.gif
T/images/graemlins/club.gif 5/images/graemlins/spade.gif
7/images/graemlins/heart.gif 7/images/graemlins/spade.gif

[/ QUOTE ]

If the hero draws a 8 here is not dead.

[aloiz]

Think I got one with four...

hero 22
board 4557

A3
89
TJ
QK

aloiz

[dfscott]

[ QUOTE ]
Think I got one with four...

hero 22
board 4557

A3
89
TJ
QK

aloiz

[/ QUOTE ]

Not quite: a 5 and you fill up but no one else improves.

[dfscott]

[ QUOTE ]
[ QUOTE ]
Actually, there's an inefficiency in mine. I've removed one of the opponent hands and changed another:

You: T/images/graemlins/diamond.gif 7/images/graemlins/club.gif

Board 3/images/graemlins/spade.gif 2/images/graemlins/heart.gif 4/images/graemlins/spade.gif T/images/graemlins/heart.gif

other hands:
T/images/graemlins/spade.gif 6/images/graemlins/spade.gif
K/images/graemlins/heart.gif 4/images/graemlins/heart.gif
Q/images/graemlins/club.gif J/images/graemlins/club.gif
2/images/graemlins/club.gif 8/images/graemlins/club.gif
3/images/graemlins/diamond.gif 9/images/graemlins/diamond.gif
T/images/graemlins/club.gif 5/images/graemlins/spade.gif
7/images/graemlins/heart.gif 7/images/graemlins/spade.gif

[/ QUOTE ]

If the hero draws a 8 here is not dead.

[/ QUOTE ]

The 8 /images/graemlins/heart.gif and 8 /images/graemlins/spade.gif will kill him, but you're right about the the 8 /images/graemlins/diamond.gif.

[DrSavage]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Actually, there's an inefficiency in mine. I've removed one of the opponent hands and changed another:

You: T/images/graemlins/diamond.gif 7/images/graemlins/club.gif

Board 3/images/graemlins/spade.gif 2/images/graemlins/heart.gif 4/images/graemlins/spade.gif T/images/graemlins/heart.gif

other hands:
T/images/graemlins/spade.gif 6/images/graemlins/spade.gif
K/images/graemlins/heart.gif 4/images/graemlins/heart.gif
Q/images/graemlins/club.gif J/images/graemlins/club.gif
2/images/graemlins/club.gif 8/images/graemlins/club.gif
3/images/graemlins/diamond.gif 9/images/graemlins/diamond.gif
T/images/graemlins/club.gif 5/images/graemlins/spade.gif
7/images/graemlins/heart.gif 7/images/graemlins/spade.gif

[/ QUOTE ]

If the hero draws a 8 here is not dead.

[/ QUOTE ]

The 8 /images/graemlins/heart.gif and 8 /images/graemlins/spade.gif will kill him, but you're right about the the 8 /images/graemlins/diamond.gif.

[/ QUOTE ]

any 8 will give 2/images/graemlins/club.gif 8/images/graemlins/club.gif 2 pair

[dfscott]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Actually, there's an inefficiency in mine. I've removed one of the opponent hands and changed another:

You: T/images/graemlins/diamond.gif 7/images/graemlins/club.gif

Board 3/images/graemlins/spade.gif 2/images/graemlins/heart.gif 4/images/graemlins/spade.gif T/images/graemlins/heart.gif

other hands:
T/images/graemlins/spade.gif 6/images/graemlins/spade.gif
K/images/graemlins/heart.gif 4/images/graemlins/heart.gif
Q/images/graemlins/club.gif J/images/graemlins/club.gif
2/images/graemlins/club.gif 8/images/graemlins/club.gif
3/images/graemlins/diamond.gif 9/images/graemlins/diamond.gif
T/images/graemlins/club.gif 5/images/graemlins/spade.gif
7/images/graemlins/heart.gif 7/images/graemlins/spade.gif

[/ QUOTE ]

If the hero draws a 8 here is not dead.

[/ QUOTE ]

The 8 /images/graemlins/heart.gif and 8 /images/graemlins/spade.gif will kill him, but you're right about the the 8 /images/graemlins/diamond.gif.

[/ QUOTE ]

any 8 will give 2/images/graemlins/club.gif 8/images/graemlins/club.gif 2 pair

[/ QUOTE ]

Oops, you're right -- my board reading has been atrocious lately...