Collective Outs Challenge

[Bozeman]

The extra credit question has been answered in the Gedankenexperiment #3 thread in the general texas holdem forum for play on the turn. On the turn, it is possible for the current best hand to be drawing dead against 5 opponents.

On a different note, as you get more opponents, is it easier or harder for the current best hand to not be a money favorite?

Craig

[brassnuts]

Hero holds A [img]/images/graemlins/diamond.gif[/img] K [img]/images/graemlins/diamond.gif[/img], and the opponents' cards are in the results.
Flop is A [img]/images/graemlins/spade.gif[/img] 6 [img]/images/graemlins/diamond.gif[/img] T [img]/images/graemlins/spade.gif[/img].

cards win %win lose %lose tie %tie EV
8 [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/spade.gif[/img] 437 48.39 466 51.61 0 0.00 0.484
A [img]/images/graemlins/diamond.gif[/img] K [img]/images/graemlins/diamond.gif[/img] 375 41.53 528 58.47 0 0.00 0.415
J [img]/images/graemlins/club.gif[/img] T [img]/images/graemlins/club.gif[/img] 91 10.08 812 89.92 0 0.00 0.101

Basically, what I found that Hero is behind opponent A in any situation that opponent A has an inside straight/flush draw and opponent B has any pair on the board or a pocket pair, as long as oppenent B's cards don't intefere with opponent A's straight or flush draw. I even gave Hero a backdoor flush draw here. This is of course just one set of circumstances that satisfies the conditions.

[Louie Landale]

Sorry. Hero wins 41.5% which is well above his fair share of 33%. If the opponents are going to call he should cap it. And he does better, I think, if JT folds (all the more reason to cap it).

[Louie Landale]

We are talking about "best hands" featuring "big pairs". Yes, you can get a "best" hand of 22 drawing slim or dead. As for your second question, I'm suggesting that its almost IMPOSSIBLE for the big pair "best" hand not to be a money favorite and and challenging folks to contrive examples to prove otherwise.

[Louie Landale]

Cheater!!! OK, if Hero is currently tied it doesn't count.

[Bozeman]

Your post seems condescending and incorrect.

Louie Landale said "Extra Credit. Lets give hero 88 and its "best"; and I believe you CAN contrive and [sic] example where collective outs kill this hand. Even so, such contrived examples will be very rare in real life. "

In addition, in my example, it is an overpair. (Underpairs will never be drawing dead if they are currently best.)

As for my second question, it is certainly possible to have a heads up matchup where the current best hand is a money dog (on new money), and people have come up with examples for 2 and 3 opps. It appears that these samples become more difficult as the number of opponents goes up. I is this true?

Craig

[maurile]

This doesn't fit within the guidelines Louie originally gave (since it's not an AK hand), but it's an interesting situation anyway, from a Mike Caro column:

Hero has 9[img]/images/graemlins/diamond.gif[/img] 9[img]/images/graemlins/heart.gif[/img]

Flop comes 9[img]/images/graemlins/club.gif[/img] 6[img]/images/graemlins/spade.gif[/img] 3[img]/images/graemlins/diamond.gif[/img]

Here are the other nine hands:

AA
KK
QQ
JJ
66
33
78 (suited)
45 (suited)
57 (suited)

Hero is a huge favorite against any single opponent, but against the field Hero has only one out -- the case nine.

[Louie Landale]

Looks like a winner.

BUT WAIT!!! I count 23 cards accounted for leaving 29 in the deck. There are 29choose2 possible outcomes for the turn and river = (29*28)/2=406 possible outcomes.

In order for Hero NOT to snag a 9 the turn and river must both be composed of 28 other cards; 28choose2 = 28*27/2=378 bad outcomes. 406-378=28 good outcomes (that feature a 9 and any other card).

Hero is therefore a 378:28 underdog = 13.5:1 dog, above the 9:1 fair share threshold.

Yes, this is a winner but not by all THAT much.

Thanks.

Leave it to Caro to come up with a top-set is underdog example.

- Louie

Actually, you need to give 87s hand the 87 of spades. That way when Hero snags his 9spades there are still 2 cards to outrun him, making Hero a 14.6:1 dog.

[BugsBunny]

Hero is *not* an underdog, but it's close. You missed the boat possibilties.

For the case where the 78s is composed of the 78spades

42,620,256 games 201.199 secs 211,831 games/sec

Board: 9c 3d 6s

equity (%) win (%) / tie (%)

Hand 1: 11.4122 % [ 11.41 00.00 ] { 9h9d }
Hand 2: 02.8120 % [ 02.81 00.00 ] { AA }
Hand 3: 01.9568 % [ 01.96 00.00 ] { KK }
Hand 4: 01.1015 % [ 01.10 00.00 ] { QQ }
Hand 5: 00.2463 % [ 00.25 00.00 ] { JJ }
Hand 6: 06.5590 % [ 06.56 00.00 ] { 66 }
Hand 7: 06.3766 % [ 06.38 00.00 ] { 33 }
Hand 8: 29.8440 % [ 27.76 02.08 ] { 8s7s }
Hand 9: 15.6085 % [ 14.19 01.42 ] { 54s }
Hand 10: 24.0832 % [ 20.58 03.50 ] { 75s }

Hand Distribution ( 1): 9h9d
Hand Distribution ( 2): AdAc, AhAc, AsAc, AhAd, AsAd, AsAh
Hand Distribution ( 3): KdKc, KhKc, KsKc, KhKd, KsKd, KsKh
Hand Distribution ( 4): QdQc, QhQc, QsQc, QhQd, QsQd, QsQh
Hand Distribution ( 5): JdJc, JhJc, JsJc, JhJd, JsJd, JsJh
Hand Distribution ( 6): 6d6c, 6h6c, 6s6c, 6h6d, 6s6d, 6s6h
Hand Distribution ( 7): 3d3c, 3h3c, 3s3c, 3h3d, 3s3d, 3s3h
Hand Distribution ( 8): 8s7s
Hand Distribution ( 9): 5c4c, 5d4d, 5h4h, 5s4s
Hand Distribution (10): 7c5c, 7d5d, 7h5h, 7s5s


For the generic 78s:
170,481,024 games 745.842 secs 228,575 games/sec

Board: 9c 3d 6s

equity (%) win (%) / tie (%)

Hand 1: 11.6585 % [ 11.66 00.00 ] { 9h9d }
Hand 2: 02.8325 % [ 02.83 00.00 ] { AA }
Hand 3: 01.9704 % [ 01.97 00.00 ] { KK }
Hand 4: 01.1084 % [ 01.11 00.00 ] { QQ }
Hand 5: 00.2463 % [ 00.25 00.00 ] { JJ }
Hand 6: 06.5408 % [ 06.54 00.00 ] { 66 }
Hand 7: 06.3492 % [ 06.35 00.00 ] { 33 }
Hand 8: 29.0675 % [ 27.00 02.06 ] { 87s }
Hand 9: 15.8422 % [ 14.43 01.42 ] { 54s }
Hand 10: 24.3842 % [ 20.91 03.48 ] { 75s }

Hand Distribution ( 1): 9h9d
Hand Distribution ( 2): AdAc, AhAc, AsAc, AhAd, AsAd, AsAh
Hand Distribution ( 3): KdKc, KhKc, KsKc, KhKd, KsKd, KsKh
Hand Distribution ( 4): QdQc, QhQc, QsQc, QhQd, QsQd, QsQh
Hand Distribution ( 5): JdJc, JhJc, JsJc, JhJd, JsJd, JsJh
Hand Distribution ( 6): 6d6c, 6h6c, 6s6c, 6h6d, 6s6d, 6s6h
Hand Distribution ( 7): 3d3c, 3h3c, 3s3c, 3h3d, 3s3d, 3s3h
Hand Distribution ( 8): 8c7c, 8d7d, 8h7h, 8s7s
Hand Distribution ( 9): 5c4c, 5d4d, 5h4h, 5s4s
Hand Distribution (10): 7c5c, 7d5d, 7h5h, 7s5s

[Trix]

Hi, Gary Carson have a chart for pocket pairs:

Number of collective outs to make an overpair a dog by number of opponents:

Number of outs - Number of opponents
14 - 1
20 - 2
24 - 3
26 - 4
28 - 5
29 - 6
31 - 7
32 - 8

I guess you will have to be reverse dominated with AK to use these numbers, as you otherwise will have 3 more outs than with pock pairs.