Gedankenexperiment (Thought Experiment) #1

[PDosterM]

Ciaffone and Brier in Middle Limit Holdem Poker explain that the flop can dramatically change the relative value of players’ hands. Once the flop comes, they say, “The preflop pecking order may well be history.”

Certainly true, but it might be interesting to consider the upper limits of this transformation. It’s quite easy to contrive a situation where three players see a flop that causes the order of the hands to completely reverse.

Player A – A[img]/images/graemlins/spade.gif[/img]A[img]/images/graemlins/heart.gif[/img]
Player B – 7[img]/images/graemlins/club.gif[/img]7[img]/images/graemlins/spade.gif[/img]
Player C – 9[img]/images/graemlins/diamond.gif[/img]7[img]/images/graemlins/heart.gif[/img]

Here Player A is ahead, B is second, and C trails the field until the flop comes:

9[img]/images/graemlins/spade.gif[/img]9[img]/images/graemlins/heart.gif[/img]7[img]/images/graemlins/diamond.gif[/img]

Now Player C is ahead with nines full of sevens, B is second with sevens full of nines, and A (I know how he feels) is last with a solitary pair of aces.

So without creating any ties, can you create a situation where four players see a flop that completely reverses the order? How about five players? How about six? Better yet, what is the theoretical maximum number of players who can see a flop that completely reverses the order?

Answer later with a comment on why this knowledge has some (but admittedly limited) value.

[ChristinaB]

[ QUOTE ]
and A (I know how he feels) is last with a solitary pair of aces.



[/ QUOTE ]

Doesn't player A have two pair?

He has 2 outs to a win.

[daryn]

correct. but he is in last place on that flop. that is the key to the question i believe

[PDosterM]

Right.

I phrased it poorly; he has two pair -- improving to the worst hand.

[ChristinaB]

Just trying to keep your thread alive until you get some good responses that are on topic, as the answer to your original question will take some thought to compose. [img]/images/graemlins/smirk.gif[/img]

[shemp]

I understand this is showdown value, but it seems 77 has the worst hand because he can't win.

[DrSavage]

Here's an example for 4:
A)As Ad (55.92%)
B)7s 7d (15.97%)
C)3c 4c (13.96%)
D)2h 4h (12.56%)

flop 5h 6h 7h

D leads with flush, C is second with straight , B is third with a set and A is last with a pair.
Had to change it slightly, used cardplayer calculator the first time and sure enough the numbers were off.

[Schneids]

Player A - Ac Kc
Player B - 9d 9s
Player C - 6d 6s
Player D - 8s 7s
...this is using twodimes to determine the % of the time these four hands win when faced off against eachother. Is that ok to figure out their relative values? Or, do I have to list AKc as #3 even though it wins against these 36.85% of the time?

Flop:
6h 5d 4s

So, now those hands have totally flipped in relative value (as well as the likelihood they will be the winner when it's finally over).

If I can't have AKc ranked above 99 because it's unpaired, I'm sorry.

[Schneids]

[Schneids]

Ac Kc 28.08%
5h 3h 19.31
Ts 9s 19.14
8s 8c 18.97
9d 6d 13.18

flop: 8d 3d Td
flush vs set vs pair vs lower pair vs high card. Immediate showdown value and likelihood of having best hand at the river both come out this way, in this example.