Flopped set vs. pocket pair with flush draw on monotone flop

ispiked · #1 01-27-2007, 11:01 PM

Here's the hand:

Full Tilt Poker
No Limit Holdem Ring game
Blinds: $200/$400
2 players
Converter

Stack sizes:
SB: $55395.50
BB: $28613

Pre-flop: (2 players)
SB raises to $1200, BB raises to $3600, SB calls.

Flop: 6[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/club.gif[/img] 5[img]/images/graemlins/club.gif[/img] ($7200, 2 players)
BB is all-in $25013, SB calls.

Turn: K[img]/images/graemlins/club.gif[/img] ($57226, 1 player + 1 all-in - Main pot: $57226)

River: A[img]/images/graemlins/diamond.gif[/img] ($57226, 1 player + 1 all-in - Main pot: $57226)

Results:
Final pot: $57226
SB showed 5d 5s
BB showed 2h 2c

I watched this hand and thought to myself that the 2h 2c would have an advantage here, but when I entered this hand into CardPlayers calculator I was wrong -- 5d 5s is about 60% to 30% to win here.

It seems to me that 2h 2c has so many more outs than 5d 5s does on this flop. It can hit any one of the remaining 4s or clubs in the deck and make a hand that beats a set. So why isn't it a favorite to win here? Is is the fact that 5d 5s already has made a set and the 2h 2c needs to catch one of those out to win?

Fiksdal · #2 01-28-2007, 07:53 AM

It is because if the board pairs, 55 gets a full house, and 22 goes to one out, the 4[img]/images/graemlins/club.gif[/img]

pzhon · #3 01-28-2007, 01:42 PM

[ QUOTE ]
It seems to me that 2h 2c has so many more outs than 5d 5s does on this flop.

[/ QUOTE ]
The set of 5s does not need outs to win. Don't count outs for the hand that is ahead (although redraws matter). AA is much stronger than AK despite having fewer single cards that will improve it.

As far as I know, a set is always a favorite over an open-ended straight-flush draw. This is the case even if the straight-flush draw also has outs to a higher set, and to counterfeit the set with trips on the board. Ignore exposed cards and other poker variants.

http://twodimes.net/h/?z=2342985
990 enumerated boards containing T[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/club.gif[/img]
cards win %win lose %lose tie %tie EV
8[img]/images/graemlins/club.gif[/img] 8[img]/images/graemlins/heart.gif[/img] 486 49.09 492 49.70 12 1.21 0.497
7[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/heart.gif[/img] 492 49.70 486 49.09 12 1.21 0.503

In this example, 88 has 17 outs plus runner-runner combinations like TT, and is a favorite to improve. However, 77 has redraws to a full house (or to split with a straight on the board), and still comes out a slight favorite.

In your hand, 22 has only 12 outs. The straight draw is a gutshot, which can be counterfeited easily with a straight on the board. The flush draw is to the lowest possible one-card flush, so if two clubs come without the 4[img]/images/graemlins/club.gif[/img] both players will play the flush on the board. The player with 22 doesn't have outs to a higher set or to counterfeit the set. The set is a clear favorite.