Why is a low pair a fav vs. 2 overcards, but a DOG to two such hands?

[teddyFBI]

Noticed something interesting the other day.

Whereas a pair of 66s is a favorite against a hand like Q [img]/images/graemlins/diamond.gif[/img]J [img]/images/graemlins/diamond.gif[/img], when you add a 3rd hand of K [img]/images/graemlins/spade.gif[/img]T [img]/images/graemlins/spade.gif[/img] suddenly the sixes are a dog to BOTH opponents! Why is this?

I mean, intuitively, just consider the 2 hands we started with: 66 and QJd. It's hard to understand why the addition of a 3rd pair of known cards could all of a sudden make the 66 a dog to the QJd (35% to 30%) -- if anything, I would think that it would INCREASE the 66's advantage b/c the KT hand interferes with the QJd's straight possibilities.

[Dynasty]

[ QUOTE ]
...if anything, I would think that it would INCREASE the 66's advantage b/c the KT hand interferes with the QJd's straight possibilities.

[/ QUOTE ]

QJ (or KT) doesn't need to make a straight to beat 66. It just needs to make a pair. And, now there are only 46 cards left in the deck rather than 48. So, the chances of hitting that pair have gone up.

[MLG]

The numbers only define the percentage of the time that a given hand wins. So, if a K were to hit then while 66 still beats QJ, it loses the hand. To put it simply, the 30% represents the time when no K,Q,J,10 or straight or flush comes. Those are the only times 66 wins.

[mosch]

6 [img]/images/graemlins/club.gif[/img] 6 [img]/images/graemlins/heart.gif[/img] versus J [img]/images/graemlins/diamond.gif[/img] Q [img]/images/graemlins/diamond.gif[/img]

Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
6h 6c 839420 49.02 864315 50.48 8569 0.50 0.493
Qd Jd 864315 50.48 839420 49.02 8569 0.50 0.507

sixes are a small dog.

6 [img]/images/graemlins/club.gif[/img] 6 [img]/images/graemlins/heart.gif[/img] versus J [img]/images/graemlins/diamond.gif[/img] Q [img]/images/graemlins/diamond.gif[/img] versus K [img]/images/graemlins/spade.gif[/img] T [img]/images/graemlins/spade.gif[/img]

6s 6c 421592 30.76 944872 68.93 4290 0.31 0.309
Qd Jd 487264 35.55 879200 64.14 4290 0.31 0.357
Ks Ts 457608 33.38 908856 66.30 4290 0.31 0.335

sixes are a slightly bigger dog. More ways to lose with a flush now.

6 [img]/images/graemlins/spade.gif[/img] 6 [img]/images/graemlins/club.gif[/img] versus Q [img]/images/graemlins/spade.gif[/img] J [img]/images/graemlins/club.gif[/img] versus K [img]/images/graemlins/spade.gif[/img] T [img]/images/graemlins/club.gif[/img]

6s 6c 463556 33.82 901258 65.75 5940 0.43 0.340
Qs Jc 458924 33.48 905890 66.09 5940 0.43 0.336
Ks Tc 442334 32.27 922480 67.30 5940 0.43 0.324

sixes are now a small favorite, with the flush draws made as unlikely as is possible.

[LSU POKER PIMP]

also the chance of hitting the flush go up

[teddyFBI]

That's interesting - i always thought that a low pair was ALWAYS a favorite to 2 overcards...but 66 vs. JTs is actually a 48/52 DOG.

[wickss]

When you have a pair vs. two overcards there are 6 pair cards that can beat you. When you are up against 4 overcards, there are 12 pair cards that can beat you. There is a 130% chance that one of these cards will come out of 5 cards delt. (Ovbiously it can't happen every time. There are times the none of the 12 cards come but there are also times when more that one of the 12 cards come. Hence the percentage is greater than 100%.) The reason you are such a dog with the 6's is because of the increased number of outs your opponents have.

[CurryLover]

This post has pointed out two things that a lot of poker players don't know:

1. In a multi-way pot, against more than one set of overcards, a small pair is not the most likely winner. The best set of overcards has the most pot equity.
A common strategy used by some of the fish in the early stages of my local rebuy tourney is to get all-in preflop in a multi way pot with baby pairs. They believe they are 'getting value'. However, they are often wrong - depending on the exact nature of the cards that are against them. When all the cards go on their backs pre-flop they think to themselves 'Hey, my pair of deuces is ahead. I'm going to quintruple up!' Then they start moaning about 'always being outdrawn' when one of the overcards makes a higher pair to beat them. In actual fact, although the 22 is 'ahead' preflop, it is not favourite to win the hand. Sometimes, it doesn't even have the pot equity needed to make this a good EV+ gambling strategy to increase chips at the start of a rebuy tourney. In other words, against 4 opponents, the 22 might have less than the break even 20% chance of winning (assume there is no dead money in the pot).
The suited connectors are often better hands to get all-in with pre-flop in a multi-way pot (during the rebuy stage). They usually have greater than their fair share of pot equity, whereas the baby pairs often have less than their share.

2. Sometimes the overcards are a slight favourite against a pair heads up. This is most often the case when they are suited and connected. The classic one is JTs against a pair of deuces.
There is a well-known hustle involving this point. You offer the sucker the following proposition: Each of you will pick a hand and you'll play them hot and cold against each other for even money. The hands to choose from are 22, JTs and AKo. Because you're such a nice guy, you'll even let him choose his hand first. The winning strategy for you is simple: If he chooses AKo, you choose 22; if he chooses JTs, you choose AKo; if he chooses 22, you choose JTs. You are taking the best of it in every match up.

Here's something else to think about. It highlights another important characteristic of these multi way pot scenario's:

4 hands all-in pre-flop. Who is favourite to win? What are the win percentages for each hand? Try to guess the answer before you run it through a hand calculator. The hands are:
6 [img]/images/graemlins/spade.gif[/img] 6 [img]/images/graemlins/club.gif[/img]
A [img]/images/graemlins/club.gif[/img] J [img]/images/graemlins/heart.gif[/img]
K [img]/images/graemlins/diamond.gif[/img] Q [img]/images/graemlins/diamond.gif[/img]
T [img]/images/graemlins/heart.gif[/img] T [img]/images/graemlins/spade.gif[/img]