Pocket Pair Statistics and Discussion

[etgryphon]

Hey All...

This post is coming out of a bit of math that I have done to try to figure out why it is correct to play JJ for set value only with lots of opponents and when the blinds are low...

Here is the formula for all these calculations:

x = the number of ranks that beat your pocket pair(PP)

P = 1 - product of [ ({(52 - 2n) choose 2} - 6x) / {(52 - 2n) choose 2}] where n = 1 ... # of opponents

Here is the chart:
__|__1___2___3___4___5___6___7___8___9___
KK | 0.5 | 1.0 | 1.6 | 2.2 | 2.9 | 3.6 | 4.5 | 5.4 | 6.4 |
QQ | 1.0 | 2.0 | 3.2 | 4.4 | 5.7 | 7.2 | 8.8 |10.5 |12.4 |
JJ | 1.5 | 3.0 | 4.7 | 6.5 | 8.5 |10.6 |12.9 |15.4 |18.1 |
TT | 2.0 | 4.0 | 6.3 | 8.6 |11.2 |13.9 |16.7 |20.0 |23.5 |
99 | 2.4 | 5.0 | 7.8 |10.7 |13.8 |17.1 |20.7 |24.5 |28.5 |
88 | 2.9 | 6.0 | 9.3 |12.8 |16.4 |20.3 |24.3 |28.7 |33.2 |
77 | 3.4 | 7.0 |10.8 |14.8 |18.9 |23.3 |27.9 |32.7 |37.7 |
66 | 3.9 | 8.0 |12.3 |16.7 |21.4 |26.2 |31.2 |36.5 |41.9 |
55 | 4.4 | 9.0 |13.7 |18.7 |23.8 |29.0 |34.5 |40.1 |45.9 |
44 | 4.9 |10.0 |15.2 |20.6 |26.1 |31.8 |37.6 |43.5 |49.6 |
33 | 5.4 |10.9 |16.6 |22.4 |28.4 |34.4 |40.6 |46.8 |53.1 |
22 | 5.9 |11.9 |18.0 |24.3 |30.6 |37.0 |43.4 |49.9 |56.3 |
----------------------------------------------------------

So here is the discussion, from reading posts and my own experiance it seems that when the probability of an over Pocket Pair (OPP) gets to be in the range of 10%-15% then it becomes less optimal to play it for set value only. I know this is a incomplete discussion because we can talk about the likelyhood of overcards when you have smaller Pocket Pairs makes them much weaker. So I would like anyones' thoughts and any points on this chart and the 10/15 rule.

-Gryph

P.S. Thanks to gaming_mouse who helped me figure out the correct formula!

[Lloyd]

I have no clue what you're talking about in terms of a 10/15 rule.

[etgryphon]

Sorry...I meant that when there is only a 10%-15% chance of someone having an over pocket pair to you, you can start to play your pocket pair as a premium hand i.e. raise 3xBB and so forth...

-Gryph

[Lloyd]

I don't know about others but if I have JJ with limpers in front of me I'm going to raise to try to win the pot right then or at least get out some marginal hands. I'm not playing JJ for set value, even on the first hand of a tournament. I'd consider raising even with TT. 9s or lower I'd definitely play for set value with limpers in front.

[Myst]

In lowerbuyins, people arent going to fold Ace rag, King rag, or even hands like QJ to a raise.

If you do raise hard and an overcard hits, whats your play? Youve invested a huge chunk of your stack and you dont know where you are at.

[morgan180]

[ QUOTE ]
In lowerbuyins, people arent going to fold Ace rag, King rag, or even hands like QJ to a raise.

If you do raise hard and an overcard hits, whats your play? Youve invested a huge chunk of your stack and you dont know where you are at.


[/ QUOTE ]

If an over card hits the flop at a low buy-in (5/10) you know exactly where you are at... behind.

Since there is a only a 9% chance that the pair of Js will make the high pair on the board on the flop and a 45% chance that an overcard to a jack will come by the turn/river its tough to play this as a super premium hand.

Not that you wouldn't want to raise it late, etc. but there are a lot of hands you have to worry about with it.

*Stats from Gary Carson's book "Hold 'em Poker" pg. 62-63

[Lloyd]

The percentage of the time that an overcard will come by the river in meaningless unless you have an all-in situation. If you have AA in early position and raise and get called by 5 or 6 people with hands like Ax and QJ, you still don't know where you stand. You raise with JJ pre-flop because you most likely have the best hand and want to at least give people a chance to fold pre-flop. Some won't but some will.

[zaxx19]

You raise hard with 10-10 on the first hand of a tourney?? You got alot more balls than I ever will. Even at higher levled buyins alot of bad players will just smooth call with their overs and see a flop. JJ is a different story- though postion dependant. 10-10 isnt really a hand I feel like is worthy of "defending" early in a tourney where play can get so wacky. I mean its an insta muck if you get reraised correct?? I m not really into making ALOT or raises very early with hands I cant even think about playing if I am reraised.

[woodguy]

Pocket pairs are good hands that should be raised over limpers to:

a) get rid of the trash hands like QTo when they are overcards to your pair
b) put the other players on the defensive and create fear of your hand
c) for value

If you just played them for set value, you wouldn't be able to make plays like this:

Party Poker No-Limit Hold'em Tourney, Big Blind is t20 (8 handed) converter

saw flop|<font color="#C00000">saw showdown</font>

UTG+1 (t1110)
MP1 (t800)
MP2 (t2235)
CO (t960)
Hero (t1335)
SB (t935)
BB (t875)
UTG (t955)

Preflop: Hero is Button with 9[img]/images/graemlins/spade.gif[/img], 9[img]/images/graemlins/heart.gif[/img].
UTG folds, UTG+1 folds, MP1 calls t20, MP2 calls t20, CO folds, <font color="#CC3333">Hero raises to t125</font>, SB folds, BB calls t105, MP1 folds, MP2 folds.

Flop: (t300) 7[img]/images/graemlins/diamond.gif[/img], 4[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets t300</font>, BB folds.

Final Pot: t600

Results in white below: <font color="#FFFFFF">
No showdown. Hero wins t600. </font>

Having your opponets think that you have the best hand is more important than actually having it.

Regards,
Woodguy

[morgan180]

Great post Woodguy, and I agree 100% late position these hands are strong raising hands. And you can represent hands when weakness has been shown before you. But you lose this advantage early.

I'll raise with JJ to knock out the junk over hands unless I'm at a super agg table, I have to agree with zaxx early on I think I'm laying down TT (JJ too) to an all-in reraise because I would estimate that the majority of the time those reraises mean at least overcards (AK/AQ), and then I'm looking at a coin flip (ok, i know the pair is a slight favorite), but I think I should find a better spot?