rec.gambling.poker FAQ

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    Board        Hole Cards     Best High Hand
    =====        ==========     ==============
As Kc Qc 8d 2d   Ac 2c Jd Th    Jd Th makes ace-hi straight.
As Kc Qc Jh Td   Ac 2c Jd 8h    Ac Jd makes ace-hi straight.
As Kc Qc Jh Td   3c 2c Jd 8h    Jd 8h makes pair of jacks.  No straight
                                is possible using two hole cards.
As Ks 8h 9d 2s   Qs 4h 4d 4s    Qs 4s makes AKQ42 "nut" flush.
As Ks 8s 9s 2s   Qs 4h 4d Qd    Qs Qd makes pair of queens.  No flush is
                                possible using two hole cards.
As Ts 8s 8h 4d   Td Tc Ad 9c    Td Tc makes TTT88 full house.
As Ts 8s 8h 4d   Td 8c Ad 9c    Ad 8c makes 888AA full house.
As Ac 8s 8h 4d   Ah 2h 3h 5h    Ah 5h makes trip aces AAA85.  No full
                                house is possible using two hole cards.
As Ac 8s 8h 4d   Ah 2h 3h 4h    Ah 4h makes full house AAA44.

    Board        Hole Cards     Best Low Hand
    =====        ==========     =============
As Kc Qc 8d 2d   8c Jc Jd Th    Jd Th makes the low hand JT82A, which
                                does not qualify as 8-or-better.
3d 5h 8d Tc Ts   Ac 2c Jd Th    Ac 2c makes the "nut low" 8532A.
3d 5h 8d Tc Ts   Ac 3c 4d Th    Ac 4d makes 8543A.
3d 5h 8d Ad Ts   Ac 3c 5d 8h    Any two make T853A, not qualifying.
Ac 2c 3d 4h 5s   Ad 2d Th Td    Ad 2d makes "nut low" 5432A.
Ac 2c 3d 4h 5s   4d 5d Th Td    4d 5d makes "nut low" 5432A.
5h 7h 8d Ac 2c   Ad 2d Th Td    Ad 2d makes 8752A, but the nut low is
                                5432A with a 3 and 4.  On the flop we
                                had the best possible low, but the turn
                                and river "counterfeited" us.

  size of pot before                   3 x previous bet
  previous bet         previous bet   + size of pot before
                                        previous bet
                                         = next bet
       1                   -                 1
       1                   1                 4
       2                   4                14
       6                  14                48
      20                  48               164
      68                 164               560
     232                 560              1912

   Half-pot                                  Pot-limit
Start:  call 100, raise 125                       call 100, raise 250
Flop:   pot 600, bet 300                          pot 850, bet 850
Turn:   pot 1200, bet 600                         pot 2550, bet 2550 
River:  pot 2400, bet 1200                        pot 7650, bet 7650
        raise 2400, final pot 9600                raise 22,950, final pot 68,850

+-------------------------+----------------+----------------+----------------+
| Declaration and hands:  | Variation #1   | Variation #2   | Variation #3   |
+-------------------------+----------------+----------------+----------------+
| A: high with KQJT9      | A gets 1/2 the pot for high                      |
| B: low with an 8532A    | B gets 1/2 the pot for low                       |
+-------------------------+----------------+----------------+----------------+
| A: high with KQJT9      | A gets 1/2 the pot for high                      |
| B: low with an 7532A    | B gets 1/2 the pot for low                       |
| C: both ways with 76543 |                                                  |
+-------------------------+----------------+----------------+----------------+
| A: low with an 7532A    | A wins the whole pot                             |
| B: both ways with 76543 |                                                  |
+-------------------------+----------------+----------------+----------------+
| A: high with three 9s   | B wins the whole pot                             |
| B: both ways with 76543 |                                                  |
| C: low with 8532A       |                                                  |
+-------------------------+----------------+----------------+----------------+
| A: high with flush      | A gets 1/2 the pot for high                      |
| B: both ways with 76543 | C gets 1/2 the pot for low                       |
| C: low with 6542A       |                                                  |
+-------------------------+----------------+----------------+----------------+
| A: high with three 9s   | C wins the pot | A gets 1/2 pot | A gets 1/2 pot |
| B: both ways with 76543 |                | C gets 1/2 pot | C gets 1/2 pot |
| C: low with 6 low       |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: high with 98765      | A wins the pot | A gets 1/4 pot | A gets 1/2 pot |
| B: high with 98765      |                | B gets 3/4 pot | C gets 1/2 pot |
|     and low with 7653A  |                |                |                |
| C: low with 76542       |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | none eligible* | A gets 1/2 pot | C wins the pot |
| B: both ways with 76543 |                | B gets 1/2 pot |                |
| C: high with KKJJ9      |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | B wins the pot | A gets 3/4 pot | B wins the pot |
| B: high with 76543      |                | B gets 1/4 pot |                |
| C: high with KKJJ9      |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | B wins the pot | A gets 3/4 pot | B gets 1/2 pot |
| B: low with 76543       |                | B gets 1/4 pot | C gets 1/2 pot |
| C: high with KKJJ9      |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | none eligible* | A gets 1/2 pot | none eligible* |
| B: both ways with 76543 |                | B gets 1/2 pot |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | none eligible* | B wins the pot | none eligible* |
| B: both ways with flush |                |                |                |
|      and 76543          |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | none eligible* | B wins the pot | C wins the pot |
| B: both ways with flush |                |                |                |
|      and 76543          |                |                |                |
| C: high with KKJJ9      |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | none eligible* | none eligible* | none eligible* |
| B: both ways with flush |                |                |                |
|      and 8543A          |                |                |                |
+-------------------------+----------------+----------------+----------------+

Hand                  3 cards           5 cards           7 cards
====                  =======           =======           =======
Straight Flush             48                40            41,584
Four of a Kind              0               624           224,848
Full House                  0             3,744         3,473,184
Flush                   1,096             5,108         4,047,644
Straight                  720            10,200         6,180,020
Three of a Kind            52            54,912         6,461,620
Two Pair                    0           123,552        31,433,400
One Pair                3,744         1,098,240        58,627,800
High Card              16,440         1,302,540        23,294,460
=================================================================
TOTALS                 22,100         2,598,960       133,784,560

Hand Type      Kinds   Each   Total     Cuml   Rating
---------      -----   ----   -----     ----   ------
straight flush   12      4       48       48   0.9978
trips            13      4       52      100   0.9955
straight         12     60      720      820   0.9629
flush  **       274      4     1096     1916   0.9133
pair  ***       156     24     3744     5660   0.7439
Ace high         64     60     3840     9500   0.5701
King high        54     60     3240    12740   0.4235
Queen high       44     60     2640    15380   0.3041
Jack high        35     60     2100    17480   0.2090
Ten high         27     60     1620    19100   0.1357
Nine high        20     60     1200    20300   0.0814
Eight high       14     60      840    21140   0.0434
Seven high        9     60      540    21680   0.0190
Six high          5     60      300    21980   0.0054
Five high         2     60      120    22100   0.0000

** More on Flushes           
------------------           
High Card       Kinds Percent  Total    Cuml   Rating
---------       ----- -------  -----    ----   ------
Ace high         64    23.4     256     1076   0.9513
King high        54    19.7     216     1292   0.9415
Queen high       44    16.1     176     1468   0.9336
Jack high        35    12.8     140     1608   0.9272
Ten high         27     9.9     108     1716   0.9224
Nine high        20     7.3      80     1796   0.9187
Eight high       14     5.1      56     1852   0.9162
Seven high        9     3.3      36     1888   0.9146
Six high          5     1.8      20     1908   0.9137
Five high         2     0.7       8     1916   0.9133

*** More on Pairs
-----------------
Hand Type      Kinds   Each    Total    Cuml   Rating
---------      -----   ----    -----    ----   ------
   AAx           12     24      288     2204   0.9003
   KKx           12     24      288     2492   0.8872
   QQx           12     24      288     2780   0.8742
   JJx           12     24      288     3068   0.8612
   TTx           12     24      288     3356   0.8481
   99x           12     24      288     3644   0.8351
   88x           12     24      288     3932   0.8221
   77x           12     24      288     4220   0.8090
   66x           12     24      288     4508   0.7960
   55x           12     24      288     4796   0.7830
   44x           12     24      288     5084   0.7700
   33x           12     24      288     5372   0.7569
   22x           12     24      288     5660   0.7439

 Chances of making a hand on the turn, river, turn or river (t|r), 
 turn and river (t&r):
        turn    turn  | river   river  |   t|r     t|r  |   t&r     t&r
Outs     (%)   (X:1)  |   (%)   (X:1)  |   (%)   (X:1)  |   (%)   (X:1)
----------------------|----------------|----------------|--------------
  20    42.6    1.35  |  43.5    1.30  |  67.5    0.48  |  17.6    4.69
  19    40.4    1.47  |  41.3    1.42  |  65.0    0.54  |  15.8    5.32
  18    38.3    1.61  |  39.1    1.56  |  62.4    0.60  |  14.2    6.07
  17    36.2    1.76  |  37.0    1.71  |  59.8    0.67  |  12.6    6.95
  16    34.0    1.94  |  34.8    1.88  |  57.0    0.75  |  11.1    8.01
  15    31.9    2.13  |  32.6    2.07  |  54.1    0.85  |   9.7    9.30
  14    29.8    2.36  |  30.4    2.29  |  51.2    0.95  |   8.4   10.88
  13    27.7    2.62  |  28.3    2.54  |  48.1    1.08  |   7.2   12.86
  12    25.5    2.92  |  26.1    2.83  |  45.0    1.22  |   6.1   15.38
  11    23.4    3.27  |  23.9    3.18  |  41.7    1.40  |   5.1   18.65
  10    21.3    3.70  |  21.7    3.60  |  38.4    1.60  |   4.2   23.02
   9    19.1    4.22  |  19.6    4.11  |  35.0    1.86  |   3.3   29.03
   8    17.0    4.88  |  17.4    4.75  |  31.5    2.18  |   2.6   37.61
   7    14.9    5.71  |  15.2    5.57  |  27.8    2.59  |   1.9   50.48
   6    12.8    6.83  |  13.0    6.67  |  24.1    3.14  |   1.4   71.07
   5    10.6    8.40  |  10.9    8.20  |  20.4    3.91  |   0.9  107.10
   4     8.5   10.75  |   8.7   10.50  |  16.5    5.07  |   0.6  179.17
   3     6.4   14.67  |   6.5   14.33  |  12.5    7.01  |   0.3  359.33
   2     4.3   22.50  |   4.3   22.00  |   8.4   10.88  |   0.1 1080.00
   1     2.1   46.00  |   2.2   45.00  |   4.3   22.50  |   0.0      NA

   Number of Outs Given a Particular Hand to Improve
 Outs   Given                           In attempt to make
-----------------------------------------------------------------------
  15    Open Straight Flush Draw        Straight, Flush, Straight Flush
  12    Inside Straight Flush Draw      Straight, Flush, Straight Flush
   9    Flush Draw                      Flush
   8    Open Straight Draw              Straight
   4    Gut Shot Straight               Straight
   4    2 Pair                          Full House
   2    1 Pair                          Three of a kind
   1    Three of a Kind                 Four of a kind

G      B        P8          P7          P6          P5
0      0      0.1834      0.0849      0.0294      0.0058
1      2      0.0423      0.0181      0.0060      0.0012
2      1      0.1963      0.1072      0.0465      0.0125
2      2      0.0740      0.0370      0.0148      0.0037
3      0      0.4827      0.3325      0.1895      0.0715
3      1      0.3238      0.2091      0.1119      0.0398
3      2      0.1480      0.0888      0.0444      0.0148
4      0      0.7132      0.5872      0.4288      0.2343
4      1      0.5698      0.4496      0.3145      0.1647
4      2      0.3478      0.2609      0.1739      0.0870

  715     C(13,4)       all four cards in same suit
 2860     4*C(13,4)     two suits (3,1), no pairs
 2145     3*C(13,4)     two suits (2,2), no pairs
  858     13*C(12,2)    two suits (3,1), one pair
  858     13*C(12,2)    two suits (2,2), one pair
   78     C(13,2)       two suits (2,2), two pairs
 4290     6*C(13,4)     three suits, no pairs
 2574     13*3*C(12,2)  three suits, one pair
   78     C(13,2)       three suits, two pairs
  156     13*12         three suits, triplets
  715     C(13,4)       four suits, no pairs
  858     13*C(12,2)    four suits, one pair
   78     C(13,2)       four suits, two pairs
  156     13*12         four suits, triplets
   13     13            four suits, quads

16432                   total

                 Copyright 1998, 1999, Abdul Jalib
               Permission to copy for personal use.

[This is a technical report on play balancing.  If you are looking
for general concepts on how to play, you've come to the wrong place.]

I've been using Texas Turbo hold'em to examine preflop strategies
that disguise my holdings without sacrificing much expected value (EV)
to opponents who aren't paying attention anyway.  Turbo isn't
ideal for this task, but in any case, I mostly wanted to
share the general concepts of this approach.  The two main means I have
identified of avoiding giving away information preflop are:

  1) to impose general restrictions (e.g., never more than 3-bet)
  2) to make suboptimal plays within those restictions in order to
     balance the probabilities of the properties of your hands in
     different situations.

The easiest way to restrict your preflop opening play is to always make
the same initial play, either always open-limping or always open-calling
no matter what the hand.

OPEN-LIMPING

I tried to reduce preflop under the gun (UTG) strategy to just 3 options
for opening the pot and responding to subsequent action:

1. Open-limp, then raise if it's raised behind, but if it's
   raised and reraised behind then just call.
2. Open-limp, and if it's raised 1 or 2 (or more) times, then call.
3. Open-limp, and if it's raised once then call, but fold for two more bets.

Relative to also allowing similar open-raise options, Turbo simulations
estimate that this restricted strategy reduces EV UTG in a *tight*
10-handed $10-$20 game from $1.14 to $1.04 per hand.  The corresponding
always-open-raise strategy won $1.01.

Here are the 3 options again but with hands filled in, and these hands
have been juggled around a bit, making some suboptimal plays in order
to balance the information. Asterisks (*) denote hands to which I have
assigned suboptimal plays.

1. Open-limp, then raise if it's raised behind, but if it's
   raised and reraised behind then just call:
   QQ, JJ, TT, 99*, AKs, AQs, AJs*, KQs, QJs* AK

2. Open-limp, and if it's raised 1 or 2 (or maybe more) times, then call:
   AA*, KK*, 88, 77, ATs, JTs, T9s*, AQ

3. Open-limp, and if it's raised once then call, but fold for two more bets:
   66*, A9s, A8s, KJs, KTs, QTs*, J9s*, AJ, KQ*

With this restricted strategy, there are only 4 possible ways in which
I can see the flop:

A. I open limp, an opponent raises, I reraise.
=> I have a hand in group #1.

B. I open limp, an opponent raises, another opponent reraises, I call.
=> I have a hand in group #1 or group #2.

C. I open limp, an opponent raises, I call.
=> I have a hand in group #2 or group #3.

D. I open limp and nobody raises.
=> I have any playable hand: group #1, #2, or #3.

I'll try to quantify how much information I reveal by computing
various conditional probabilities:

                                 PREFLOP ACTION SCENARIO
                                    A    B    C    D
total number of distinct hands     10   18   17   27
% chance pocket pair               43   46   29   34
% chance suited                    36   31   35   35
% chance offsuit nonpair           21   23   35   30
% has pair >= 2 with 2 on board    43   46   29   34
% has pair >= 3 with 3 on board    43   46   29   34
% has pair >= 4 with 4 on board    43   46   29   34
% has pair >= 5 with 5 on board    43   46   29   34
% has pair >= 6 with 6 on board    43   46   27   33
% has pair >= 7 with 7 on board    43   45   21   29
% has pair >= 8 with 8 on board    43   39   18   27
% has pair >= 9 with 9 on board    40   36   21   28
% has pair >= T with T on board    28   37   28   28
% has pair >= J with J on board    29   31   31   31
% has pair >= Q with Q on board    24   35   35   31
% has pair >= K with K on board    29   25   26   27
% has pair >= A with A on board    36   36   33   34

Scenario D, where I limp in and no one raises, has the
same probabilities as the priors, since this strategy employs
open-limping with everything playable.  The differences in the
figures for the other scenarios show how much information I'm
giving away.  Note that the probability that I have a pair of
kings or better with a king on board remains nearly constant
across all the scenarios, and similarly constant for aces for
when an ace flops.  Thus I give away almost no information for
those particular cases.  In general, I'm trying to play each
hand fairly appropriately and yet give away minimal information
for each scenario.  The probabilities for having a pair
with a low board in scenarios A and B, where I put in 3 bets,
are a bit different from the probabilities for scenario C,
where I'm raised but elect not to reraise, but of course
giving away a certain amount of information is unavoidable.

All the changes I made would cost about 15 cents in the Turbo
simulation, bringing the EV down from $1.09 to $0.94.  The
limp-calling with aces and kings instead of limp-reraising is
responsible for almost half of this 15 cents in reduction.
Turbo players almost make little use of information from previous
rounds for future rounds.  Whether these sacrifices
to preserve information would be worthwhile against human
opponents is unknown.

OPEN-RAISING

If you want to consider open-raising all the time rather than open-limping,
then one problem is that there are very few hands that you can 4-bet with
after you've open-raised and it's been reraised - pretty much just
AA, KK, and QQ.  AKs, AQs, and AK can 4 bet with small losses (possibly
a profit in some games) relative to their optimal plays.  Avoiding the
4 bet play altogether, however, costs 4 cents.

1. Open-raise, then reraise if it's raised back to you:
   AA, KK, QQ, AKs*, AQs*, AK*

2. Open-raise, then call if it's 1 or 2 more bets bet:
   JJ, TT, 99, AJs, KQs, JTs

3. Open-raise, then call if it's 1 more bet back, fold for 2 more bets:
   88, 77, ATs, A9s, KJs, KTs, QJs, AQ, AJ, KQ*

There are four possible scenarios where I can see the flop:

A. I open raise, an opponent reraises, I cap it.
=> I have a hand in group #1.

B. I open raise, an opponent reraises, and another caps it, I call.
=> I have a hand in group #1 or #2.

C. I open raise, an opponent raises, I call.
=> I have a hand in group #2 or #3.

D. I open raise, and no one raises.
=> I have any playable hand (group #1, #2, or #3).

                                      PREFLOP ACTION SCENARIO
                                    A       B       C       D
total number of distinct hands      6      12      16      22
% chance pocket pair               47      53      31      35
% chance suited                    21      29      33      29
% chance offsuit nonpair           32      18      37      35
% has pair >= 2 with 2 on board    47      53      31      35
% has pair >= 3 with 3 on board    47      53      31      35
% has pair >= 4 with 4 on board    47      53      31      35
% has pair >= 5 with 5 on board    47      53      31      35
% has pair >= 6 with 6 on board    47      53      31      35
% has pair >= 7 with 7 on board    47      53      28      34
% has pair >= 8 with 8 on board    47      53      22      29
% has pair >= 9 with 9 on board    47      51      19      27
% has pair >= T with T on board    47      47      20      28
% has pair >= J with J on board    47      43      27      33
% has pair >= Q with Q on board    53      33      27      34
% has pair >= K with K on board    68      40      20      32
% has pair >= A with A on board    60      36      30      39

The modifications this time add up to about $.19, bringing
it down to $.90 per hand.  This is lower than the $0.94 of my open-limping
strategy, but it would be a mistake to place too much faith in the
simulation numbers, as it's hard to say whether the Turbo simulations
are realistic enough.  Mostly, I wanted to discuss the general concepts.
All the numbers in the tables are not simulation numbers, they're
exact computations, except for the hopefully small perturbations caused by
the fact that your opponents actions also convey information.  You
can use the same approach to evaluate, and balance, the preflop strategy
of your choosing.

The probability of having a pair of kings or better with
a king on board in scenario C is pretty low.  I'd suggest backing off
with AK versus a 3 bet about 1/3 of the time in order to boost scenario
C's king (and ace) pair probability.  This will actually save you some
money in raw theoretical terms too, since 4 betting with AK was a
suboptimal deviation in the first place.

As you can see by how different the columns in the table are from
each other and in particular from the last column (the priors),
this strategy gives away a ton of information.  Perhaps a better
job could be done in balancing the information.

BOTH OPEN-LIMPING AND OPEN-RAISING

Allowing both limps and raises for your opening causes problems.
First, you just inherently give away more information.  Second,
if you are going to limp-reraise with your best hands, then it's
hard for you to be able to call with your weaker hands when you
open-raise and it's raised and reraised behind you.

Here is an attempt to balance the hands for this case:

1. Open-raise, then call if it's 1 or 2 bets back:
   JJ, 99, 88, KQs, QJs*, KTs, QTs, JTs*, J9s*, T9s*, 98s*, AK

2. Open-raise, then call if it's 1 more bet back, fold for 2 more bets:
   77, AQ, AJ, KQ

3. Open-limp, then raise if it's raised back, but if it's raised twice
   make it four bets.
   QQ, TT, AKs, AQs*, AJs*

4. Open-limp, then if it's raised once call, but fold for two more bets.
   ATs*, A9s, A8s, A7s, KQs*, KJs,

5. Open-limp, then if it's raised once call, but if it's raised twice
   make it four bets.
   AA*, KK*

This strategy results in 6 preflop scenarios:

A. I open-raise, an opponent reraises, I call.
=> I have a hand in category #1 or #2.

B. I open-raise, two opponents reraise, I call.
=> I have a hand in category #1.

C. I open-raise, and nobody raises.
=> I have a hand in category #1 or #2.

D. I limp, an opponent raises, I call.
=> I have a hand in category #4 or #5.

E. I limp, two opponents raise, I reraise.
=> I have a hand in category #3 or #5.

F. I limp, and nobody raises.
=> I have a hand in category #3, #4, or #5

                                             PREFLOP ACTION SCENARIO
                                  Prior   A     B     C     D     E    F
total number of distinct hands     29    16    12   same    8     7   13
% chance pocket pair               29    23    29    as    33    67   40
% chance suited                    41    31    52     A    67    33   60
% chance offsuit nonpair           29    46    19           0     0    0
% has pair >= 2 with 2 on board    29    23    29          33    67   40
% has pair >= 3 with 3 on board    29    23    29          33    67   40
% has pair >= 4 with 4 on board    29    23    29          33    67   40
% has pair >= 5 with 5 on board    29    23    29          33    67   40
% has pair >= 6 with 6 on board    29    23    29          33    67   40
% has pair >= 7 with 7 on board    30 21 29 43 67 46
% has pair >= 8 with 8 on board    28    18    31          43    67   46
% has pair >= 9 with 9 on board    29    18    32          43    67   46
% has pair >= T with T on board    27    18    31          43    64   43
% has pair >= J with J on board    29    22    21          43    60   41
% has pair >= Q with Q on board    32    28    15          43    56   38
% has pair >= K with K on board    28    25    26          48    38   33
% has pair >= A with A on board    35    28    15          52    40   48

Again, you shouldn't place too much faith in this strategy from Turbo,
as it was based on a small number of trials and Turbo is not totally
realistic.  I don't think the hands are well balanced to avoid
information leakage.  In general, it's going to be hard to balance
six different scenarios.  On the other hand, this approach gets a lot
of bets into the pot at times.

This strategy results in an EV of $1.00, just 9 cents down from
optimal, and actually this is without 4-betting, so it actually
does better than $1.00.  But it does give away tons of information.

COMPARISON TO S&M PREFLOP STRATEGY

S&M recommend a mix of raising, limp-reraising, and limping,
with some mixing of those plays for individual hands.  For
example, they recommend open-raising with T9s 1/3 of the time,
limping the other 2/3's, in early position.  Perhaps you could
open-raise and open-limp without giving away much information
if you mixed up which you did on many particular hands.  You'd
have to be careful, however, and the systematic procedure I've
presented should help you develop a mixed preflop strategy that
hides information.

I think S&M are generally wrong in their overall preflop
game plan in tight games.  S&M suggest raising with your really
strong hands (AA, KK, QQ) and often limping with your
marginal hands (JTs, T9s, 88.)  It shouldn't be hard to see
why this is a mistake in a tight game.  In a tight game, you've
got a good shot at taking down the blinds if you raise.  If you
succeed, you win $15.  This is a disaster for AA, KK, and QQ,
which have EV's in excess of $20, pushing $60 for AA, according to
Turbo.  (And in fact Mason Malmuth seems to realize this, having advocated
in a recent 2+2 forum article open-limping with AA UTG in a very tight
game, if I recall correctly.)  Stealing the blinds is a huge coup for
maginal hands like JTs, T9s, and 88.  Therefore, if you don't have to worry
about giving away information, then you should actually open-limp (and
then reraise) with your huge hands, and open-raise with your weak hands,
in tight games.  Aside from the hand-waving argument, that's what the
Turbo simulation results suggest.  On the other hand, in many loose games
you should open-raise with your AA, as the idiots will call 2 bets cold
almost as readily as 1 bet.

CONCLUSIONS

Perhaps this whole exercise seems exceedingly paranoid to you.
After all, how many opponents watch your play that carefully?  Well,
I play against a lot of the same people a lot of the time, and some
of them are pretty sharp.  It's quite likely that some of them could
pick up some partial heuristics, such as knowing when I'm not too
likely to have a king based on my actions, that would allow them to
use some of the information I'm giving away.  And even if my opponents
are mostly unconscious in the $20-$40 games I find myself playing most
of the time now, I always try to gear my game for my ultimate goal of
playing much higher games against much stiffer competition.

Perhaps this whole exercise seems exceedingly anal to you.
After all, shouldn't our play be constantly changing depending upon
the exact circumstances?  I can't really argue with that, but you
have to first make yourself undefeatable before you worry about
defeating the enemy, and so you have to worry about information
leakage.

10% rake to $4, $1 toke
      Est. Total Hourly
Limit Expense (Big Bets)
----- -----------------
10-20 0.76 to 0.88
5-10  1.23 to 1.66
3-6   1.91 to 2.62
2-4   2.25 to 3.50

5% rake to $3, $0 toke
Est.  Total Hourly
Limit Expense (BB)
----- ------------
10-20 0.45 and up
5-10  0.55 and up
3-6   0.58 and up
2-4   0.53 and up

    irc nickname irc.poker.net
or      irc nickname 24.163.47.154

    /list

    /names

    /join #holdem

    p fold

    p commands

    p join password         % join the game (pick any password)
                            % this starts your bankroll at $1000
    p quit                  % quit the game
    p fold                  % fold when the action gets to you
    p check                 % check (do not bet or fold)
    p call                  % call a bet
    p raise                 % raise the bet

    p raise 50

    /msg hbot p raise

TP = Tight Player
STP = Semi-Tight Player
LP = Loose Player
AGG = Aggressive
PSV = Passive
PR = Hands that opponent pre-flop raises
P = Hands that opponent plays or limps in with
PP = Pocket Pair
FF = Face cards
RR = Rags
+ (denotes "better or bigger than")
- (denotes "worse or lesser than")

LP, AGG
PR: +PP, -PP, FF
P: A2s, 65s, 73s, 42o, QT

Raise and call 2	QQ JJ TT KQs KTs JTs
Raise and call 1	77 QJs KJs AQ AJ
Limp-reraise / raise & call	AKs AQs AK
Limp & call 1	66 55 A9s A8s A7s KQ
Limp-reraise	AA KK 99 88 AJs ATs

QQ	Raise to add support, but limp-reraise is more immediately profitable.
55	Limp if (and only if) you limp-reraise often with other hands.
ATs	Limp-reraise, scaring AQ and AJ in the process.
76s	Fold. A raise would be better than a call, though, to steal the blinds.
AQ	Raise, for win share and to get heads up.
JT	Fold. Dominated. Even KQ is debatable.

Limp-call 2 / raise & reraise	99 88
Limp-reraise / raise & reraise	AK AKs
Raise & reraise	AA KK
Raise & call 2	A5s A4s A3s KQs AQ
Raise & call 1	AJ KQ
Limp & call 1	QJs JTs QTs 66
Limp & call 2	ATs A9s A8s A7s A6s KJs KTs 77
Limp-reraise	QQ JJ TT AQs AJs

QQ	Limp-reraise, except raise in very loose/passive games.
55	Borderline call/fold. Play if you can see flop cheaply.
ATs	Limp and call all raises, fearing that raises indicate AK, AQ, or AJ.
76s	Fold, but it's close for very loose-passive games.
AQ	Raise to destroy the implied odds of the fish and narrow the field.
JT	Fold. Dominated. KJ & QJ suffice in very passive games with no rake.

QQ	Raise. No one is likely to raise for you. Provide cover to steals.
55	Raise if you can get heads up, call if you can get 4 callers, else fold.
ATs	Limp-reraise if you are limp-reraising with AA and KK, else raise.
76s	Fold. Likely dominated downstream. Cannot count on enough callers.
AQ	Raise, for the same reason as early position.
JT	Fold. You'd need a minimum offsuit of about KJ or QJ to open here.

Opening Hand Rankings and Minimum Openers
# Off Button	Pairs	Suited Hands							Offsuit Hands							# Off Button
	AA
	KK
	QQ
	JJ	AKs
	TT	AQs							AK
	99	AJs							AQ
6	88	ATs	KQs													6
5	77	A9s	KJs	QJs					AJ							5
4	66	A8s	KTs	QTs	JTs				AT	KQ						4
3	55	A7s	K9s		T9s	J9s				KJ	QJ					3
2	44	A3s	K7s	Q9s	98s	T8s			A9							2
1	33	A2s	K6s	Q8s	87s	97s	J8s		A7	KT	QT	JT				1
0	22		K2s	Q4s	65s	75s	T7s		A3	K7	Q9	98	J9			0
SB				Q2s	32s	42s	52s	Xxs	A2	K2	Q2	43	53	63	Jx	SB

QQ	Raise. It is too conspicuous to limp here.
55	Raise. Your pair is quite strong here, if you get heads up.
ATs	Raise.
76s	Borderline raise/fold. Laying odds. Fold versus loose small blind.
AQ	Raise. This is a monster. A3 would suffice.
JT	Raise. On the button or one off it is likely best, barely.

QQ	Raise. No need to worry about stealing blinds. Calling is a mistake.
55	Borderline fold. Unlikely to get heads-up and cannot get 4 callers.
ATs	Call. Proceed with caution if you flop an ace for fear of limping AJ.
76s	Fold. Similar to 55 case. Borderline fold/call versus 3 tight limpers.
AQ	Raise. Same with AJ and KQ. Your hand is likely best. Get heads up.
JT	Fold. Dominated. Fold QJ/KJ too. Calling here is a huge mistake.

QQ	Raise. You will win the pot more than your fair share, though < 50%.
55	Call. About 8-way to flop, but it will win less than 1 in 8 times.
ATs	Raise. Big suited's win more than their fair share in multiway pots.
76s	Raise. Even suited zero gappers win more than their fair share here.
AQ	Raise. Your hand is likely best, by far.
JT	Fold. If you want to play offsuit cards, you must have the best.

QQ	Call, for fear of AA, KK, or losing to something like AK.
55	Fold. You need about 99 to call, two levels higher than his 77.
ATs	Fold. Dominated. You could call with AQs, barely.
76s	Fold. Implied odds are shot to hell. JTs/QJs/KQs should fold too.
AQ	Fold. Against looser raises you could call. See AQs note under ATs.
JT	Fold, unless you are a fish.

QQ	Reraise. You do not fear AA or KK here.
55	Reraise. Your hand plays much better heads up than 3-way.
ATs	Borderline call/reraise. For fear of AJ, AJs is the first safe reraise.
76s	Borderline reraise/fold. Your hand plays better heads up than 3-way.
AQ	Reraise. Keep it heads-up for best chance of winning unimproved.
JT	Borderline fold. Could call versus an even looser raise.

QQ	Call. Go for check-raise on the flop.
55	Call. Do not necessarily give up if you do not flop a set.
ATs	Call. On flop play hard except check-call when ace flops.
76s	Call. Check-raise the flop if you have a draw or flop a pair.
AQ	Call. Consider a check-raise on the flop even if you miss.
JT	Call. Proceed with caution if you flop a pair.

Blind Size	Example
1/3	$2 blind in $6-$12 with $2 and $6 blinds
1/2	$5 blind in $10-$20 with $5 and $10 blinds
2/3	$10 blind in $15-$30 with $10 and $15 blinds

QQ	Raise. Calling would give the big blind a free shot to beat you.
55	Call. A raise will be unlikely to get rid of the big blind.
ATs	Borderline raise/call. Call when you have to put in 2/3's of a bet.
76s	Borderline call/fold. Fold for 2/3 bet, since 3-way is bad.
AQ	Raise. You want to be heads up so you can win unimproved.
JT	Call for 1/2 or 1/3 of a bet, fold for 2/3 of a bet. Be careful.

QQ	Raise, for the same reason you would normally after limpers.
55	Call. See if you flop your set before investing more.
ATs	Raise, for the same reason as in late position after limpers.
76s	Call. Harder to win pot out of position so may not win fair share.
AQ	Raise, as you will win more than your fair share.
JT	Call. You certainly cannot raise. Enough of a discount to call.

Betting or Raising Breakeven Win Chance & Outs for # of Opponents
# Opponents Who Will Be Calling	Chance to Win You Need to be Breakeven on Bet	Corresponding Number of Outs
1	1 in 2	23
2	1 in 3	15 1/3
3	1 in 4	11 1/2
4	1 in 5	9 1/5
5	1 in 6	7 2/3
6	1 in 7	6 1/2
7	1 in 8	5 3/4
8	1 in 9	5 1/9

Event	Date	Buy-in	Event	Notes
#1	Apr 22	$500.00	Casino Employee's Limit Hold'em	One Day Event
#2	Apr 23	$2,000.00	No-Limit Hold'em	Two Day Event
#3	Apr 24	$1,500.00	Seven Card Stud	Two Day Event
#4	Apr 25	$1,500.00	Limit Hold'em	Two Day Event
#5	Apr 26	$1,500.00	Omaha Hi-Lo Split	Two Day Event
#6	Apr 27	$1,500.00	Pot Limit Hold'em	Two Day Event
#7	Apr 28	$1,000.00	No-Limit Hold'em with Rebuys (First Two Hours)	Two Day Event
#8	Apr 29	$2,000.00	Pot Limit Omaha with Rebuys (First Two Hours)	Two Day Event
#9	Apr 30	$1,500.00	No-Limit Hold'em	Two Day Event
#10	May 1	$2,000.00	Seven Card Stud Hi-Lo Split	Two Day Event
#11	May 2	$2,500.00	Limit Hold'em	Two Day Event
#12	May 3	$2,000.00	H.O.R.S.E. (Hold'em, Omaha, Razz, Stud, Stud/ 8)	Two Day Event
#13	May 4	$5,000.00	No-Limit Hold'em	Two Day Event
#14	May 5	$1,500.00	Seven Card Stud Hi-Lo Split	Two Day Event
#15	May 6	$2,000.00	Limit Hold'em	Two Day Event
#16	May 7	$5,000.00	No-Limit Deuce to Seven Draw with Rebuys	One Day Event
#17	May 7	$1,500.00	Limit Hold'em Shootout@ 2pm	Two Day Event
#18	May 8	$1,500.00	No-Limit Hold'em Shootout	Two Day Event
#19	May 9	$2,000.00	Omaha Hi-Lo Split	Two Day Event
#20	May 9	$1,000.00	Ladies Limit Hold'em @ 2pm	Two Day Event
#21	May 10	$2,000.00	Pot Limit Hold'em	Two Day Event
#22	May 11	$5,000.00	Omaha Hi-Lo Split World Championship	Two Day Event
#23	May 12	$1,500.00	No Limit Hold'em	Two Day Event
#24	May 13	$5,000.00	Seven Card Stud World Championship	Two Day Event
#25	May 14	$3,000.00	Pot Limit Hold'em	Two Day Event
#26	May 15	$1,500.00	Seven Card Razz	Two Day Event
#27	May 16	$1,000.00	Deuce to Seven Triple Draw with Rebuys	One Day Event
#28	May 16	$1,000.00	Seniors No-Limit Hold'em @ 2pm	Two Day Event
#29	May 17	$5,000.00	Limit Hold'em	Two Day Event
#30	May 18	$3,000.00	No-Limit Hold'em	Two Day Event
#31	May 19	$5,000.00	Pot Limit Omaha with Rebuys (First Two Hours)	Two Day Event
#32	May 20	$1,500.00	A-5 Draw Lowball	One Day Event
	May 21	$225/ $200	4 Super Satellites 10am-3pm-7:45pm and 11pm	Win your $10,000 Seat
	May 21		Media Charity No-Limit @ 6pm	Media Only
#33	May 22	$10,000.00	No Limit Hold'em World Championship Event @ 1PM	5 Full Levels 1/2 Field
	May 23		World Championship Event- Day 2	5 Full Levels 1/2 Field
	May 24		World Championship Event- Day 3	4 Full Levels
	May 25		World Championship Event- Day 4	4 Full Levels
	May 26		World Championship Event- Day 5	Play to 36
	May 27		World Championship Event- Day 6	Play to 9

Total Buy-in	Breakdown: Prize pool plus house fee	House "Percentage"	House percentage defined as juice over buy-in	Dealer/staff toke deducted from prize pool
$500	$465 + $35	7.00%	7.53%	3.00%
$1,000	$940 + $60	6.00%	6.38%	3.00%
$1,500	$1420 + $80	5.00%	5.63%	3.00%
$2,000	$1900 + $100	5.00%	5.26%	3.00%
$2,500	$2375 + $125	5.00%	5.26%	3.00%
$3,000	$2850 + $150	5.00%	5.26%	3.00%
$5,000	$4800 + $200	4.00%	4.17%	2.00%
$10,000	$9600 + $400	4.00%	4.17%	2.00%

Outs When Drawing One Card
Draw on the Turn	Outs
4-straight & 4-flush => straight or flush	15
set => full house or quads	10
4-flush => flush	9
overpair vs 2-pair => better 2-pair or set	8
4-straight => straight	8
4-straight vs 4-flush => straight vs no flush	6
overcards => top pair	6
pair using board card => trips or two pair	5
gutshot straight draw => straight	4
two pair => full house	4
pocket pair => set	2

Equivalent Outs When Drawing Two Cards
Draw on the Flop and Turn	Outs
4-straight & 4-flush => straight or flush	25 1/2
set => full house or quads	15 1/2
4-nut-flush => nut flush	16 1/2
4-baby-flush vs. one => 5-flush	15
4-straight => straight	14 1/2
overpair vs 2-pair => 2-pair, set, etc	12 1/2
4-baby-flush vs. many => only 5-flush	12
nonpair => pair	11 1/2
gut shot straight draw => straight	7 1/2
two pair => strong full house or quads	7
3-straight & 3-flush => straight or flush	3
3-flush => flush	1 1/2
3-straight => 4-straight => straight	1 1/2

Acting in Turn

Handling Cards

Protecting Cards

Accidentally Checking

String Bets

Splashing the Pot

One Chip Rule

Raising Forever

The Showdown

Raking in the Pot

Touching Cards or Chips

Tipping

Correcting Mistakes

Taking a Break

Color Change

Leaving

House Charges

Online Poker Etiquette

Basics

Variations

The Chip Race

Winning

Satellites

Schedules

Tournament Strategy

Tournament Structures

Online Tournaments

Commercial Programs

Exact Enumeration Calculators

Pokersource (Source Code)

Hotpoker (formerly Netpoker)

0. Table Selection.

1. Hand selection

2. Reading opponents' hands

3. Opponent assessment

4. Heads up play, semi-bluffing, and bluffing

5. Seat selection

6. Check-raising

7. Getting tells

8. Pot odds calculations

Before the Tournament

The Early Stages

The Middle/Late Stages

The Final Stage

WSOP 2004 Event Schedule

House Fees, Dealer and Staff Tokes

1. Choosing The Right Stakes

2. The rules of Texas Hold'em bankroll management

No Limit Cash Games

Limit Cash Games

Sit and Go Tournaments

Multi Table Tournaments

3) Important points of bankroll management

4) Moving Limits

Reading high quality Poker books

General strategy books

No Limit Texas Hold'em

Limit Texas Hold'em

Strategy discussions on Poker forums

Using tracking software to analyse your play

Plenty of practice

Options for playing poker on Ubuntu.

(1) No download poker rooms for Ubuntu.

(2) Using Wine to download and run poker room clients on Ubuntu.

How well do poker rooms run on Ubuntu?

Is it safe to play for real money?

Which method is best?

Will there ever be a poker room client developed specifically for Ubuntu users?

What are Player Notes?

How to effectively take notes?

Using acronyms to save space

Expert note tips

Conclusion