Sunday, March 22, 2009

Suited Aces EV, posted en masse

Under the Gun EV
for Suited Aces
(100K Trials)
Starting
Hand
Open
Call
Open
Raise
A9s-0.110.15
A8s-0.47-0.31
A7s-0.56-0.53
A6s-0.87-0.87
A5s-1.04-0.80
A4s-1.08-0.89
A3s-1.22-1.09
A2s-1.24-1.18


Early Position EV for Suited Aces (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
A9s0.150.530.470.91-2.09-4.10
A8s-0.130.050.130.52-2.28-4.36
A7s-0.46-0.26-0.030.11-2.44-4.29
A6s-0.74-0.66-0.21-0.13-2.46-4.43
A5s-0.69-0.48-0.24-0.12-2.28-4.09
A4s-0.93-0.58-0.46-0.33-2.42-4.15
A3s-0.93-0.77-0.48-0.43-2.47-4.12
A2s-1.19-0.81-0.76-0.49-2.57-4.14


Middle Position EV for Suited Aces (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
A9s0.200.520.771.18-1.56-2.22
A8s-0.140.130.330.62-1.83-2.47
A7s-0.58-0.260.020.22-1.96-2.86
A6s-0.69-0.55-0.130.05-2.03-2.97
A5s-0.87-0.33-0.110.11-1.94-2.47
A4s-0.96-0.66-0.31-0.09-2.03-2.78
A3s-1.04-0.79-0.42-0.36-2.08-2.84
A2s-1.15-0.81-0.60-0.49-2.29-3.02


Late Position EV for Suited Aces (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
A9s0.861.040.701.37-1.13-1.41
A8s0.390.750.360.89-1.40-1.92
A7s0.170.380.120.58-1.67-2.13
A6s-0.100.170.080.30-1.80-2.51
A5s-0.040.14-0.010.47-1.75-2.21
A4s-0.170.03-0.300.25-1.79-2.27
A3s-0.31-0.02-0.290.00-1.80-2.47
A2s-0.33-0.23-0.460.02-1.99-2.47


EV on the Button for Suited Aces (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
A9s0.971.350.811.61-1.31-2.07
A8s0.621.020.291.02-1.75-2.52
A7s0.400.810.110.72-2.06-2.86
A6s0.300.67-0.100.46-2.07-2.97
A5s0.290.590.010.54-1.87-2.70
A4s0.140.57-0.200.18-1.84-2.85
A3s0.060.42-0.320.01-2.03-2.78
A2s-0.140.35-0.41-0.11-2.17-2.94


Small Blind EV for Suited Aces
(100K Trials and Baseline -1.00)
Starting
Hand
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
A9s0.161.39-1.57-1.56
A8s-0.160.74-1.94-1.86
A7s-0.390.28-2.20-2.22
A6s-0.72-0.17-2.21-2.22
A5s-0.66-0.19-2.23-2.27
A4s-0.86-0.44-2.26-2.32
A3s-0.81-0.36-2.32-2.04
A2s-0.91-0.72-2.47-2.17



Big Blind EV
for Suited Aces
(100K Trials and Baseline -3.00)
Starting
Hand
Cold
Call
Reraise
A9s-2.45-2.48
A8s-2.71-3.13
A7s-2.96-3.44
A6s-2.90-3.42
A5s-2.83-3.50
A4s-3.00-3.34
A3s-3.19-3.62
A2s-3.17-3.64

Monday, March 9, 2009

Big Blind EV for offsuit broadways

As always in 3/6 hold'em, the baseline EV for the big blind is not 0.00 but -3.00.

Big Blind EV for Offsuit Broadways (100K Trials)
Starting
Hand
Cold
Call
Reraise
AKo0.291.59
AQo-1.47-0.86
AJo-2.35-2.54
A10o-3.22-3.40
KQo-2.90-3.14
KJo-2.85-3.12
K10o-3.19-3.64
QJo-3.01-3.35
Q10o-3.37-3.84
J10o-3.13-3.77

Small Blind EV for offsuit broadways

As always in 3/6 hold'em, the baseline for profitability from the small blind is not 0.00 but -1.00.

Small Blind EV for Offsuit Broadways (100K Trials)
Starting
Hand
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
AKo0.612.901.422.17
AQo0.252.22-0.320.00
AJo-0.191.38-0.48-1.17
A10o-0.270.86-2.19-2.05
KQo-0.590.74-1.68-1.67
KJo-0.330.50-2.18-1.86
K10o-0.63-0.13-2.56-2.40
QJo-0.55-0.02-2.37-2.28
Q10o-0.92-0.37-2.77-2.50
J10o-0.79-0.44-2.57-2.51

Sunday, March 8, 2009

EV for offsuit broadways on the button

EV for Offsuit Broadways on the Button (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
AKo1.802.561.783.951.361.77
AQo1.252.051.113.11-0.54-0.81
AJo0.921.700.602.42-1.71-2.33
A10o0.851.440.491.52-2.23-3.01
KQo0.581.070.191.38-2.10-3.18
KJo0.771.000.410.84-2.12-3.02
K10o0.460.700.010.23-2.53-3.53
QJo0.650.700.210.54-2.39-3.57
Q10o0.330.69-0.26-0.20-2.59-3.81
J10o0.290.50-0.28-0.25-2.59-3.52

Late Position EV for offsuit broadways

Late Position EV for Offsuit Broadways (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
AKo1.962.811.843.451.482.17
AQo1.171.990.772.35-0.450.10
AJo0.701.570.251.80-1.43-1.52
A10o0.661.130.160.90-2.05-2.09
KQo0.250.620.000.91-1.82-2.33
KJo0.410.68-0.230.39-1.83-2.70
K10o0.080.29-0.23-0.32-2.42-3.01
QJo0.080.45-0.08-0.08-2.13-2.66
Q10o-0.100.07-0.49-0.68-2.52-3.42
J10o-0.30-0.15-0.58-0.77-2.33-3.19

Saturday, March 7, 2009

Middle Position EV for offsuit broadways

Middle Position EV for Offsuit Broadways (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
AKo2.402.702.162.760.761.99
AQo0.531.520.481.78-1.14-0.33
AJo0.010.780.071.17-2.21-2.21
A10o-0.180.54-0.160.62-2.71-2.94
KQo-0.460.120.010.33-2.75-3.07
KJo-0.28-0.05-0.060.15-2.66-3.50
K10o-0.63-0.46-0.43-0.64-2.81-3.85
QJo-0.43-0.34-0.31-0.30-2.78-3.81
Q10o-0.78-0.52-0.84-0.97-3.02-4.04
J10o-0.88-0.74-0.87-0.94-2.82-3.69

Friday, March 6, 2009

Early Position EV for offsuit broadways

Early Position EV for Offsuit Broadways (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
AKo1.292.291.082.42-0.030.38
AQo0.341.360.331.70-2.28-2.60
AJo-0.200.60-0.250.94-3.42-4.60
A10o-0.260.22-0.540.25-3.38-4.82
KQo-0.47-0.39-0.64-0.13-3.82-5.17
KJo-0.32-0.32-0.44-0.64-3.00-4.38
K10o-0.82-0.81-1.11-1.10-3.29-4.68
QJo-0.68-0.72-0.96-0.83-3.24-4.69
Q10o-1.06-0.88-1.34-1.68-3.41-4.70
J10o-1.19-0.99-1.52-1.70-3.11-4.45

Thursday, March 5, 2009

Under the Gun EV for offsuit broadways

Moving along to offsuit broadways:

UTG EV for
Offsuit Broadways
(100K Trials)
Starting
Hand
Open
Call
Open
Raise
AKo1.172.13
AQo0.201.02
AJo-0.410.24
A10o-0.59-0.13
KQo-0.85-0.72
KJo-0.65-0.56
K10o-0.96-1.06
QJo-0.91-0.87
Q10o-1.36-1.30
J10o-1.34-1.37

Wednesday, March 4, 2009

Big Blind EV for suited broadways

Remember that for the big blind, our baseline for profitability isn't 0.00 but -3.00, since the cost of folding to a raise in the big blind is $3, thus any hand that we play against a raise must net better than -3.00.


Big Blind EV for
Suited Broadways (100K Trials)
Starting
Hand
Cold
Call
Reraise
AKs1.533.21
AQs0.110.78
AJs-1.23-0.67
A10s-1.72-1.54
KQs-1.64-1.47
KJs-1.63-1.39
K10s-1.95-2.09
QJs-1.91-1.72
Q10s-2.11-2.27
J10s-2.11-2.26

Tuesday, March 3, 2009

Small Blind EV for suited broadways

Remember that for small blind hands, our baseline fr profitability isn't 0.00, but -1.00, since we receive a net loss of $1 every time we fold preflop in the small blind and we must net above that to make playing the hand profitable.

Small Blind EV for Suited Broadways (100K Trials)
Starting
Hand
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
AKs1.764.292.793.60
AQs1.173.580.971.67
AJs0.973.020.620.59
A10s0.822.35-0.69-0.67
KQs0.412.18-0.18-0.20
KJs0.561.88-0.80-0.54
K10s0.291.17-1.41-1.02
QJs0.241.59-1.08-0.98
Q10s-0.020.65-1.44-1.37
J10s-0.110.47-1.45-1.16

Sunday, March 1, 2009

EV for suited broadways on the button

EV for Suited Broadways on the Button (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
AKs2.263.153.045.282.653.68
AQs1.772.602.204.471.031.09
AJs1.442.221.953.82-0.32-0.54
A10s1.551.911.652.81-0.72-1.19
KQs0.971.601.452.71-0.68-1.45
KJs1.211.361.372.42-0.82-1.77
K10s1.021.011.051.61-1.18-2.04
QJs1.161.381.051.84-1.20-2.17
Q10s0.910.840.621.12-1.36-2.04
J10s0.880.930.571.01-1.30-1.92

Friday, February 27, 2009

Late Position EV for Suited Broadways

Late Position EV for Suited Broadways (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
AKs2.843.593.214.952.893.66
AQs2.122.852.354.031.161.46
AJs1.592.311.683.260.300.13
A10s1.381.961.542.50-0.48-0.32
KQs1.081.541.322.30-0.41-0.73
KJs1.091.271.181.93-0.58-0.98
K10s0.830.890.881.19-0.84-1.64
QJs0.881.111.041.47-0.87-1.22
Q10s0.650.740.550.59-1.03-1.45
J10s0.520.560.450.47-1.25-1.46

Wednesday, February 25, 2009

Middle Position EV for Suited Broadways

(This will be the last post today. Late Position and subsequent trials will post tomorrow.)

Middle Position EV for Suited Broadways (100K Trials)
Starting
Hands
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
3bet
Raiser
AKs3.623.494.034.492.512.96
AQs2.462.592.943.540.810.98
AJs1.272.001.762.91-0.39-0.36
A10s0.951.571.462.45-0.86-1.23
KQs0.921.061.441.86-0.90-1.03
KJs0.811.011.351.47-0.96-1.72
K10s0.450.520.741.01-1.41-2.15
QJs0.490.620.951.34-1.31-1.96
Q10s0.190.240.590.53-1.48-2.42
J10s0.130.080.370.44-1.57-2.26

Early Position EV for Suited Broadways

Early Position EV for Suited Broadways (100K Trials)
Starting
Hands
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
3bet
Raiser
AKs3.533.343.644.291.872.17
AQs1.722.372.263.28-0.42-0.85
AJs1.441.881.582.54-1.40-2.55
A10s1.081.381.272.06-1.61-3.07
KQs0.680.911.021.37-1.99-3.54
KJs0.840.740.850.92-1.36-2.78
K10s0.220.240.250.29-1.60-2.89
QJs0.390.360.380.66-1.64-2.89
Q10s0.050.01-0.05-0.10-1.69-3.04
J10s0.05-0.09-0.23-0.52-1.41-2.77

UTG Expected Value for Suited Broadways

Let's move along to suited Broadways: any two unpaired cards ten or higher, such as Ace-King or Jack-Ten, with matching suits.

We will begin our trials from under the gun, and proceed around the horn.

Under the Gun EV
for Suited Broadways
(100K Trials)
Starting HandsOpen CallOpen Raise
AKs3.413.18
AQs1.492.11
AJs1.151.36
A10s0.811.05
KQs0.430.73
KJs0.490.53
K10s0.160.03
QJs0.320.33
Q10s-0.78-0.19
J10s-0.37-0.06

Tuesday, February 24, 2009

EV for Pocket Pairs from the Big Blind when raised

Since we can check and see the flop in unraised pots from the Big Blind, we will only concern ourselves with hands where we're raised. Here, as before with the small blind, our baseline is not 0.00, since we have $3 invested before the cards are dealt. Thus our baseline is -3.00. To play a hand, the EV must be greater than -3.00.

EV for Pocket Pairs
Big Blind (100k Trials)
Starting
Hand
Cold
Call
3-Bet
Raiser
AA12.4917.28
KK6.739.36
QQ3.455.49
JJ1.062.18
TT-0.420.24
99-1.48-1.04
88-2.08-1.74
77-2.24-2.45
66-2.51-2.75
55-2.71-3.01
44-2.90-3.25
33-2.99-3.72
22-3.17-3.92

EV for Pocket Pairs in the Small Blind

Keep in mind here that, unlike the other positions, where we can fold without investing a single dollar in the pot, we are forced to invest $1 in the small blind every time in a 3/6 game. Therefore we are looking not for hands whose EV is above 0.00, but whose EV is above -1.00, the net result when we fold our hand in the small blind.

EV for Pocket Pairs
Small Blind (100k Trials)
Starting
Hand
Limp
Behind
Raise
Limpers
Cold
Call
3-Bet
Raiser
AA8.0912.5113.2415.81
KK5.078.707.449.00
QQ3.676.694.435.62
JJ2.234.872.182.63
TT1.223.340.561.02
990.081.73-0.55-0.33
88-0.590.78-1.17-1.04
77-1.12-0.02-1.77-1.68
66-1.52-1.04-2.12-1.98
55-1.87-1.43-2.56-2.40
44-2.13-1.93-1.89-2.49
33-2.51-2.22-1.94-2.67
22-2.78-2.58-2.08-3.00

Monday, February 23, 2009

EV for Pocket Pairs on the Button

EV for Pocket Pairs on the Button (100k Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
3-Bet
Raiser
AA6.497.049.9814.1514.8618.32
KK4.304.956.8610.478.109.80
QQ3.373.915.127.914.525.24
JJ2.653.103.526.062.082.23
TT1.952.362.584.270.750.82
991.331.671.422.76-0.10-0.47
880.830.990.821.87-0.63-1.34
770.310.380.291.15-0.98-1.58
66-0.090.080.030.66-1.14-1.93
55-0.45-0.30-0.290.13-1.44-2.35
44-0.78-0.59-0.54-0.35-1.67-2.52
33-1.04-0.91-0.68-0.56-1.80-2.78
22-1.27-1.10-0.82-0.79-1.96-2.67

Saturday, February 21, 2009

Late Position EV for Pocket Pairs

Again, cumulative notes to follow later.

Late Position EV for Pocket Pairs (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
3-Bet
Raiser
AA8.588.9611.4014.2714.9117.70
KK5.576.277.3010.528.4510.04
QQ4.234.845.318.034.945.87
JJ3.033.503.535.762.813.11
TT2.022.512.423.991.051.46
991.341.491.162.370.04-0.02
880.520.760.571.37-0.60-0.66
77-0.020.21-0.010.69-0.87-1.33
66-0.52-0.13-0.080.39-1.07-1.54
55-0.89-0.67-0.32-0.17-1.39-2.08
44-1.22-0.99-0.69-0.49-1.64-2.15
33-1.35-1.08-0.85-0.75-1.85-2.41
22-1.66-1.22-1.02-0.88-1.88-2.49

Thursday, February 19, 2009

Middle position EV trials

Notes to follow at a later date.

Middle Position EV for Pocket Pairs (100K Trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
Reraise
AA11.9510.7613.8614.7516.5817.89
KK6.827.378.3310.419.1010.21
QQ4.735.136.167.764.885.71
JJ3.343.553.865.252.192.72
TT1.952.412.263.400.630.49
990.851.391.061.73-0.29-0.81
88-0.090.550.380.88-0.92-1.32
77-0.59-0.46-0.180.30-1.43-2.04
66-1.07-0.73-0.30-0.07-1.56-2.27
55-1.48-1.19-0.74-0.42-1.86-2.58
44-1.74-1.49-0.85-0.92-2.01-2.74
33-2.05-1.70-1.11-1.07-2.09-2.88
22-2.22-2.04-1.43-1.54-2.17-2.97

Friday, February 13, 2009

Early position trial results with notes

Early Position Expected Values
for Pocket Pairs (100,000 trials)
Starting
Hand
Open
Call
Open
Raise
Limp
Behind
Raise
Limpers
Cold
Call
3-bet vs
Raise
AA12.8811.2914.5714.8917.9718.91
KK7.077.568.5610.569.7210.36
QQ4.885.165.937.264.894.83
JJ3.083.373.404.861.921.83
TT1.672.081.742.690.00-0.39
990.260.860.981.49-1.08-2.07
88-0.160.120.360.83-1.79-3.14
77-0.77-0.33-0.110.07-2.19-3.64
66-1.14-0.75-0.40-0.41-2.15-3.82
55-1.43-1.25-0.74-0.48-2.37-3.98
44-1.66-1.33-0.81-0.89-2.60-4.32
33-1.86-1.57-1.03-1.08-2.54-4.34
22-2.03-2.02-1.18-1.20-2.70-4.37


- Once again, open limping AA carries greater value than open raising, but once we see action in front, AA once again profits most from raising. It appears the key to AA's success is to ensure you have some action, which open limping does.

- Open raising remains the supreme play for all other playable pairs when facing one bet.

- Open raising is profitable until we get down to the marginally profitable 88. The smaller the profit, the smaller the margin for error. Playing 88 the slightest bit unprofitably can turn it into an unprofitable hand.

- Likewise, against limpers, pairs are profitable when raised down to 77, where the profit margin is even smaller. A novice could do well to not play these hands at all. We can explore the best way to play hands like these once we explore postflop strategies.

- Acting when facing a raise presents some interesting data. AA and KK, of course, are most profitable when reraised (3-betting). But by a thin margin, QQ and JJ are most profitable when calling two bets. The margin is so thin, however, that you could just reraise those hands as well and not see a significant dropoff. In fact, since win percentages increase when you raise over calling and reduce your variance with these hands as a result, it can be argued that reraising may be worth the slight loss of profitability since you'll win more often by pricing out weaker hands that may outdraw you.

Early position pocket pair recommendations:

When 1st to act, limp in with AA and raise with KK-88.

Against limpers, raise with AA-77.

Against a raise, reraise with AA and KK, but call with QQ and JJ.

Thursday, February 12, 2009

Raw UTG preflop data with notes

UTG Expected Values:
Pocket Pairs Over 100,000 trials
Starting
Hand
Open
Call
Open
Raise
AA13.4811.87
KK7.607.70
QQ4.935.14
JJ2.963.07
TT1.411.88
990.470.51
88-0.190.00
77-0.80-0.65
66-1.21-1.04
55-1.40-1.46
44-1.62-1.66
33-1.75-1.86
22-2.00-2.06


- Each hand was tested 100,000 times at a 9 handed 3/6 table with a general profile, while open calling one small bet and 100,000 times while open raising to 2 bets. Obviously, being 1st to act, there's no need to test hands against limpers or raisers. The general table profile has no more than two aggressive players, no more than 2-3 loose players and generally sees 3.6 players per flop. This is not a juicy game, but it's consistent with the play in most cardrooms, in line with the research goal to determine the optimal strategy for such a game.

- If raised by someone acting after us, the simulator automatically calls for one extra bet, but only calls for 2 or more extra bets with tens or better, reraising with Queens or better if possible. Tens or better are very strong hands that consistently profit even against top hands. Any pocket pair weaker than this is thrown away when facing two more bets (and previous research confirmed that nines and below are big losers when played for three or more bets preflop. I can simulate and outline this scenario at a later date to illustrate this).

- Most pocket pairs need to flop a set or a disguised open ended straight draw to continue playing on the flop... or they must be folded. Stronger pairs can often win on their own provided that pair's rank is either higher than the high card on the flop, or sometimes when right below it. Middle and low pairs almost always need to flop a set to have value, and even then they run the costly danger of another player flopping a better set or making a flush or straight to beat them.

- The surprising stat from above: pocket aces turns a bigger profit when open limped than when open raised, over $1.50 more per hand. All other hands turned a better profit when raised. AA's result was such a baffling outlier that I ran 100,000 more trials for each scenario with AA to make sure, but the 2nd results were no greater than 4 to 5 cents off the original results.

The most likely cause is that when someone raises after we limp, which happens rather often, AA reraises or calls a full number of bets, and is so far ahead of all other hands that it wins most of the resulting larger pots. All other pairs run the risk of being dominated or outdrawn in such a scenario.

- Due to the parameters of Wilson Software's Turbo Texas Hold'Em simulator, I cannot set the simulator to raise nines through Kings, then limp Aces, if I were to test an overall strategy. The simulator only allows you to set a minimum bar for raising pocket pairs, with no more specific definition.

However, since you only see pocket Aces roughly once every 221 hands, the difference in profitability overall would add up to about a penny per hand over a lengthy simulation. And of course, AA is still immensely profitable when raised instead. We'll note reality, but in subsequent simulations we'll let it slide and raise Aces preflop UTG.

- Clearly, as noted a while back, the dividing line for profitable pocket pairs under the gun is nines or better. Eights break even when raised, though the actual return was a very small profit, so small that the average profit per hand was 0.00. Not playing them under the gun at all may be the better play in order to reduce variance.

- Conclusion: Under the gun before the flop, raise with pocket pairs nine or better, except for Aces, which can be limped.

Tuesday, February 10, 2009

Re-evaluating the testing process

Pardon the absence during a busy time for me. Normal posting will resume shortly.

I have run multiple test trials over the last few weeks, lately gravitating to more specific scenarios in an attempt to more accurately gauge where hands make their money using a conventionally solid postflop strategy. However, I'm running into a problem: I've so expanded the scope of this project as a result that to ultimately complete the task strikes me as overwhelming. Each hand in each situation requires a minimum of 50,000 trials to minimize the variance so we get a useful net profit number.

If I run too few trials, the variance ends up so high that the data is useless. The variance over 25,000 trials can get into the $0.30 range, rendering most trials useless. You need at least 50,000 to get variance within $0.15 and you would prefer 100,000. If I don't run trials by position, an overall number for all positions of a given hand doesn't tell me very much about the hand's profitability (is it profitable when open raised but not when calling other players? Does it profit against multiple players? Is it profitable in late position?). A single number over a large span of cumulative trials won't educate me about how or where a hand is best played before the flop.

Also, we eventually need to transition to evaluating postflop play to see if we can improve on conventionally solid strategy, and there are so many variables there (Yes, I do have a framework from which I will run tests). But one step at a time: if we can simply get a reliable barometer on profitable preflop hands, that is a big step forward.

To make the task less overwhelming, I now plan to do these tests by the sets listed. I will start with pocket pairs, then the suited broadways, the offsuit broadways, the suited Aces, Kings, Queens, then Jacks, then the suited connectors, and then I shall add other hands as low-end hands show the potential for profitable play. I previously hadn't tested the top hands like AA and AK, but I will now include them to provide general barometers of how hands improve in profitability with position.

I will test all groups in the following circumstances:

Open (1st in) call, Open (1st in) raise, limp behind, raise limpers, call raise, reraise

I will test all the above circumstances for the following positions:

UTG, EP, MP, LP, Button, SB, BB

Already, we face a daunting task. Now, the groups:

(AA, KK, QQ) JJ, TT, 99, 88, 77, 66, 55, 44, 33, 22

AKs, AQs, AJs, A10s, KQs, KJs, K10s, QJs, Q10s, J10s

AKo, AQo, AJo, A10o, KQo, KJo, K10o, QJo, Q10o, J10o

A9s, A8s, A7s, A6s, A5s, A4s, A3s, A2s

K9s, K8s, K7s, K6s, K5s, K4s, K3s, K2s

Q9s, Q8s, Q7s, Q6s, Q5s, Q4s, Q3s, Q2s

J9s, J8s, J7s, J6s, J5s, J4s, J3s, J2s

T9s, 98s, 87s, 76s, 65s, 54s


For each group I will do the following:

1. Program the simulator to run trials for each respective hand,
setting button positions for each hand.

2. Run 1st in trials for calls and raises (26 50K trials for each position)
- Button
- LP
- MP
- EP
- UTG

3. Run limper trials for calls and raises (26 50K trials for each position)
- SB
- Button
- LP
- MP
- EP

4. Run raiser trials for calls and raises (26 50K trials for each position)
- BB
- SB
- Button
- LP
- MP
- EP

5. Rip my hair out.

Now, to wit: the simulator can run about 3.3 million hands an hour, give or take depending on what scenario you research. Running 5 million trials takes about an hour and a half. 13 separate 100K trials adds up to 1.3 million trials. Run any of the above listed scenarios for every position and you get either 6.5 million trials or 7.8 million trials. That's about 2 hours for each. Not including time to manually notate the results, that's 6 hours to run trials on one set of hands. And that assumes we can set the simulator up to quickly run them all at once, without any manual manipulation inbetween.

Sunday, January 18, 2009

A digression: No Limit Hold'Em tournament research

We'll return to our 3/6 Limit Hold'Em research shortly, but first I wanted to touch on some of my ongoing No Limit Hold'Em tournament simulation research, conducted for the most part of Donohoe Digital Software's DDPoker simulator, which allows me to customize tournament formats.

For a while, I lost my sense of how to play fast no limit hold'em tournaments. Arnold Snyder's suggested strategy in Poker Tournament Formula has its flaws, especially once everyone gets short stacked, though that was the approach I cut my teeth using. Later, I replaced Snyder's short stack strategy with the one used in Kill Phil, where you are prepared to shove with a fairly wide range that gets wider as you get shorter or as you gain position.

A while back in my tournament trials, I stumbled into an approach that worked very, very well in my simulations and routinely got me deep into tournaments that by all other definitions should be far too fast to play profitably. I posted a bunch of first places because I would either tear through with a big stack or gain such a commanding chip lead at the final table that 1st place was academic.

The preflop strategies I utilized would vary, but one consistent approach came when my stack was above average but around 20 big blinds or less, which is generally considered the high end of short stacked. Once I reach this short stacked point, I would open all playable hands with a minraise. At this point, a minraise was such a large part of any player's stack that playing back at it took as strong a hand as calling a standard raise earlier in the tournament did.

If I'm going to play against a raiser in front at all, I either want to reraise or fold, or get the other guy all-in when he's short. I want to establish that pots played with me will be expensive. I tend to reraise a preflop raiser no matter what when I have a strong hand that I feel would play well heads-up against a preflop raising range. The typical goal is to get a pot heads up on the flop (though obviously when you have AA or KK, you reraise for value, and when you 3bet a lot, you get more value from your reraises since they're not taken as seriously). Once heads-up on the flop, I will have position on my villain. If the villain checks to me, I can fire out a large bet or take a free card, depending on the opponent and flop scenario. If he bets, I can go away if the bet is too large for comfort or I don't have enough of the flop to continue.

Others behind me can call a preflop reraise at their own peril, and in the few cases when they do, great. If someone or the original raiser re-reraises, I can get out of the way unless I have a top hand or a ton of chips relative to the bet. If we see a 3+ way flop, sometimes I hit the flop hard and stand to win a very large pot, and can bail in the instances when I don't and another player bets out.

Again, once the blinds get up there and the average stack has ~20 big blinds, I switch to a minraise mode, which puts any short stack in peril if they play. I open with this raise with strong hands out of position and with lesser but playable hands in position. I avoid playing pots raised in front of me unless the raiser is loose or I have a strong hand, in which case I will reraise, and if the raiser is short enough I will reraise him all in. I make it clear I am either prepared to play for all my chips or prepared to make you play for all your chips.

I have finally devised a simple preflop strategy that I can use out of position in any position regardless of stack size. In position when 1st in, I will raise a LOT, and put the onus on opponents behind me to call or reraise to continue playing. Even when not 1st in, if there's a couple of limpers I may make a huge raise on the button, knowing I will have position when called. If folded to when in the small blind, I will use my read to decide how often to raise the big blind. Often I will just call and look to see a cheap flop heads up out of position. If the blinds are high, I will raise the big blind more often, and again put the onus on that big blind to pay to play.

For hand selection, I use proportion. At a 10 handed table, I open raise with the top 10% hands. If you're at a 10 handed table, raise 1/10th of your hands and get the blinds uncontested as a result, you break even. Obviously, you will raise more often in position and should get ahead of the game, but such a selection can help you stay above water when you're struggling to find spots to raise and take pots. This is easy to remember and makes little difference when used in middle position or early position.

I rated all 169 possible hands by their win% against popular raising hands that many players are willing to get all-in with preflop, such as pocket pairs 7 and higher, Ace-King, Ace-Queen, Ace-Jack and King-Queen. I sorted these hands by win% and selected from the top of the list down in PokerStove until it told me I had the proper percentage of hands. The resulting 10% looks a bit odd in selection and omits some hands you would expect to see, but the key is to have maximum equity against the sort of hands people will call a raise with.

The top 10%: AA-99, AK-AJ, A10s, A5s-A3s, KQ, KJs, K10s, QJs, Q10s, J10s

If the table is 9 handed, again we go proportional, using the top 1/9th of available hands, 11.1% total: AA-99, AK-AJ, A10s, A5s-A3s, KQ, KJs, K10s, QJ, Q10s, J10s

A tournament table often drops to 8 handed, and SPO typically plays 8 handed and below. 1/8 equals 12.5%: AA-99, AK-AJ, Axs, KQ, KJs, K10s, QJ, Q10s, J10s

7 handed (14.3%): AA-55, AK-AJ, Axs, KQ, KJs, K10s, QJ, Q10s, J10s

6 handed (16.7%): AA-33, AK-A10, Axs, KQ, KJs, K10s, QJ, Q10s, Q9s, J10s

You will almost always see 4-5 handed play at a final table where blinds are fairly high. At this point, play should be more straightforward and not require hand charts: Any seat not in the blinds is in position and you can raise most, if not all of the time and expect not to get called by strong hands. And if you do have a good hand, any two broadway, a decent pocket pair... you're ready to get it in against any short stacked player that raises you. You show more caution against other big stacks unless they're playing very aggressively, in which case you show them no respect when you have the goods, especially when in position.

If players are calling your raises a lot, you can use the following strategies to determine when to raise, which will lead to you folding hands in raising positions, which can allow you to regain table respect:

5 handed (20.0%): All pairs, AK-A10, Axs, KQ-KJ, K10s, QJ-Q10, Q9s, Q8s, Q6s, J10s-J9s, 10-9s

4 handed (25.0%): All pairs, AK-A10, Axs, A5, QJ-Q10, Q9s-Q3s, J10, J9s-J8s, KQ-KJ, K10s, K6s, 10-9s, 10-8s, 76s, 65s, 54s

3 handed (33.3%): All pairs, AK-A10, A5-A2, Axs, KQ-K10, K9s-K3s, QJ-Q10, Qxs, J10, J9s-J7s, J5s, 10-9s, 10-8s, 10-7s, 98s, 87s, 76s, 75s, 65s, 64s, 54s

Typically, fast tournaments will conclude once 4-6 handed due to the high blinds. Players will ask to make a deal, and given the crapshootish nature of the tourney at this point, it's typically best to take the split of the remaining prize pool and call it a day. This typically happens when the average stack has 5-10 big blinds or less. But sometimes everyone involved will still have enough chips to play, and it's a sound idea to have some sense of how to play these shorthanded high-blind situations.

Once heads up, the blinds should be fairly high, enough for minraises to hold significant value to both players, so continue minraising preflop. How you play will depend on your opponent's style, though if you're on the short end and he's raising a lot himself preflop, you're looking to get your money in with any decent hand, any Ace, most Kings, Queens with kickers 7 and higher, Jacks-7 and up, 10s-7 and up, though tend to only include the lower range when they're suited or your opponent's rising more frequently. Generally, see a lot of flops with decent holdings or in position, and look for a spot to get your money in, typically with at least 2nd pair or better, or a strong draw to better, on the flop.

On the other side, with a big stack, tend to punish your shorter stacked opponent with preflop raises. Bet a lot of flops and show him he will usually need to pay to continue. This will also tend to make a thinking opponent wary when you do check a flop here and there, as many will think you're slowplaying a monster if you usually bet out.

Another benefit of betting most flops is that, when you do catch a good hand, like top pair or better, or a strong draw to a straight or better, your opponent, knowing you bet a lot of flops, will tend to call you more often and thus pay off your strong hands more often. This is also key to getting him all in when you've got him beat. You want him to get all his chips in with a weak pair or Ace-high when you've got him crushed with top pair or better.

Kill Everyone tends to suggest that you put a short stack all in preflop when his M is 8 or lower. But this makes it too easy for your opponent to catch up, since he can fold all but his best holdings, and typically double through when he does call, which only makes the task of finishing 1st that much harder for us. Just play him straight and aggressive.

Given this approach, it's possible to consistently win at faster tournaments that are widely considered to be a crapshoot by even experts at their style of play. You just need to shorten the raises to meet the scope of play, while remaining aggressive and getting even more aggressive in position as the field thins.