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
AKs	2.84	3.59	3.21	4.95	2.89	3.66
AQs	2.12	2.85	2.35	4.03	1.16	1.46
AJs	1.59	2.31	1.68	3.26	0.30	0.13
A10s	1.38	1.96	1.54	2.50	-0.48	-0.32
KQs	1.08	1.54	1.32	2.30	-0.41	-0.73
KJs	1.09	1.27	1.18	1.93	-0.58	-0.98
K10s	0.83	0.89	0.88	1.19	-0.84	-1.64
QJs	0.88	1.11	1.04	1.47	-0.87	-1.22
Q10s	0.65	0.74	0.55	0.59	-1.03	-1.45
J10s	0.52	0.56	0.45	0.47	-1.25	-1.46

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
AKs	3.62	3.49	4.03	4.49	2.51	2.96
AQs	2.46	2.59	2.94	3.54	0.81	0.98
AJs	1.27	2.00	1.76	2.91	-0.39	-0.36
A10s	0.95	1.57	1.46	2.45	-0.86	-1.23
KQs	0.92	1.06	1.44	1.86	-0.90	-1.03
KJs	0.81	1.01	1.35	1.47	-0.96	-1.72
K10s	0.45	0.52	0.74	1.01	-1.41	-2.15
QJs	0.49	0.62	0.95	1.34	-1.31	-1.96
Q10s	0.19	0.24	0.59	0.53	-1.48	-2.42
J10s	0.13	0.08	0.37	0.44	-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
AKs	3.53	3.34	3.64	4.29	1.87	2.17
AQs	1.72	2.37	2.26	3.28	-0.42	-0.85
AJs	1.44	1.88	1.58	2.54	-1.40	-2.55
A10s	1.08	1.38	1.27	2.06	-1.61	-3.07
KQs	0.68	0.91	1.02	1.37	-1.99	-3.54
KJs	0.84	0.74	0.85	0.92	-1.36	-2.78
K10s	0.22	0.24	0.25	0.29	-1.60	-2.89
QJs	0.39	0.36	0.38	0.66	-1.64	-2.89
Q10s	0.05	0.01	-0.05	-0.10	-1.69	-3.04
J10s	0.05	-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 Hands	Open Call	Open Raise
AKs	3.41	3.18
AQs	1.49	2.11
AJs	1.15	1.36
A10s	0.81	1.05
KQs	0.43	0.73
KJs	0.49	0.53
K10s	0.16	0.03
QJs	0.32	0.33
Q10s	-0.78	-0.19
J10s	-0.37	-0.06

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
AA	12.49	17.28
KK	6.73	9.36
QQ	3.45	5.49
JJ	1.06	2.18
TT	-0.42	0.24
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
AA	8.09	12.51	13.24	15.81
KK	5.07	8.70	7.44	9.00
QQ	3.67	6.69	4.43	5.62
JJ	2.23	4.87	2.18	2.63
TT	1.22	3.34	0.56	1.02
99	0.08	1.73	-0.55	-0.33
88	-0.59	0.78	-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

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
AA	6.49	7.04	9.98	14.15	14.86	18.32
KK	4.30	4.95	6.86	10.47	8.10	9.80
QQ	3.37	3.91	5.12	7.91	4.52	5.24
JJ	2.65	3.10	3.52	6.06	2.08	2.23
TT	1.95	2.36	2.58	4.27	0.75	0.82
99	1.33	1.67	1.42	2.76	-0.10	-0.47
88	0.83	0.99	0.82	1.87	-0.63	-1.34
77	0.31	0.38	0.29	1.15	-0.98	-1.58
66	-0.09	0.08	0.03	0.66	-1.14	-1.93
55	-0.45	-0.30	-0.29	0.13	-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

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
AA	8.58	8.96	11.40	14.27	14.91	17.70
KK	5.57	6.27	7.30	10.52	8.45	10.04
QQ	4.23	4.84	5.31	8.03	4.94	5.87
JJ	3.03	3.50	3.53	5.76	2.81	3.11
TT	2.02	2.51	2.42	3.99	1.05	1.46
99	1.34	1.49	1.16	2.37	0.04	-0.02
88	0.52	0.76	0.57	1.37	-0.60	-0.66
77	-0.02	0.21	-0.01	0.69	-0.87	-1.33
66	-0.52	-0.13	-0.08	0.39	-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

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
AA	11.95	10.76	13.86	14.75	16.58	17.89
KK	6.82	7.37	8.33	10.41	9.10	10.21
QQ	4.73	5.13	6.16	7.76	4.88	5.71
JJ	3.34	3.55	3.86	5.25	2.19	2.72
TT	1.95	2.41	2.26	3.40	0.63	0.49
99	0.85	1.39	1.06	1.73	-0.29	-0.81
88	-0.09	0.55	0.38	0.88	-0.92	-1.32
77	-0.59	-0.46	-0.18	0.30	-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

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
AA	12.88	11.29	14.57	14.89	17.97	18.91
KK	7.07	7.56	8.56	10.56	9.72	10.36
QQ	4.88	5.16	5.93	7.26	4.89	4.83
JJ	3.08	3.37	3.40	4.86	1.92	1.83
TT	1.67	2.08	1.74	2.69	0.00	-0.39
99	0.26	0.86	0.98	1.49	-1.08	-2.07
88	-0.16	0.12	0.36	0.83	-1.79	-3.14
77	-0.77	-0.33	-0.11	0.07	-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.

Raw UTG preflop data with notes

UTG Expected Values: Pocket Pairs Over 100,000 trials
Starting Hand	Open Call	Open Raise
AA	13.48	11.87
KK	7.60	7.70
QQ	4.93	5.14
JJ	2.96	3.07
TT	1.41	1.88
99	0.47	0.51
88	-0.19	0.00
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.

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.

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.

Late position hands versus a raise and reraise

Everyone agrees that no matter what you position, if action gets raised and reraised in front of you preflop, you get supertight and play only the absolute best hands, or fold. The universally agreed upon standard is to only play AA, KK, QQ, AKs and AKo, and to cap the betting with a 3rd raise if you can. Some will advocate playing JJ here as well, and maybe even to reraise wth AQs.

The Maverick profile is super loose with pairs by these standards, cold calling 3 bets with as little as 99 and capping with JJ and up, though it won't play any non-pair other than AKs and AKo. For my trials, due to the lengthy period of time it takes Turbo Texas Hold'Em to run 100,000 raised and reraised trials, I will only run trials for a small handful of hands, with the button locked one seat to the left of the trial player, with obviously AA and KK excluded since we know these hands still thrive against 3 preflop bets.

Pairs	Net $ Per-Hand (3/6)
QQ	4.32
JJ	-0.24
TT	-3.08
AKs	0.23
AKo	-2.81

As expected, QQ was profitable, with JJ and TT posting losses. The surprise is that AKs showed only a slight profit, with AKo posting a huge loss! Perhaps the high rake of 3/6 kills the profitability of AK.

Late position trials versus a raise

With the button locked in one seat to the trial player's left, 100K trials were run against a raise in front for the Maverick's desired range (hands in parentheses are played sometimes):

3bet: AA-99, AKs-AJs, AKo-AQo, KQs
Call: 88-66, A10s, AJo, KJs(-K10s), QJs(-Q10s)

Fairly tight range. Here are the results, again with top hands omitted since we know they play profitably:

Pairs	Net $ Per-Hand (3/6)
TT	1.72
99	0.16
88	-0.59
77	-0.82
66	-0.98

Aces	Net $ Per-Hand (3/6)	Aces	Net $ Per-Hand (3/6)
AKs	3.84	AKo	2.59
AQs	1.84	AQo	0.24
AJs	0.54	AJo	-1.35
A10s	-0.27

Kings	Net $ Per-Hand (3/6)	Kings	Net $ Per-Hand (3/6)
KQs	-0.58	QJs	-0.63
KJs	-0.42	Q10s	-0.73
K10s	-0.45	J10s	-0.69

Pairs: Tens do fine, but then 99 shows only a marginal profit (a subsequent trial with 99 cold calling only showed a $0.03 profit), before we see a huge loss for 88. I did not run a trial where 99 was cold called, since I figured it would post a loss that way given a raise reduces the field enough to not give 99 proper odds to try and flop a set. And 88 showed such a large loss that I did not believe a trial with 88 reraising would improve it to profitability even if I believed such a trial would show a better profit (and my middle position trials showed that 3-bet raises against a range with smaller pairs typically led to even bigger losses).

Aces: Suited aces see profitability until after AJs, where A10s showed a loss. AKo showed a big win, but AQo showed only a marginal profit, and AJo posted a massive loss ($-1.35 per hand is equal to a loss of $40 an hour, nearly 7 big bets!).

Others: None of the other hands showed a profit. KQs was a big loser (and a manual trial with KQs being limped did not show a significant improvement). Prior middle position tests indicate that 3-betting the other hands instead of cold calling with them will not improve their results.

From this, we can gather that, against a raise and yet to enter the pot, we tighten up considerably, reraising every playable hand listed: AA-99, AKs-AJs, AKo-AQo

This makes up 5.4% of playable hands. Everything else is folded. Basically, the numbers show us that we want no part of any pot that gets raised in front, unless we have a hand we're willing to 3-bet with.

Keep in mind this is much different from a pot we enter, whether limped or raised ourselves, that gets raised by someone after us. Once it comes back to us, we typically need to call one bet to stay in the pot and there's quite a bit of money already in the pot as a result, so we have usually odds to try and draw against what's probably a better hand.

Late position hands vs limpers

With limpers behind us, our range tightens up, but now our options expand, because players limping in front generally means more money in the pot improve our pot odds for drawing. Even if raised behind, many of those players will call and we will call as well, improving the payout when our biggest draws come in.

However, do we limp behind or do we raise? Unlike when 1st in, raises probably will not thin the field, as those who limped behind us will probably call. A raise with limpers in should be for value to build a pot for big hands and draws.

The Maverick profile plays this way with limpers behind:

Raise: AA-77, AKs-A9s, AKo-A10o, KQs-KJs, KQo, QJs
Limp behind: 66-44, A8s-A2s, K10s-K2s, KJo, Q10s, QJo, J10s-J8s, 10-9s to 10-8s, 98s

With the button locked in one seat to the test profile's left, I conducted 100,000 hand trials for each hand listed using the Maverick's strategy for each respective hand. Again, top hands like AA and AKs were omitted since we already know these hands are hugely profitable in each situation and running a test to verif this would be as big a waste of time as having a calculator output the results of the equation 3+3 one hundred times. We know 3+3=6, and we know pocket Aces and AKs are very profitable against limpers.

Pairs	Net $ Per-Hand (3/6)	Pairs	Net $ Per-Hand (3/6)
99	2.61	66	0.00
88	1.45	55	-0.35
77	0.73	44	-0.50

Aces	Net $ Per-Hand (3/6)	Aces	Net $ Per-Hand (3/6)
AQs	4.03	A4s	-0.09
AJs	3.21	A3s	-0.24
A10s	2.61	A2s	-0.33
A9s	1.61	AQo	2.61
A8s	0.44	AJo	1.64
A7s	0.20	A10o	1.19
A6s	0.05	A9o	0.10
A5s	0.06	A8o	-0.51

Kings	Net $ Per-Hand (3/6)	Kings	Net $ Per-Hand (3/6)
KQs	2.39	K8s	-0.20
KJs	2.02	KQo	1.03
K10s	0.96	KJo	0.22
K9s	0.24

Others	Net $ Per-Hand (3/6)	Others	Net $ Per-Hand (3/6)
QJs	1.53	J9s	-0.19
Q10s	0.54	J8s	-0.51
Q9s	-0.16	10-9s	-0.23
Q8s	-0.40	10-8s	-0.56
QJo	-0.15	98s	-0.55
J10s	0.51

Pairs: Again, we see a profit until we pass 77, where 66 breaks even and everything below posts a loss.

Aces: Suited Aces see a profit until it reduces to a trickle for A6s, and becomes a loss for A4s and below. A9o and A8o were added in manually, as A10o, the bottom end of Maverick's range, showed a large profit. Offsuit Ace-broadway posts big wins, but then we see a precipitous drop for A9o, though we still see a slight profit. At A8o, however, we see a loss.

Kings: Suited King-broadway shows a big profit, then K9s shows a slight profit when limped before K8s shows a loss. KQo shows a sizable profit, then KJo shows a small but discernible profit. I did not add and test K10o, anticipating it would post a loss given the downward trend between KQ and KJ.

Others: Queen-broadway posted a profit, but then we see a huge drop to Q9s, which posts a loss. And this is where the offsuit broadway profitability ceases, as QJo shows a slight loss. J10s showed a good profit, but J9s showed a loss. Ten-9 suited posted a loss, and 98s posted a loss.

***

That all said, some of these hands were limped behind rather than raised. I manually adjusted the Maverick profile to raise with the limping hands, and ran subsequent 100K trials from the same position to compare their profitability.

(I also added some hands that Maverick did not originally play: these hands are left blank in the 'Net Limp Behind' column and won't have data for the 'Net Raise Advantage' column.)

Hand	Net Limp Behind	Net Raise Limpers	Raise Net Advantage
A8s	0.44	1.14	0.70
A7s	0.20	0.67	0.47
A6s	0.05	0.41	0.36
A5s	0.06	0.56	0.50
A4s	-0.09	0.31	0.40
A3s	-0.24	0.22	0.46
A2s	-0.33	0.08	0.41
K10s	0.96	1.47	0.51
K9s	0.24	0.55	0.31
KJo	0.22	0.73	0.51
K10o		-0.02
Q10s	0.54	1.13	0.59
Q9s	-0.16	0.13	0.29
QJo	-0.15	0.36	0.51
Q10o		-0.31
J10s	0.51	0.86	0.35
J9s	-0.19	0.06	0.25

In literally every case, raising the limpers instead of limping behind added value to each hand played. Both previously unplayed hands still posted a loss, but every hand that was previously unprofitable when limped became at least slightly profitable when raised instead.

Therefore, it may be advised to take a raise or fold approach to entering a pot in late position. With this data, we can adopt a revised preflop strategy against limpers:

Raise AA-77, Axs, AKo-A9o, KQs-K9s, KQo-KJo, QJs-Q9s, QJo, J10s-J9s

This makes up a little over 17% of possible hands. Given their minimal profitability, you could omit J9s, A9o and A2s if you wished, which leaves a little less than 16% of possible hands. It may be best to compromise with these hands: entering the pot with J9s and A2s only with several limpers in (at least 3, if not 4 or more) behind due to their drawing strength, or entering with A9o only with one limper or two due to its need for isolation.

Late position hands when first in

Rather than itemize subsets, I'll go ahead and post results en masse of large-scale trials, and then itemize key points afterward.

The Maverick profile on Turbo Texas Hold'Em plays the following hands in late position when 1st in:

AA-44, AKs-A2s, AKo-A10o, KQs-K2s, KQo-K9o, QJs-Q5s, QJo-Q10o, J10s-J7s, J10o, 10-9s to 10-7s, 10-9o, 98s-96s, 87s-86s, 76s.

I tested each hand over 100,000 trials, with the button locked one seat to the test profile's left, and with no other players having entered the pot.

Due to the high volume of playable hands in late position that I needed to test, hands that would obviously turn a profit when raised were omitted. There's no need to run 100,000 trials for open raising AA or AKs, when we know those hands turn huge profits in most situations, let alone when 1st in. Several other hands that showed a healthy profit in middle position were also omitted.

All hands 1st in opened with a raise. We've seen in previous trials that, with few exceptions, hands show maximum profitability when 1st in with a raise over limping when 1st in. As you find later position preflop, raising becomes even more important, as you vastly improve the chances of folding marginal hands behind you and that only players in the blinds will call, often with lighter holdings than they'd typically play against a raise due to having blinds in the pot and receiving a discount to call. Thus you not only will usually have the best position in the hand postflop, but your holdings on average will be stronger than theirs.

Pairs	Net $ Per Hand (3/6)
88	0.90
77	0.25
66	-0.12
55	-0.57
44	-0.85

Aces	Net $ Per Hand (3/6)	Aces	Net $ Per-Hand (3/6)
A9s	1.20	A5s	0.26
A8s	0.70	A4s	0.15
A7s	0.47	A3s	-0.01
A6s	0.19	A2s	-0.06
A10o	1.11	A9o	0.39

Kings	Net $ Per-Hand (3/6)	Kings	Net $ Per-Hand (3/6)
K10s	1.08	K3s	-0.67
K9s	0.52	K2s	-0.70
K8s	-0.01	KQo	0.68
K7s	-0.20	KJo	0.70
K6s	-0.32	K10o	0.31
K5s	-0.47	K9o	-0.33
K4s	-0.61

Queens	Net $ Per-Hand (3/6)	Queens	Net $ Per-Hand (3/6)
QJs	1.15	Q7s	-0.60
Q10s	0.84	Q6s	-0.63
Q9s	0.27	QJo	0.51
Q8s	-0.30	Q10o	0.12

Others	Net $ Per-Hand (3/6)	Others	Net $ Per-Hand (3/6)
J10s	0.70	J10o	0.00
J9s	0.10	10-9o	-0.74
J8s	-0.30	98s	-0.48
J7s	-0.70	97s	-0.84
10-9s	-0.02	87s	-0.80
10-8s	-0.32	86s	-0.98
10-7s	-0.83	76s	-0.97

Pairs: You can profitably open with pairs down to 77. 66 and any lesser pair posts a loss.

Suited Aces: Even the marginal A9s posts a big profit when open raised. The other aces show progressively lesser profitability until we see a small loss with A3s and A2s. It's possible the smallest Aces can still profit if there are enough callers in the hand due to their drawing status and the need for great pot odds to draw.

Ace-10 offsuit is a big winner. A9o also showed a profit, though the drop was precipitous enough that A8o was figured as a loss (a 100K side trial confirmed that A8o posted a -0.12 net).

Kings: K10s and K9s posted a reasonable profit, but K8s posted a small loss, and losses mounted for the remaining suited Kings. Offsuit King-broadway hands posted a win, but K9o posted a sizable loss, over $0.60 per hand less than K10o.

Queens: QJs posted a sizable gain, as did Q10s. Q9s even showed some profit when opened, but Q8s showed a sizable profit drop and a loss, with subsequent lower hands posting big losses. QJo posted a significant profit, with Q10o posting a slight profit, indicating a small margin for error in playing such a hand profitably.

Lesser hands: J10s showed a sizable profit and J9s showed a slight profit, but J8s and J7s showed losses. No ten high suited or lower suited hand showed a profit. J10o broke even and 10-9 offsuit posted a big loss. The drawing power of these hands do not make enough profit against the rake in 3/6, so they aren't playable as they would be in many other limit hold'em games.

Using this data as an indicator, a revised preflop open raising strategy would raise profitably with these hands:

AA-77, AKs-A4s, AKo-A9o, KQs-K9s, KQo-K10o, QJs-Q9s, QJo-Q10o, J10s-J9s

This makes up a bit over 18% of all possible hands.

Ill finish this entry with a digression: Since this was tested in a game with 3-4 players to each flop, a $3 max rake and $1-2 jackpot drop, and a little under half of the hands played being raised before the flop, obviously some adaption would be required for looser games.

But on average, 3/6 games in many areas often feature the aforementioned sub-optimal environment, and that's the main goal of this project in any case: to devise a winning strategy in a sub-optimal 3/6 game. We already have strategies designed to succeed in more ideal low limit games that work when 6-7 players see a flop in a passive game. Small Stakes Hold'Em was written exactly for these games, and the strategies in most books are designed for these games. When it comes to more sub-optimal games, basically every writer recommends that players not play in these games.

Most of us don't have the luxury of being able to headhunt for great games, thus these efforts.

King-high hands in middle position

King-high hands carry 2nd nut flush potential when suited, and top pair potential either way. King-broadway hands also carry higher chances of a straight than Ace-high hands, as they have chances of flopping an open ended straight draw, which has higher odds of trning the straight than a broadway or gutshot straight draw. However, they are behind right off the bat to any Ace-high hands and can be outkicked when the kicker pairs, if someone holds an Ace and pairs the same card.

The only King hand Maverick likes to raise against limpers is KQs. After that, it will only limp behind with KJs, K10s and KQo. Every other hand, even though you open raise with them, gets folded against any action in front. Against a raise, Maverick will only play KQs and KJs.

Hand	Action When 1st in	Action With Limpers	Action When Raised	Net $ Per Hand (3/6)
KQs	Raise	Raise	Call	1.09
KJs	Raise	Limp	Call	1.02
K10s	Raise	Limp	Fold	0.72
K9s	Raise	Fold	Fold	0.00
K8s	Raise	Fold	Fold	-0.31
K7s	Raise	Fold	Fold	-0.21
KQo	Raise	Limp	Fold	0.04
KJo	Raise	Fold	Fold	-0.03

And as we can see, Maverick's selective for good reason. KQs was the most profitable at $1.09 a hand, a little over 1/3 of a small bet. Only KJs and K10s showed any significant profitability besides KQs. KQo finished a hair above even and K9s finished just about even. All other hands were a loser.

Offsuit aces in middle position

Maverick only plays offsuit Aces with a broadway kicker in MP, raising when facing one bet, but only playing for two or more bets with AK or AQ. The key with these hands, if they don't hit the unlikely Broadway straight, trips or two pair, is to flop top pair with either top kicker or a strong kicker.

Hand	Action When 1st in	Action With Limpers	Action When Raised	Net $ Per Hand (3/6)
AKo	Raise	Raise	Reraise	2.60
AQo	Raise	Raise	Call	1.39
AJo	Raise	Raise	Fold	0.91
A10o	Raise	Raise	Fold	0.55

All four hands deemed playable turned a profit. No hands below A10o were tested given early position trials showed significant dropoffs and subsequent losses for hands A9o and below. 10's tend to show as the profitability cutoff point in these trials.

Suited aces in middle position

Suited Aces carry the key strength of the maximum potential for a nut flush when 3 cards of their suit hit the board. In middle position, Maverick raises limpers with broadway Ace suited hands, calls with other Aces down to A4s, open raises with any suited Ace, and will only play against a raise with Ace broadway suited: it will call with AJs and A10s, but will 3-bet with AQs and AKs.

Hand	Action When 1st in	Action With Limpers	Action When Raised	Net $ Per Hand (3/6)
AKs	Raise	Raise	Reraise	4.10
AQs	Raise	Raise	Reraise	2.79
AJs	Raise	Raise	Call	1.96
A10s	Raise	Raise	Call	1.44
A9s	Raise	Call	Fold	0.62
A8s	Raise	Call	Fold	0.40
A7s	Raise	Call	Fold	0.06
A6s	Raise	Call	Fold	-0.07
A5s	Raise	Call	Fold	-0.07
A4s	Raise	Call	Fold	-0.26
A3s	Raise	Fold	Fold	-0.29
A2s	Raise	Fold	Fold	-0.29

Proftiability as played remains until you get down to A7s, where the profitability as played is slight at best, then everything below A7s is a loser. Once you get below A10s, the suited Aces' only real value comes from their flush potential, as when the Aces pair, their kickers are weak, leaving holders with a second best hand when someone else plays their stronger Ace.

Even when you pair the weaker kicker, the pair is rarely top pair on the flop, let alone by the river, typically leaving you with 5 outs to improve (three Aces and two more of your weaker kicker). Only when a player lands two pair or trips does the hand retain strong value. Axs is a hand limited in its drawing potential if the x isn't 10 or higher.