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
AKo	2.40	2.70	2.16	2.76	0.76	1.99
AQo	0.53	1.52	0.48	1.78	-1.14	-0.33
AJo	0.01	0.78	0.07	1.17	-2.21	-2.21
A10o	-0.18	0.54	-0.16	0.62	-2.71	-2.94
KQo	-0.46	0.12	0.01	0.33	-2.75	-3.07
KJo	-0.28	-0.05	-0.06	0.15	-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

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

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

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.

Middle position profitability for middle pairs in middle position

For each hand set, I will list the Maverick preflop strategy when 1st to enter the pot, when others have limped in front, and when someone has raised in front. When a player behind reraises after the simulator has entered a pot, the simulator is instructed to call an extra bet for nearly all hands listed.

If it's two or more bets back to the simulator, it won't continue without a supremely strong hand like AA, KK, QQ or AK, maybe JJ. If the simulator reraised itself, it did so with a very strong hand like AA, KK, AQ or QQ. It's likely the action will not come back to him, or that betting will be capped preflop if it does, in which case the simulator would probably stay in. If it's two more bets back to the simulator, it's likely someone has one of the aforementioned monsters, and obviously there's little value to continuing with a hand like AJ or KQ, which is probably way behind before the flop.

The following table illustrates 100,000 hand trials in middle position for playable pairs 99 to 55, which fall in the Maverick profile's playable range. Pairs ten and up aren't included, since those hands are definite winners in any position for two bets, even more in most cases. For example, there's no need to run trials for pocket Aces, when we know pocket Aces is a big winner whether for one, two or four bets.

Hand	Action When 1st in	Action With Limpers	Action When Raised	Net $ Per Hand (3/6)
99	Raise	Raise	Call	1.25
88	Raise	Raise	Call	0.40
77	Raise	Call	Call	-0.56
66	Raise	Call	Fold	-0.63
55	Raise	Fold	Fold	-1.42

Notice how the profitability coincides with the aggressiveness exercised when other players limp in front. For all playable pairs (as with all hands under Maverick), you would raise if 1st in, but your strategy varies when others enter the pot before you.

My key observation is that hands that limp behind other limpers show far less profitability, but they're also lower in rank, increasing the risk of overcards and getting outdrawn on the flop (if they're not already facing overpairs preflop). Granted, this is a risk regardless, and the idea overall is probably to play cheap and hope to flop a set, or fold. 88 and higher play strong enough that they could win on their own in some cases, plus of course Broadway pairs (AA-TT) usually can win on their own.

Nonetheless, limping allows other marginal hands to limp behind, increasing this likelihood that a hand will outdraw on the flop. So I tested 77 and 66 over 100K hands each with a strategy to raise against limpers instead of limping along, to deter marginal hands behind and thin the field. I omitted 55 because it's -1.42 loss rate indicates that even an improved strategy wouldn't make it profitable from MP.

Hand	Limp Net $	Raise Net $
77	-0.56	-0.38
66	-0.63	-0.30

Raising limpers reduced the loss of each hand, but did not make the hand profitable. And as we saw in previous trials, open limping these hands instead of open raising them almost always reduces the expected value of a hand, and when it improves the value, the improvement is typically insigificant. The potential improvement of limping either of these hands likely wouldn't offset the $0.30+ losses per hand that these hands see.