EV comparison of hands in early position: Limping vs raising

The following hands were tested over 100,000 trials each from 2nd position at a 9 handed $3/$6 table under two conditions. In the first scenario, every hand listed was limped in. In the second scenario, every hand was raised. The simulator entered every pot that wasn't raised in front by the under the gun player, except in cases of big hands like AA-QQ, sometimes JJ, and AK. However, in the limped trials, no more than one small bet was placed in the pot unless the pot was raised, in which case the simulator reraised.

I notated the net expected value (EV) per hand and winning percentage of each hand over 100,000 hands.

Net Value in dollars for given starting hands
(Pairs and Ace-Broadway suited)

Hand	Limp EV	Limp Win%	Raised EV	Raised Win%
AA	12.63	67.9	12.98	74.4
KK	8.63	56.6	8.90	63.1
QQ	5.57	50.3	5.94	57.2
JJ	3.23	44.6	3.83	52.0
TT	2.05	39.7	2.63	47.5
99	0.88	34.5	1.57	31.5
88	0.40	29.5	0.48	35.8
77	0.05	26.9	-0.05	24.1
AKs	2.70	46.0	4.23	54.3
AQs	1.55	39.6	2.18	49.7
AJs	1.28	34.6	1.34	45.3
A10s	1.12	30.3	1.15	39.6

Net Value in dollars for given starting hands
(Offsuit and Marginal Hands)

Hand	Limp EV	Limp Win%	Raised EV	Raised Win%
AKo	1.13	42.9	1.94	51.2
AQo	0.20	34.6	1.94	47.2
AJo	-0.19	31.5	0.23	40.8
KQs	0.78	36.1	0.80	42.1
KJs	1.13	27.3	0.62	34.7
K10s	0.68	25.7	0.18	30.2
KQo	-0.36	29.5	0.52	30.3
QJs	0.72	28.3	0.28	33.7
Q10s	0.24	24.5	-0.04	29.4
J10s	0.23	26.2	-0.23	28.6
A9s	0.35	29.3	0.30	36.4
A8s	0.08	28.7	-0.10	35.0

Though it's considered common knowledge, the above data confirms that raising before the flop raises the EV and the chances of winning for nearly all of these hands, let alone the top hands, with few exceptions.

Some of these hands maximize their EV when limped instead of raised, though in some marginal cases (like 77 and A8s), the maximum EV is so small that you can argue the hand's not worth playing at all.

The gray area between greater EV when raised and greater EV when limped fell around the AJs/A10s area. With pairs, the shift only occured with 7's, which are a marginal play in any case: any pairs 8 and above are maximized when raised. King high suited hands, save for KQs, showed a greater profit when limped. K9s, not listed above, showed a very marginal EV of 0.05 when limped, and showed a greater loss when raised. The Queen high and Jack high suited hands listed all showed greater EV when limped.

The obvious risk with raising the strongest hands while limping the marginal hands is that, to astute opponents, you may telegraph the strength of your hand when you limp in from early position. For the most part, your opposition in 3/6 limit won't be nearly attentive enough to notice, assuming you limp more hands in middle and late position. If anything, a high enough frequency of raises run a greater risk of tilting the table. Once a player starts raising too often at a low limit table, frequently the other players cease having fun, they tighten up, and will join in the raising act, replacing the profitable loose-passive environment with a tighter, more aggressive game, which vastly reduces profitability at a low limit game where the rake and drop alone leaves you with very little margin for error.

The good news in early position is that few of your hands are playable. Assuming we eliminate the marginal A8s and 77, you will only see a playable hand in early position 9.2% of the time according to PokerStove, and if we base our decision to raise on the highest EV possible per the above chart, we will only raise 7.4% of the time, only one in 13.5 early position hands. If we devised a separate strategy for under the gun, as we'll explore soon, the starting requirements would tighten slightly, meaning even fewer instances of playable hands. In a 4 hour session (roughly 120 hands) or even an 8 hour playing session (240 hands), even if your opponents take notice of your raises, it's highly unlikely you will make enough raises from early position to drive the table nuts and screw the game up.

In fact, once we explore strategies in later positions, we'll find that opportunities to play are so infrequent that we shouldn't get in the way of our opponents very often, which, ultimately, is what we want. We want our weaker opponents pushing most of the action. This way, they're more likely to have fun and remain motivated to keep their money on the table, if not buy-in once they bust and add even more money to the table.