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Deciding whether or not to raise medium and small pocket pairs is a frequently discussed topic among poker players.  The hands are flexible holdings that can get value from several different avenues.  In this series of articles we are going to discuss what factors we should be considering and what adjustments to make in different games and with different stack sizes.

Hands generally derive their value from some combination of winning without a showdown and having the best hand at showdown. Some hands generally derive most of their value from winning before showdown and others they derive it from making the best hand and winning in a showdown.  Pocket pairs are flexible holdings that can make money both ways.  Try to predict the most likely scenarios that will come up postflop, and how you can make your opponents make mistakes. Figure out which mistakes your opponents are most likely to make.  Your preflop strategy with these hands should be tailored to exploit the mistakes they are most likely to make.¹

Playing in Loose-Passive Games
This is the game of your dreams. You are seeing 5 or 6 players(or more) to the flop in most pots. You can get away with raising to 10 times the big blind with AA and still get a couple callers. Players in these type of games tend put in too much money with hands like top pair with a terrible kicker, medium pair, flush draws, etc. That means that you can do a lot more value betting, and easily get your stack when you want to.

In games like this you can make big money off of hitting big hands and getting paid off.  Simply put, loose-passive games offer high implied odds. These players are willing to go broke with top pair and a mediocre kicker, so use that against them. Poker is a game of adjusting to take advantage of your opponents’ weaknesses. These players’ biggest weakness is that they put in too much money with weak hands. Make sure that you get to see a cheap flop(not necessarily the cheapest) and that there is plenty of money left behind to win.  You will maximize your expected value by hitting a big hand, say a set or better, and then getting paid off.  This is often referred to as set-mining.

There are two schools of thought for how to best maximize your earn for set-mining.  One idea is to simply limp in and see a cheap flop(you are probably calling a raise if the pot is going to be multiway).  The other idea is to make a small raise to juice the pot up.  Let’s look at some scenarios to see how the hand would play out if you limp versus if you make a small raise.

Let’s say that you are playing a $1/2 game with 100 big blind effective stacks at your local poker room.  You look down at a pair of deuces.  You put your $2 in and four other players limp behind you.  The small blind calls $1 and the big blind checks.  Seven players go to the flop and the pot is $14.  You have $198 behind which gives you a stack-to-pot ratio (SPR) of approximately 14(198/14 ~= 14).  With an SPR of 14 there is a little over three pot-sized bets left to bet.  Actually, against players like these it is even reasonable to believe that you could over-bet the pot on the flop to make your turn and river bets smaller. This leaves you plenty to win postflop but not so much that is unrealistic that you can get your entire stack in.

Now, let’s take a look at making a small raise to see how it affects the play of the hand.  Same game as above only now you pick up a pair of deuces and raise to $6.  You get three callers and both blinds call.  Six players go to the flop(this is assuming that not as many people will call a raise as will limp in, but that many will still call the raise).  Now the pot is $36 and you have $194 behind.  This gives you an SPR of about 5.4.  There is a little over two pot-sized bets left.  It certainly will be much easier to get a players stack in when you flop a set.

Several rough expected value (EV) calculations should give us an idea of which particular factors should influence our decision to raise or limp.² We are going to look at raising versus limping and see which does better with different number of players seeing the flop.  My assumptions are that you are going to be playing purely for set value.  If you don’t hit a set, you are done with the hand so you will merely check and fold to any bet.  I am also ignoring the fact that sometimes the flop (and possibly the turn) will get checked through and you will hit a hand because this will account for such a small part of your EV.  Using the above scenarios, I am going to assume that when you limp and flop a set you will win a stack 50% of the time and win the preflop pot the other times.  For simplification, I am ignoring the fact that sometimes you will be raised because this essentially will turn into the same calculation had you yourself raised only there is a much smaller chance that you won’t see a flop.  I am also going to assume that when you raise to $6 you will win a stack 70% of the time and win the preflop pot the other times in a 6-way pot.³  I also adjust these numbers down for a four and five way pots since the SPR will be higher.  You have more money behind and less players that are likely to pay off thus you are not as likely to win a whole stack. In addition, I am going to assume that you get 3-bet about 10% of the time.  This is a decidedly small percentage of the time to reflect the passiveness of these games.

EV of limping for set value(expecting 6-way action):
(.13)*[(.50)*($198) + (.50)*($12)] + (.87)*(-$2) =
(.13)*[$99 + $6] – 1.74 =
$13.65 – $1.74  = $11.91

EV of raising and playing for set value(expecting 6-way action):
(.90)*[(.13)*[(.70)*($194) + (.30)*($36)] + (.87)*(-$6)] + (.10)*(-6) =
(.90)*[(.13)*[$135.80 +  10.8] -  5.22] - $.6 =
(.90)*[$19.06 - $5.22] - $.6 =
(.90)*($13.84) - $.6 =
$12.46 - $.6 = $11.86

EV of limping for set value(expecting 5-way action):
(.13)*[(.45)*($198) + (.55)*($10)] + (.87)*(-$2) =
(.13)*[$89.10 + $5.5] – 1.74 =
$12.30 – $1.74  = $10.56

EV of raising and playing for set value(expecting 5-way action):
(.90)*[(.13)*[(.65)*($194) + (.35)*($30)] + (.87)*(-$6)] + (.10)*(-6) =
(.90)*[(.13)*[$126.10 + $10.5] - $5.22] - $.6 =
(.90)*[$17.76 – $5.22] - $.6 =
(.90)*($12.54) - $.6 =
$11.29 - $.6 = $10.69

EV of raising and playing for set value(expecting 4-way action):
(.90)*[(.13)*[(.60)*($194) + (.40)*($24)] + (.87)*(-$6)] + (.10)*(-6) =
(.90)*[(.13)*[$116.40 + $9.6] - $5.22] - $.6 =
(.90)*[$16.38 – $5.22] - $.6 =
(.90)*($11.16) - $.6 =
$10.04 - $.6 = $9.44

EV of limping for set value(expecting 4-way action):
(.13)*[(.45)*($198) + (.55)*($8)] + (.87)*(-$2) =
(.13)*[$89.10 + $4.4] – 1.74 =
$12.16 – $1.74  = $10.42

Let’s make a couple observations.

1. The more players that are in the pot, the better our expected value is when we are playing purely for set value.
2. Limping is better when there are fewer players in the pot.
3. Limping is a slightly more stable option.  It doesn’t show as big of a swing depending on the number of players in the pot.

From these observations you can see that whether limping or raising is better depends on many factors.  If you only expect 4-way action or even less players to call your raise a high percentage of the time you would certainly do better to limp.  This is because your EV for raising lowers at a faster rate when less players enter the pot than your EV of limping.  The chance of winning at stack doesn’t increase enough to justify the preflop risk when there are few players that will call a raise.  When you raise you won’t make up enough EV those times that you get four or more callers to make up for the times that you get three or less callers if the standard is for 3 or less players to call a raise.

Let’s take a look at that in math-land.   For a very rough estimate, let’s say that when you raise you expect a 4-way pot 60% of the time, a 5-way pot 30% of the time, and 6-way pot callers the remaining 10% of the time.  If you limp you expect a 4-way pot 30% of the time, a 5-way pot 40% of the time, and a 6-way pot the remaining 30% of the time.

EV of raising:
(.60)*($9.44) + (.30)*($10.69) + (.10)*($11.86) =
$5.66 + $3.21 + $1.19 = $10.06

EV of limping:
(.50)*($10.42) + (.40)*($10.56) + (.10)*($11.91) =
$5.21 + $4.22 + $1.91 = $11.34

Limping is better if you expect 4-way action a majority of the time.

Remember also that you raise size itself will play a role on how many callers you get.  If you expect four or more callers if you limp or if you min-raise, then min-raising is probably a better play.

Remember that stacks sizes can have a huge affect on what your proper strategy is here.  If the stack sizes get slightly lower, say 75 big blinds, then you reward for winning a stack is smaller and you already have a higher chance of winning a stack.  There is no need to take the same risk for less reward when the probability that you will win a stack is already higher than if you had 100 big blind stacks.  Given these two considerations, limping pulls becomes a clear favorite.  If the stack sizes get much deeper, say 150 big blinds, then raising becomes a favorite because your reward for winning a stack is higher and you want to increase the chance of getting that reward.  Also, as the stacks get deeper you may be able to profitably call a reraise so the fear of the reraise is diminished.  With stack sizes around 100 big blinds the decision is very close.  Limping appears to have a slight edge given the assumptions that we made.

If you are in early position in a game like this you need figure out how players react to raises in the game.  If four or more players are often calling preflop raises then you can occasionally make a small raise with these hands (assuming, of course, that you aren’t going to get 3-bet a lot).  If you are unsure, it is best to limp until you get a clearer picture.  Also, if 3-bets are extremely rare in a game like this then raising will pick up a little extra EV because you will be forced to fold preflop less.  Either way, limping or making a small raise is very close in a game like this as long as you realize that your major profit center comes from flopping sets and getting paid off.

This article originally appeared in the July Edition of the Two Plus Two Publishing Internet Magazine.

1. The correct strategy is dependent on the size of the stacks.  This article will strictly look at 100 big blind effective stacks. [↩]
2. These EV calculations are not meant to be amazingly accurate, but they will give you a rough idea of how the EV’s of raising and limping compare. [↩]
3. The percentages that I am using for winning a stack are just my best estimations.  The important thing is that all of the estimates do logically follow from each other. [↩]

I have decided to begin coaching poker.  You can check out all the information on the coaching page.  I am really looking forward to getting into coaching.  I enjoyed teaching guitar for five years and I plan to use my experience on teaching to help get ideas internalized.  My poker knowledge will help beginning and intermediate players get a very strong grasp of the game so that they will be able to beat the game at a good clip.

Contact me at Jacob@Threads13 if you have any questions or interest in beginning private coaching.

Twoplustwo.com has recently published the second part of my article on playing pocket pairs in early position.  You can check it out here.  As always, feel free to discuss anything in the comments section of this post.

Jacob’s Law:

If you suck at poker, you still suck at poker if you put sunglasses on.

I bet you guys think I have just be lazing around and enjoying the good life, right? Hardly! I’ve been keeping hard at work with getting my band up and going, playing poker full time, and writing as time permits. As is, most of my writing work has been aimed at material that will be published in other mediums first. A new article has been published on the TwoPlusTwo.com Internet Magazine. This article is the first part of a series that addresses playing medium and small pocket pairs in early position at a full ring No Limit Hold ‘Em table.  Read it here! 

This is the second time that I have been fortunate enough to get an article published there and it is definitely is a thrill to see something that little ol’ me wrote sittin side by side with the likes of Sklansky, Malmuth, etc.  Check out the article and, as always, feel free to give some feedback.