Squeaking Out Value in Limit Poker
By Tony Guerrera
No-limit hold’em (NLHE) has been the most popular poker variant for quite awhile, but that doesn’t mean that limit poker is dead. Limit hold’em games of $100-$200 and beyond occur daily. H.O.R.S.E. and unique poker variants such as Triple Draw and Crazy Pineapple are increasing in popularity.
In no-limit poker, pots can become quite large with respect to the blinds. As a result, no-limit poker can potentially be a trapping game. No matter how much small-pot poker you play, most no-limit cash-game sessions and tournaments boil down to the results of a few big confrontations. Making seemingly losing plays for table-image sake to set-up sessions yielding an overall profit is a common ploy. A great way to do this in the no-limit setting is to take lots of stabs at small pots, giving you an aggressive image that will trick your opponents into making big mistakes in big pots.
Meanwhile, in limit poker, you rarely end up in pots that are huge with respect to the blinds and antes. Without huge pots, it’s hard to set your opponents up for big mistakes. A big mistake in limit hold’em might be calling a check-raise on the turn from a tight opponent when you have top pair, and following that call on the turn up with a crying call on the river. This mistake, a big one in limit hold’em, amounts to two big bets (equal to four big blinds). With big mistakes from your opponents resulting in you gaining on the order of a measly four big blinds, being a successful limit poker player really boils down to maximizing your profits in every slight way possible. As soon as you recognize a situation where you can derive marginal profit, you need to pounce.
Suppose you’re playing $10-$20 limit hold’em. The table is nine-handed, and you’re on the button. You are dealt A
8
. Two players in middle position limp, and you call. The small blind calls, and the big blind checks. The pot contains $50 going to the flop.
The flop is Q
7
3
. The first player bets, and everyone calls. You have 9 flush outs and 3 additional overcard outs making 12 outs. Of course, you need to acknowledge the possibility of an opponent holding AQ, A7, or A3. Against those hands, hitting an ace won’t do you any good, and remember that the number of outs you have is always a function of your opponents’ hand distributions. Having acknowledged that, let’s make a conservative estimate that you have a 10-outer on the flop. The table below gives the probabilities and odds associated with hitting draws in hold’em with two cards to come:
|
Number of Outs |
P(Hit with 2 Cards to Come) |
Odds Against Hitting With 2 Cards to Come |
|
1 |
.04255 |
22.50 |
|
2 |
.08418 |
10.88 |
|
3 |
.12488 |
7.01 |
|
4 |
.16466 |
5.07 |
|
5 |
.20352 |
3.91 |
|
6 |
.24144 |
3.14 |
|
7 |
.27845 |
2.59 |
|
8 |
.31452 |
2.18 |
|
9 |
.34968 |
1.86 |
|
10 |
.38390 |
1.60 |
|
11 |
.41721 |
1.40 |
|
12 |
.44958 |
1.22 |
|
13 |
.48104 |
1.08 |
|
14 |
.51156 |
0.95 |
|
15 |
.54117 |
0.85 |
|
16 |
.56984 |
0.75 |
|
17 |
.59759 |
0.67 |
|
18 |
.62442 |
0.60 |
|
19 |
.65032 |
0.54 |
|
20 |
.67530 |
0.48 |
|
21 |
.69935 |
0.43 |
*When using the results in this table, it’s very important to know that you will actually get to see the turn and the river. If you’ll be shut out of the hand on the turn should you not hit your draw on the turn, then the numbers in this table aren’t valid. It’s much more difficult to get shut out of a drawing hand on the turn in limit hold’em than it is in no-limit hold’em, but this concept should always be in mind when using these numbers.
With 10 outs, the odds against you hitting your hand by the river are 1.60:1. Calling is clearly profitiable; however, raising is potentially more profitable. If you raise, and everyone calls, you end up getting $40:$10 = $4:$1 on your raise when you are 1.60:1 to hit your draw…a long term expected profit of $9.23 (i.e. if you were to play this same hand out repeatedly, this raise would earn you an average of $9.23 per hand). Additionally, if you raise, there’s a good chance that your opponents will check to you on the turn. Being able to see the river for free saves you money because if you haven’t hit your draw on the turn, the odds against you hitting a 10-outer are 36:10 = 3.6:1. If an early position opponent bets, and at least one opponent folds, you lose some equity on the turn, since the turn action alone would only be yielding $3:$1 at best. Obviously, calling the bet on the turn is still profitable because of the overall pot odds, but the most profitable line of play involves getting a free card on the turn unless…
Suppose you miss your draw on the turn. The first player bets $20, and the other three players call. In that case, you should consider raising the turn for value. For this raise to be profitable, you need to be absolutely sure that all your opponents will say in the pot so that you get $4:$1 on your raise in a situation where you’re 3.6:1 to win. (Note that I said that you should consider raising; considering raising and actually raising are two entirely different things).
When raising for value with drawing hands in limit poker, you need to know your opponents really well. For example, if you raise on the flop, and the initial bettor 3-bets, then everyone else might fold, meaning that would have been better off had you simply called. If we want to get really technical, we can talk about situations where narrowing the field can be a good thing if some of your outs are overcard outs. But we won’t go there in this article. The main idea is that whenever you’re drawing in limit poker, you need to know the odds against you hitting your draw, and you need to always figure out whether a raise for value is in order.
Your knowledge of your opponents is always imprecise at best. This imprecise knowledge will result in some uncertainty regarding the possibilities of 1) an aggressive opponent isolating you and 2) too many players folding to your aggression. Be comfortable with the existence of this uncertainty, but also let it prevent you from pushing edges that are too thin (or edges that aren’t really there at all).
Aggressively pushing small edges is the key to playing winning limit poker. The example discussed in this article was a drawing situation, but many other situations exist in limit poker where you must push marginal edges to optimize your results. One such situation is value betting in position on the river, as is discussed in the article here at Poker Helper entitled “Don’t Bet the River in Limit Hold’em Just Because You Have a Good Hand.” Basically, whenever you’re heads-up in position on the last round of betting in limit poker, and you have a decent hand, you should bet any time where more than 50% of the calls you’ll get are from hands that you beat (note that this percentage increases if your opponent will toss in a mixture of check-raise bluffs and check-raises with hands that have you beaten…if your opponent never check-raise bluffs, then you can always lay down, meaning that the 50% number still holds, but if your opponent check-raise bluffs only a small percentage of the time, pot odds will force you to make calls that will result in you having to call when you’re probably beaten a majority of the time) .
To properly recognize all of your pushable edges, you have to be pay close attention to your opponents and the odds. Many players like limit poker because it seems to be a more carefree way to pass time than its no-limit and pot-limit counterparts. However, a major part of limit poker is paying close attention and recognizing situations where you can squeeze out extra EV. By paying close attention and squeezing out as much extra EV as you can, you’ll find that your results at the limit tables will be more profitable (and therefore, more enjoyable).
Tony Guerrera is the author of Killer Poker By The Numbers and co-author of Killer Poker Shorthanded (with John Vorhaus)
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