15/12/2011

Marginal Hands in Shoving Situations

Alex Rousso

One situation every tournament player finds themselves in often is the decision to shove or not with a marginal hand when down to a stack of between five and eight Ms.

A lot of these situations are standard. If opening from the button with an M of 5, when there are antes and fairly tight players in the blinds, you’re pretty much shoving anything. If under the gun with an M of 7 against a table with a couple of players who have limp/folded recently, you’re saving your chips with virtually anything but premium hands.

However, all too often we find ourselves in marginal situations. When opening with a shortish stack from mid position, it’s not clear whether one should be shoving or folding with hands like A6o or JTo. Certainly, with antes out there and a stack with anything under an M of 5, I think a shove is warranted, but there are lots of contributing factors. I want to have a closer look at these marginal situations.

First, let’s consider these other factors:

  1. Table dynamic. Is the table passive? Are you getting walks in the blinds? Are people limp/folding? If the answer is yes to any of these, you might consider being less risky with your open shoves.
  2. Position. If you have one player behind you, the chances that he has Kings or Aces is about 1%. With five players behind, it’s about 5%. The more players behind, the more likely you are to get called, regardless of player type.
  3. Fold equity. Steal success is also down to how tight the players are behind you. Players who are folding everything but Aces and Kings should be shoved on with anything – the maths is irresistible here. However, note that this factor has two dimensions – the looser a player is, the more equity your hand will have against it when called.
  4. Hand value. Last but not least, we have your actual hand. Where fold equity is usually the reason that stealing is profitable, you should expect to be looked up by opponents too. How your hand fares in this situation can be a major contributor to equity in your hand.

It’s this final factor that I want to pay particular attention to here.

In the table below, I’ve taken a motley collection of hands which I find can be marginal in those not-quite-short-stacked-yet situations. These are times when continuing to fold will mean having to shove a whole bunch of rubbish in a couple of rounds, but shoving just yet doesn’t seem like a money-making play given your opposition, your position and your holding.

I’ve pitted each of these hands against a calling/shoving range from the opponent of top 5%, 10%, 15% and so on up to top 50% hands. Note that the resulting equities are just as valid if you find yourself looking to call a shove with one of these hands (presumably with much shorter effective stacks) or whether you are doing the shoving yourself and looking to steal or have some show down value.

I’ve put Q7o in there too just to show what the so-called “middle of the range” hand looks like in comparison. Note that Pokerstove (my resource for these equity figures) actually puts Q7o at slightly above the median hand (it says Q7o is around top 48% - reckoning T7o is the median hand).

I’ve colour shaded the equities to make it more obvious how steep the rise in equity is for certain hands as compared with others. Note also the right most two columns. The “percentile” column is where Pokerstove places that hand in ranking. So J8s is in the top 24% of hands according to Pokerstove. The “P(next 5)” column is the probability that you will NOT get a hand in a higher percentile in the next five hands (if you fold of course).

Hand 5% 10% 15% 20% 25% 30% 40% 50% percentile P (next 5)
A6o 28.2 34.6 39.2 41.7 43.6 45.5 48.6 51.1 31 16
44 33.0 40.9 43.8 45.0 46.8 47.1 49.2 50.7 37 10
22 32.0 39.8 42.6 43.7 45.1 45.5 46.6 47.3 60 1
JTo 29.5 31.7 32.2 35.2 37.6 40.3 42.8 45.6 20 33
J8s 29.2 32.6 33.9 35.8 36.9 38.5 40.4 43.6 24 25
97s 28.4 33.1 34.7 35.6 36.2 36.4 38.3 39.6 35 12
Q7o 24.7 27.1 29.3 32.0 33.2 35.2 37.5 40.6 48 4

Although it’s very rare these days that anyone will shove with only 5%, it’s certainly possible due to ICM that people will having a calling range that narrow. It’s interesting that all our marginal hands perform quite badly against such a range (all of them, including the low pocket pairs, are between 3/1 and 2/1 shots). However, if your opponent is folding 95% of their range, it’s presumably profitable to be shoving anything if there are antes and you are shortish stacked.

More interesting is the way the equities increase as opponents become looser and looser. Low pocket pairs, which start off being roughly as much of a dog as the suited and connected type hands such as JTo, J8s and 97s steal a march on them as opponent ranges get to around the 15-20% mark. At that point, the pairs are a full 10% better equity wise that the drawing hands. Yet as we expand the opponent’s range to 40-50%, the margin closes again to within a few percent.

The broad reason for this is domination. Up to the 5% part of an opponent’s range, there is a healthy portion of high pocket pairs – holdings that dominate hands like 44 as much as they do 97s. However, expand the range to 15-20% and the hands that get added are the suited and unsuited Broadways, along with a few suited Aces. These are holding which hands like 44 are not dominated by, but hands like J8s and 97s are.

Expand the range a bit further – to 40% or so – and the hands that get added are those which the likes of JTo and J8s can do better against; hands that they themselves dominate (e.g T8s). By comparison hands such as 22, much as they will always have around 45-55% equity against unpaired hands, are not getting any new “bump” in equity. They’ll be around 50/50 against 75o, just like they will against AJo.

I’m not sure one should start tinkering with shoving ranges solely depending on an opponent’s likelihood of calling. It’s also still contingent on how many players you have to beat and your stack size. Nevertheless, the table does show that certain types of hand are better against generally cally players and generally foldy players.

Against cally players weak Aces and low pocket pairs do reasonably well. Against foldy players, the hope is that they fold(!); hence we can add marginal hands such as the J8s and 97s to the range in the knowledge that our equity if called is not terribly worse than if we had shoved with a more genuine hand such as A6o or 44. The caveat here is that against generally foldy players, you need a whole bunch of them behind you (say, more than three) before you opt not to shove with ANY of these hands (excepting perhaps Q7o).

The other point of interest is the final two columns. They assess the likelihood that if you folded this hand now, you would be dealt a better hand in the next five. Note that the percentiles I’ve used are from Pokerstove’s ranking which is derived by pitting every hand against every other hand. 22 thus performs relatively badly (Pokerstove says it’s only a top 60% hand) because it doesn’t do well against 54o for example. However, it’s worth noting regardless of how the hands are ranked, that if you have a top 20% hand, the chances of you being dealt a better hand in the next five is only 33%.

The scope of this article is too narrow to conclude shoving and calling ranges based on stack sizes and number of opponents behind (I would recommend Kill Everyone and No Limit Hold Em Theory and Practice for that). However, it’s worth noting that these marginal hands – despite being quite different in other poker terms (how they flop, what depth of stack is best for playing with them) – when it comes to the shove or fold part of a tournament, they all fare quite similarly, regardless of opponent shove/calling ranges.

This article first appeared in Bluff Europe magazine.