To listen to Eileen describe the hand in question, check out this week's podcast episode.
The Hand History
5-5 table New York City Underground Game, 9-handed
Effective stacks are $1000
Villain limps in EP, second limper in MP, Hero raises in the CO to 55 with AQss, Villain calls, second limper folds
Villain checks, Hero bets 70, Villain calls
The Importance Of Theory In New Situations
This is a weird bet on the turn. Not many players will ever donk-shove 875 into 260 on the turn into an uncapped opponent. Given who the opponent is, we should assume this is a massive exploit against hero. So how can we counter such an exploit? If we call in a mathematically sound way, our opponent will only end up beating themselves.
What math should we be using to choose what hands to call here? There are two primary numbers at play. One is minimum defense frequency. How often do we have to call in order to be unexploitable? The other number here is our pot odds. What percentage chance of winning does a given hand need to be able to profitably call?
When we use these two numbers to guide us, we won't call too much when our opponent is value heavy, and we won't fold too much when our opponent is bluff heavy. It is up to our opponent to bet the proper ratio of bluffs to value to make sure he isn't the one being exploited.
Minimum Defense Frequency
Before we even look at Eileen's range on the flop, let's figure out the necessary percentage of our flop range to call. Our opponent has risked $875 to win $260. Therefore, if we call less than 23% of the time, our opponent can profitably bluff two blank cards. In practice, our opponents bluffs will often have some equity against a call. Therefore, villain needs even less than 77% fold equity with well chosen bluffs. This means we should be calling 30-35% of our turn range when villain shoves.
There is another way we can look at what hands should be making this call. We are calling 875 to win a total pot of 1135+875=2010. Therefore, we need 43.5% equity to make this call. In this spot, we are obviously most concerned about villain having the nut straight. How are some of Eileen's hands faring against the nut straight? How about against four nut-straight combos, two nut flush combos, 9Th and JTh? What if we add just two combos of low-equity draws, let's say T9cc and A9cc.
Hand - Equity against nut straight - Equity against nut straight and flush draws - Equity against nut straight flush draws and air
89 - 50% - 65.6% - 71.1%
66 - 23% - 51.4% - 59.6%
QThh - 20.5% - 29% - 46.8%
AJhh - 20.5% - 30% - 46.2%
AQhh - 20.5% - 43.9% - 56.2%
AQo - 0% - 38.1% - 44%
For me, the takeaways from these values are that sets and AQhh become a pot odds call fast. Also, as soon as we add a frequency of low equity hands, we will have many good pot odds calls.
Creating a Calling Range
Now that we have a sense of what hands do best against villain's likely range and an idea of how often we should be calling, let's take a look at Eileen's turn range.
Eileen said in the podcast that she opens about 20-25% of hands in the CO. I'm having her continue with about half of those hands on this flop. The unpaired combos are all either just the hearts combos or have an OESD. Also, 76s should be in that range.
If Eileen were to defend 35% of this range, that would be about 3% of all hands (there are card removal effects to be considered). Let's begin with the obvious hands and then see how far we would need to go to get to 35% of this range.
Range - Percentage of all hands
98s - .3%
98s, Flopped Sets - 1%
98s, Flopped Sets, Qxhh, 76ss - 1.4%
98s, Flopped Sets, Qxhh, 76ss, NFD - 2%
98s, Flopped Sets, Qxhh, 76ss, NFD, AQ-KQ - 3%
This looks like a reasonable calling range in order to be unexploitable. Our calls range from slam dunks to pure bluffcatchers. However, keep in mind that a balanced overbet of this size will be well over 40% bluffs. The fact that there is a card left to come OTT complicates things, but I think Eileen's call would be very defensible from a GTO perspective.
While I think it's important to understand that Eileen's hand is likely a theoretically correct call, it is also important to realize that in practice, folding this hand will rarely be a large mistake. I think a nice way to minimize your damage when facing an exploitatively nut-heavy range is to only call with strong hands that have equity against a straight. We can get pretty close to MDF, about 20% of our turn range, by calling just these types of hands.
It is easy to look at a huge bet like this and fold everything but the absolute strongest hands. There were plenty of reasons mentioned on the podcast about why someone maybe would not want to play a value hand like this. If we fold to much, we may be giving people incentive to be very bluff heavy in this spot. Therefore, it's important to call enough to make our opponent think twice before ripping it.
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