Quiz: Tournament – AA in Late Position Facing Two Villains

Donkey Test Question #18

Question:

You’re in a multi-table tournament. Blinds are 100/200. A novice calling station raises UTG to T500. An unknown player flat-calls in MP. Everyone, including you, has about T20K in chips. You are in the cut-off seat with Ah-Ad. What should you do?

  1. Call
  2. Raise to T1000
  3. Raise to T1600
  4. Raise to T800
  5. Raise to T2300

Answer:

(a) Raise to T2300

Introduction & Overview:

I assume that you know that calling is a poor idea; it is both dangerous (in that it allows your opponents to see a free flop and out draw you), and it doesn’t maximize expected value (because it doesn’t build value when you have the best hand). A good preflop rule of thumb is to bet or raise when you think you have the best hand. Here we have the best possible preflop hand, so raising will almost always be the right play. The harder question is to determine how much to raise. Let’s fall back to our old friend, REDi, to see what it tells us about bet sizing—and verify that raising is indeed the right play, too!

R is for Reads:

We have 100bb effective and are in the early stages of the tournament. These two facts usually means people are not feeling the pressure to do anything rash. This is usually the period when people are just feeling each other out, playing relatively straight forwardly, and maybe trying to see some cheap flops and grind up a stack. Yes, there might be some crazies, but usually, early in big, deep-stacked MTTs, people are settling in for the long-haul at this point.

Villain #1 is a novice calling station who raised UTG. By “calling station” I assume we mean a fairly passive player who will call down light. When a player like this raises preflop it is definitely noteworthy. This is especially true given that he’s UTG; even bad players these days understand that they should play relatively tight up front. From this, we can assume he almost certainly has a reasonably strong hand. We hold two rockets in our own hand, so combinatorics say that he is more likely to have 77-KK than he is to have AA or AK, but those hands are also in his range. We can also assume he has something like AJs+, AQo+, and KQs+ in his range.

Villain #2 in middle position cold calls, but we don’t know anything else significant about him. If we assume he’s a straightforward player, then he’s probably cold-calling with a small or medium pair, weak to medium strength Broadways, and/or some kind of suited connectors and hoping to get lucky on the flop. Perhaps AXs is in his range, too, but again, because we hold two of the aces, this is somewhat less likely.

We have to cognizant of the three remaining players left to act on our left (Button and the two Blinds). For purposes of this quiz, we’ll assume we know they’re going to fold–but in an real setting, you need to “look left” and try to gauge what these folks are thinking about their hands. Are they all getting ready to fold?  Is one of them gathering chips and looking like he wants to raise? Depending on what you see, what you decide to do in the hand may be affected.

E is for Evaluating, Estimating & Equities:

With us holding rockets, our pot equity (PE) against the two villain’s ranges is (obviously) great; an equity calculator puts us around 70% against both villains. We’d love to get all our money in preflop against both players and run the hand hot-and-cold to the river, as this would be the maximum EV situation for us. (Don’t listen to anyone who says you want to limit the field and/or get heads-up with Aces because it increases your chances of winning the hand. Our job in poker is not to win the most number of hands, it’s to win the most money by maximizing EV.  All-in preflop against multiple opponents with Aces is the epitome of maximizing expected value.)

Our situational fold equity (FE) is moderate. We’re multi-way and relatively deep-stacked. Further, the problem states that the UTG villain is essentially a calling station. If/when we raise and he calls, the second villain might also feel obligated to call behind with a large portion of his range, too. I’m estimating our FE is between 25-50%, with the lower end of this scale associated with smaller raises by us (i.e., we’ll tend to get fewer folds the smaller we bet), and the upper end of the scale with larger raises we make.

Depending on how much we raise (and assuming we just get called preflop by one or more of the two villains), the SPR on the flop will range between 3 and 8. Said another way, we’ll be somewhere between just pot committed and definitely not.

D is for Deciding:

Given that our PE is 70% and our FE is between 25-50%, we’re on a pure value line. (Well, duh, right? We have preflop Aces, after all.) Calling preflop is terrible in this situation, as we are a) minimizing expected value; and b) letting the villains see three “free” flop cards. A value line executed with a raise is the right play.

We should be raising to build a pot whilst simultaneously enticing the villains to call with worse hands. Further, we want to ensure we don’t price either bad guy into calling correctly and hitting their outs on the flop. Ideally, we want one of the bad guys to come back over the top on us so that we can try to get all the money in before the flop.

I is for Implementing:

So, how much should we raise? There are a number of rules of thumb and general advice to follow in this situation (e.g., 3x the V’s raise size + 1bb for every cold caller), but I tend to default back to the math to more accurately answer this question. I.e., let’s calculate the theoretically correct bet size via our old friend the EV equation: EV = (FE x Pot) – ((1-FE)((PE x (Pot + Called Amount))-((1-PE)x(Raise))).

To use this, we simply plug in the various raise sizes and see what falls out. The only tricky part about this is the fact that FE is a function of how large we raise. For purposes of this quiz question, I’ll assume that our FE is 25% if we raise to T800, and then linearly increases up to 50% for a max raise size of T2300.

Running these numbers gives us:

In other words, even though EV is rolling off somewhat with higher bet sizes, the largest raise option (T2300) still results in the maximum expected value.

So now that we know the theoretically max-EV amount to bet, the only remaining question is whether we should tweak the number up or down a bit to entice our opponents to call, or, even better, come back over the top on us. A lot of this will depend on the villain’s perception of us and how aggressive the bad guys are. For instance, if you think one or more of the bad guys will give less respect to a smaller raise, then perhaps making the bet a little smaller would be correct. On the other hand, bumping the raise up larger may look fishy (kind of like a squeeze), so betting larger than T2300 might be ideal (plus it increases EV). In this case, we know very little about our opponents, so we’re going to play straightforwardly and just bump it up to the max proffered answer: T2300.

In this case, we know very little about our opponents, so we’re going to play straightforwardly and just bump it up to the max proffered answer: T2300.

Discussion/Takeaway:

Okay, so this wasn’t a particularly challenging question. Hopefully, your instincts weren’t to flat and get tricky with fancy play syndrome. Further, you should have been thinking about betting on the larger size. In other words, the general rule you should default to whenever you are sure you have the best hand is to bet the largest amount you think you can reasonably get called with by a villain holding worse cards.

What would happen, for instance, if we just shoved preflop? Unless he’s crazy, the second villain will probably fold 100% of his range. The first villain, however, would call with the upper end of his range (namely KK+, AKs). These hands represent around 18% of his initial range. In other words, shoving should result in a situational fold equity estimation against V#1 of roughly 82%. With a single caller, the EV of shoving and getting called by the top 18% of V#1’s range is: $3400. Note that this is actually significantly higher than any of the previously calculated EV values for the answer choice options. In other words, just re-shipping here might be the best course of action. Yes, you’ll get a lot of folds, but V#1 will call with enough of his range, and you’re crushing those cards.

As always, the key in poker is to slow down and think about your options before acting. Never, ever, snap-decide on anything in poker. Make the reads. Do the math. Choose on the best line. And then maximize expected value with that line. That’s reallyk all you can do in poker. The rest is up to the cards.

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One thought on “Quiz: Tournament – AA in Late Position Facing Two Villains

  1. And the excellent posts keep coming!

    I was dithering on the T1600 and T2300 raise options. Each would most likely see stacks in the middle so I was trying to decide which would be the better line. Didn’t think to apply the EV formula. D’oh. But I find that in tourney’s EV is just one aspect of the strategic considerations.

    There were very few branches of the (mental) scenario decision tree that didn’t see stacks in the middle either on the flop or at worst on the turn with either bet size.

    I have to admit, that in the end as this was a tournament, I landed on the larger bet size as it had more chance of getting heads up with V1 and therefore a greater likelihood of me doubling i.e., lowest risk of a bad beat. In a cash game however, I’d probably go with the smaller bet size as it has more chance of both players coming along and I’d be happy to take the greater risk of a bad beat for the still better than evens chance of tripling up.

    Too nitty?

    I had a similar blog conversation with Sky some time back about tourney decisions vs cash decisions and he was all about taking the most EV path irrespective of whether it was a tourney or cash if there were no ICM considerations to account for. I haven’t come around to agreeing yet, probably because I place a higher value on my tourney life since my volume is so low these days.