There was a very interesting hand played during the final table of One Drop 1 million buy tournament. The hand inspired a lot of discussion about optimal play and intuition-based play. Tobias Reinkemeier (finished 5th for $2,053,334) made a very big fold. In this post I will go over that hand and see what PioSOLVER thinks about it (or rather what optimal play looks like). You can watch the whole hand:

First, let's describe the situation to PioSOLVER:

• Starting pot on the flop is 3,225,000, we will use 3,225 rounding to thousands of chips.
• To describe Seiver's pre-flop stealing range we will use our default "UTG/MP 6max" which should be close enough.
• To describe Reinkemeier we will use our default "6max-BBvsCO" slightly adjusted for the stacks depth (big pocket pairs will have smaller weights are they are likely to just go all-in with those stacks).
• The bet sizes are 1,500,000 and an all-in for 6,825,000 (so overall 8,325,000 invested)
• The board is 4c Qs 2c; we don't need to insert any more cards, the solver will produce a solution tree for all possible turn and river cards and we will just navigate to what actually happened at the table. We are interested in optimal play from the flop.

Here is a GIF with me going through those stages: CLICK

Facing an all-in bet Reinkemeier expresses a lot of thoughts about the hand and possible holding of his opponent. Let's go through them:

1. "With a club I would have paid the bet already"

Let's see:

It's true that AcAx is a better calling hand than AA without a club. The difference isn't that big though: about +10,500,000 for a call with AcAx and +8,000,000 for a call with AA without a club.

2. "You don't have the Ace Queen, I don't think you would jam a KQ there"

PioSOLVER disagrees:

Those hands in fact should jam the turn (the ones which check are either made flushes or have a high club). This is a common thing in optimal play which is currently out of fashion: bets for protection are often very good idea.

3. "You don't put me on aces either"

 Well, that's true. That's why we only gave 0.1 weight to AA preflop.

PioSOLVER doesn't agree but after long thought Reinkemaier makes the fold.

We can see (on the first picture) that this fold is huge mistake in terms of optimal play. It cost him about 8,000,000 in expected value. Main difference between Reinkemaier's analysis and what is actually happening in equilibrium play is his view about what AQ/KQ would do. We can see that those hands bet quite often on the turn while Reinkemaier assumed they would check (betting smaller doesn't really makes sense at this point with those stacks). With that assumption AA is similar to weak top pair hands there (it doesn't beat anything but bluffs). In fact, queens like QT/Q9/Q8 without a club should fold this river while having a club makes it an attractive call. CLICK for a GIF going through the hand and showing expected value for a call with QT/Q9/Q8/Q7. Having that in mind the fold wasn't reckless. It's just assumption about AA being similar to top pairs there was incorrect.

There are a lot of interesting points in this hand:

• It's very difficult for a human to make correct range analysis. Reinkemayers is a great player but he underestimated how often AQ/KQ and bluffs shove the turn
• Top players make a lot of guesses and reads. Current game is still more about outguessing your opponent than about being mathematically sound. There is huge opportunity for players who can just execute cold-blooded math approach.
• Solving for equilibrium tells us that the fold wasn't close. I don't think Reinkemaier would make that fold had he realized that he was giving up 8,000,000 vs optimal opponent. He probably thought the difference is small enough to justify going with the intuition.
• While Seiver's play looked reckless to many commentators it was actually very good by equilibrium standards. While KsTs a check on the flop his turn jam is what optimal solution recommends once the flop bet was made. It's a common pattern that mathematically optimal play is way more aggressive that what humans currently do. 

A lot is going to change when players become aware of optimal solutions. This hand is just a tiny demonstration. PioSOLVER was written with way more complicated multi-street deep stack cash games scenarios in mind.