Fear Factor in Seven Figure Pots: Finding Equilibrium on Doug Polk's Hand

May 30, 2023. Gardena, California.

Imagine that you are playing the most expensive game of your life. You've bought in a million dollars at the table, and the game is being streamed live to the largest audience in the history of poker. You're already down $300,000, and you get two aces in the small blind. You 3-bet and get called by a rich crypto investor. Next, you bet-bet-bet on a relatively safe runout.

The opponent thinks for a long time. You pray to hear the call. But all of a sudden, all your dreams go to waste: he announces all-in. What will you do?

This is exactly the situation Doug Polk found himself in during his recent appearance on the Hustler casino stream.

In this video, we compare Doug's thoughts with the machine's recommendations.

Preflop

Doug Polk: I look at my cards and I see aces! I will always 3-bet because it's the nuts, you need to build the pot. There is also a chance that some of the participants in the hand will want to up the stakes even more. Maybe Hank will reraise again to win the hand for the Stand-Up Game already preflop.
Tom Dwan folds, and Hank calls. I think he should almost always call with this hand and only occasionally 4-bet.

The game is $500/$1,000 with a $3,000 ante in the BB. Let's ignore Tom's limp and consider the reaction of the small blind to a raise from the hijack.

Aces, as we can see, always 3-bet.

And AJs on the hijack mostly call.

It is important to add one factor that Doug mentions: the hand is affected by the Stand-Up Game: the last player not to win at least one hand will have to pay the rest of the players a fine of $6,000 each. Doug is already safe, Hank is not. Of course, this encourages players to fight for pots more aggressively, but there is still no solver that could calculate the strategy taking into account such rules, and manually adjusting the ranges based on general considerations seems a rather risky task. Probably the most obvious adjustment would be to always take a more aggressive decision in situations where the solver insists on a mixed strategy. However, at later stages in narrower ranges, this will not matter, so we will use the standard GTO ranges for analysis.

Flop

Doug Polk: You need to bet fairly wide on this texture. I choose sizing around a third of the pot. In fact, I bet a little more, perhaps I miscalculated the size of the pot. Frequent betting with small sizing seems very logical to me here. I expect Hank to call wide preflop as he tries to win the hand for the Stand-Up Game, and our exceptional stack depth gives him very good potential to draw in position if he hits. Given Villain's very wide range and the significant advantage of my range, small sizing frequent cbets are my thing.

The solver approves of wanting to bet a lot of c-bets and generally doesn't mind a small c-bet with aces. But Doug doesn't talk about other sizings in his analysis. The standard sizing in an effective 100bb stack becomes less of a standard sizing as depth increases. The solver is a greedy creature and chooses sizings in such a way that it is comfortable to stack with the best hands.

On the right – the c-bet strategy with SPR=4, on the left – with SPR=16, as in the hand. In deep stacks, the solver will overbet 140% of the pot with about 20% of their hands, including about half of their overpairs.

Doug Polk: Hank should at least call with his backdoor flush draw. I think it's okay to put in a raise sometimes, as his hand blocks a lot of my value hands – aces, jacks, AQs, QJs, and can also barrel if the turn comes a diamond or a broadway card.

Turn

Doug Polk: On a blank turn, we usually want to continue sizing around 2/3 of the pot. We bet wide and small on the flop, bet narrower and bigger on the turn, ready to continue on the river. The lower end of value is . It is possible that with part you can check. Aces and kings will almost always bet.

It seems that Doug, unlike the solver, prefers to use only one sizing here.

This makes sense, as it is difficult for people to correctly split their range into multiple sizes. Adding a not-too-large sizing allows you to bet with weaker hands. The following diagram shows the consequences of betting 1/3 of the pot – in this case, we can barrel with top pair and weak kicker and even some underpairs, attacking small pairs and weak draws in our opponent's range.

This can be useful out of position in deep stacks where it is easy for your opponent to realize the equity of his hands.

Doug Polk: For Hank with the nut flush draw, I really like calling. Ace-Jack outs can be considered pretty clean in this case, and raising and getting a 3-bet would be a disaster. Having a position allows you to perfectly realize equity in case of arrival. For bluffs, you can use weaker hands, for example, or .
It is also logical to turn some hands with which we floated the flop into a bluff , like , but this is hardly appropriate here – they are too weak.

River

Doug Polk: The question is how do we play aces on the river. What do we want more: setting a trap with a check or getting a third barrel? Both options are logical in their own way. Technically, it's slightly better to trap when we have a queen in hand, which makes our opponent more likely to draw. When we have aces, he will have KQs, QJs, QTs more often.
Who knows, maybe he will persevere with or , but we don't have an ace of diamonds.
Of course, sometimes he will reach the river with Q9s, but you can only live with it. Since he didn't raise either on the flop or on the turn, it's pretty rare for his range to be stronger. , and with aces I should draw.
I like betting 2/3 of the pot, I don't think it makes sense to lower the sizing and block bet. I would play one size here. By the way, when we start playing with a polar range, we almost never reduce the sizing on the next street unless the texture changes too much. If the 9 of diamonds came on the river, I would mostly use block bets, but the 9 of hearts has almost no effect on the situation.

Doug Polk: If I were him, I'd throw it out and thought he played the hand well. Jack of diamonds blocks , but there may be other combinations of JTs in my range, so this is not the most important consideration.
For a bluff, I'd rather take a hand that blocks a set. Of the sets, I will most often have a set of eights (I would slowplay a set of queens at some point). Bluffs look good with , , maybe with .

“I don't think I can make that call,” Doug shakes his head, but continues to think about the situation.

“I wish I had ace-queen,” he mutters. On the other hand, I don't have many better hands.

Can you show what you have? someone at the table asks. Doug flips over his cards instantly.

“I wish I knew something about you, Hank,” he says, “besides the fact that we took a photo together with you last year, ha ha! How few strong hands you have... Sometimes sets, sometimes . Crap! I feel like I still have to make this call from time to time.

“Okay, here's what I'm going to do,” Doug continues after a long pause. – I will call once out of four. I have two aces, spades and hearts. I will shuffle them and if the ace of hearts shows up twice in a row, it will mean a call, otherwise – a fold.

First, he invites a neighbor ( another crypto investor named Wesley ) to try himself as an RNG, but the dealer apologizes and reminds that, according to the rules, other players have no right to influence the hand.

On the first try, Doug opens the spade.

His delighted opponent shows the bluff with a loud cry.

Doug Polk: There's another factor on Hank's side. Most people just don't bluff in these spots! He misses a draw and needs to risk a million dollars when I've been playing all streets aggressively and have all the nuts in my range. It's wrong to reduce poker to such simple reasoning, and we're used to high-level analytics on this channel, but to use such bluffs, you need to be not the most ordinary player...
I have no idea how Hank plays, I don't know him, this is the first time we've met at this table, apart from a photo together a year ago. When I don't know anything about my opponent, I make decisions based on the optimal strategy.
I have JTs. I will often 3-bet preflop with them, always continue on the flop and pretty often on the turn.
I never have – betting big with that on the turn looks like suicide.
Quite rarely I will have . I will occasionally slowplay them on the flop and quite often on the turn as I am blocking my opponent's calls too much. Most often from sets I will have . Fours and threes are almost unbelievable – I'll fold them preflop.
Of course, I will fold all my bluffs. He raises $200,000 to $1,000,000 and I'm allowed to fold quite a few hands.
I think it's better to fold aces and kings than – a queen in my hand blocks his set of queens and Q9s. However, one can argue with this – it is possible that there is not much difference between bluffcatchers with one pair.
I think I can fold aces quite often, but not 100% of the time. Against a very tight player I would fold them all the time, but I don't know anything about Hank. So I decided that straights and sets weren't enough to defend me, and I had to make some calls with pairs.
When he shoved, my first thought was that it was an obvious fold, but the longer I thought about it, the more I realized that the decision must be mixed. I ended up calling 25% of the time so I wouldn't overfold and let his bluffs beat me too much. Maybe some solver nerd will be able to calculate the required number!

So far, we have had nothing to add to Doug Polk's analysis, but it is worth pointing out a few points. His first impulse was to fold to a shove; recreational players don't usually bluff like that. It's one thing to bluff three barrels, it's quite another to move all-in on a man who bets three barrels with a polarized range full of the nuts. For this bluff to work, Villain needs to be able to fold some of the hands he bets for value. The vast majority of pros would have made a disciplined tight fold in Doug's place – 1400bb in the pot, and we only have one pair. It's easy to convince yourself that the pot is too big and the spot too unbluffable. Fold and wait for a better situation.

It's just that a more favorable situation may not present itself. Do not always back down in the face of aggression – it can become a bad habit. So Doug takes a break and begins a cold analysis of the situation, based on the concept of MDF – the minimum frequency of protection. His job is to prevent his opponent's bluffs from automatically making a profit. If for this you need to open the opponent's all-in for one pair with some weight, then so be it.

The solver doesn't like to open all-in with He rarely calls with this hand.

The main reason is that instead of Hank, the solver bluffs with hands containing a queen – QJs and especially QTs (and also with and ). It seems odd to bluff with top pair, but against a polarized range, a weak kicker queen becomes a pretty marginal low-expectation bluff catcher that you can get with a shove.

Is Hank technically strong enough to realize that he has to turn some top pairs into a bluff?

If there is no confidence, then we shouldn't call with . So, in the simulation where Hank is bluffing with J9s and , Doug's AQs all call the shove, and all Aces and Kings fold.

In passing, we note that combinations of AQs for protection may not be enough, since this hand, from the point of view of the solver, is not polar enough for a large third barrel. The solver prefers to play AQs with a blockbet.

Whatever the case, Doug ended up deciding that he should call with aces 25% of the time. Solver score – 30%.

Excellent result! It is obvious that Doug is well aware of both his range and the principles of poker strategy.

So how do we get rid of the fear of making a mistake in a huge pot? How to learn to make rational decisions at critical moments?

First, you should play with your bankroll.

Secondly, it is worth resigning ourselves to factors that we cannot control and focus on making ideal decisions within our own strategy. This approach allows you not to worry not only about money, but also because of the result as such, and maintains clarity of thought.

Perhaps there has never been a person in the history of poker who has mastered this method better than the one who left a million-dollar decision at the mercy of an unusual randomizer.