In my last strategy article, I posed the following question:

You have 40 big blinds and raise under the gun to 2.3 big blinds. Only the big blind with the same stack calls.

The flop comes 8h 7d 6h. The big blind checks.

Which of the following hands would you bet, and would you use a small size (third pot or less) or a large size (two-thirds pot or more)?

(A) KK
(B) AA
(C) 33
(D) Ks Qs
(E) Ks 6s

Now let’s look at the optimal strategy for each. In a number of these examples, a solver will take different actions a certain percentage of the time, technically referred to as mixing. Mixing occurs for a number of reasons I won’t go into at this stage. What’s important to understand is that when mixing occurs, all of the options mixed are acceptable. If you were playing against a perfect opponent, you would have to mix to avoid opening yourself up to exploitation. In the real world, your opponents will be far from perfect, so it’s less important to mix, and generally reasonable to simplify your strategy to taking one of the options all of the time. The option you should choose if simplifying your strategy in this way is the one the solver takes the most frequently. With that in mind, I’m going to focus on the most frequent action the solver advocates with each hand primarily, but as I said to be playing completely optimally you should be mixing. Also, there is one very strong reason to mix with draws that I’ll get to later.

(A) KK
This is a situation that humans find very difficult, and often get wrong. You get dealt kings and happily raise. When only the big blind calls you expect to win the pot most of the time, but then you get this horrible flop. Instinctively you know it’s horrible, and it is because while you still usually have the best hand, your opponent has more very strong hands in his range than you do. You can have T9s, or any of the sets, but beyond that, you have very little two pair. Your opponent in the big blind on the other hand not only has T9s but also T9o, which means he will have the nuts more often than you (16 combinations compared to your 4). He also has 8 more combinations of straights, all the 95s and all the 43s. He too has all the sets, and way more two-pair combos than you. So he has what I called in the last article “nuts advantage”. We on the other hand have range advantage because we have the best hand right now more often than not.

This is where our human intuition often fails us. Feeling entitled to win the hand because we have kings, and not wanting our opponent to outdraw us, we bet really big (pot or more) to “charge his draws”. There are a number of problems with this strategy.

First, while our opponent has tons of weak hands that have missed in his range that will fold to our big bet, that doesn’t really achieve anything for us. In fact, we have made his decision a lot easier: he can just fold unless he has a strong hand or draw. If we bet smaller we give him a more difficult decision with his weaker and marginal hands, affording him the opportunity to make one of two mistakes: either fold too many of them or call too many.

Second, if our opponent has a strong hand or draw, he’s not folding to our big bet anyway. All the big bet really does is narrow the range to hands that already have us beaten, or could have by the river.

Third, when we do get called or raised after we bet really big, we are in a guessing game as to whether we are up against a very strong hand like a straight or a very strong draw. There are a lot of cards that can come on the turn that can complete a draw (a heart, or any card between a ten and a four) where we now have to guess whether our opponent has the draw that got there, or one of the others that didn’t. Bloating the pot when it’s so unclear whether we have the best hand on the flop, or will have after many turns, is not a good idea. It just juices up the amount our opponent can win with the best hand and incentivises them to bluff when a dangerous-looking card comes on the turn of the river. A much better plan is to keep the pot small fir now by either checking, or betting big enough to give a lot of hands a difficult decision but not so big as to just bloat the pot.

Because of this, the strategy on flops like this where we have a clear range advantage but serious nutted disadvantage is generally to check a lot, and mostly bet big but not too big when we do bet. Typically the hands we want to bet are either so strong we want to grow the pot or likely to be best right now but most vulnerable to being outdrawn.

With kings in this spot, our hand is not so strong we want to grow the pot, and while it’s vulnerable to any turn card that could complete a draw or an ace, it’s one of the less vulnerable made hands in our range. Therefore, we should usually check. This has the further advantage of strengthening our checking range. If we only check our weakest hands on the flop, our opponent can attack on the turn after we check. By checking some strong hands like kings, we have some hands in our range that can comfortably call a turn bet.

(B) AA
All that I said about kings is equally or more true of aces. It’s even less vulnerable than kings (which fears an ace on the turn) so has even more reason to check.

(C) 33
This hand is far more vulnerable than aces or kings, but that’s not a good enough reason to bet it. The best plan is to just hope our hand is best, check, and get to showdown.

(D) Ks Qs
This is similar to 33 in some ways. It will be the best hand right now a lot of the time but will be vulnerable on almost any turn card. It is different in one crucial aspect: if it’s behind right now to a one-pair hand like A8 it has far more outs (6) than 33 has (2). This actually makes it a better candidate to bet, because if 33 bets and gets called by a better hand it’ll rarely improve to a winner, but if KQ does the same, it will far more often and can win a bigger pot. Nevertheless, we should usually just check KQ, but if we are mixing we should bet it more frequently than 33.

(E) Ks 6s
On this board, this is a hand that falls roughly between 33 and Ks Qs in terms of value. It’ll be the best hand right now more often than both, but if behind it has more outs than 33, but slightly less than KQ. This means that all the characteristics that make 33 and KQ a good check apply even more so. As a result, this is a hand the solver pretty much always checks.

It’s worth passing in noting that this is another hand where our human intuition often fails us. Our natural instinct is to bet to “protect” our hand, but as with the aces and kings, betting doesn’t actually accomplish much here. Most of us emphasise “protection” far too much in our strategy because it’s memorably hurtful when we get sucked out on.

Given that all of the above hands are either checks or mostly checks, you may be wondering if we ever continuation bet on this board. The answer as we will see in my next article is that we do. In that piece I’ll look at the hands we do want to bet, and explain why.