Discontinuous Poker Hand Values

How do you know what your opponent has? Well, poker is a game of hidden information; and, one can use that information to exploit one’s opponent. Specifically, even those few cards you hold are worth their weight in gold. Let’s see how it works.

Preflop Hand Selection And Card Removal

In no-limit hold’em, the preflop value of one’s hole cards is chiefly relative to the probability those hole cards connect to a random board. Secondarily, hole card value accounts for the likelihood of various board textures. That’s a big concept. High cards aren’t the only types of hands you want to play. Selecting the best set of hands (what poker players call a range of hands, or a distribution) isn’t about only ranking the top X percentage of hands. An example easily illuminates this fact. And guess what? We also get our first glimpse at discontinuous hand values.

If we play only big pairs and high cards, then low boards make it very unlikely that we have an extremely strong hand relative to competitors who call preflop. That’s because it is more likely that preflop calling hands, what are often also speculative hands, do better than our high card-heavy hand range on low boards. As the preflop raiser, if you can’t flop the nuts on 5 4 3 boards, then your ability to bet these boards diminishes and you rarely win hands as the aggressor. It’s that, or your opponent can simply bluff-raise your bets far more successfully than if you played this board texture more in line with the distribution of your holdings. Now, there is a lot of nuance there with what ratio of what deceptive and low hands (usually smaller pocket pairs and suited connectors do the trick) to add to any given range from a given position and with a particular stack size, but for now, let’s take the idea that we flop unfavorably sometimes and run with it a bit.

The most important takeaway to start is that hand values are discontinuous. This means that a head-to-head match-up of the hands is, at some point, not the key metric in ranking the value of hands. So, even though K-J suited beats 7-6 suited in a heads-up all-in confrontation, 7-6 suited might rank higher in the set of hands we prefer to raise with preflop. These deceptive substitutions are a bit more intuitive in earlier positions, as less than premium high card hands like K-J suited run into other problems like reverse implied odds caused by kicker trouble when they flop a single pair. By making a few deceptive substitutions, we protect ourselves a bit on those low boards, and that goes a long way towards thwarting aggressive players on low boards when our range is high card-heavy and we want to bluff.

Thirdly, card removal effects can sometimes absolutely dominate hand valuation. Card removal effects create some of the most interesting poker conflicts possible in the game. Let’s check out how those conflicts combine with preflop hand selection in ways that allow us to exploit discontinuous hand values.

Discontinuous Rankings And Effective Nuts

Hand rankings are relative, as we have seen with our simple preflop example, and the concept extends to postflop play and permeates the game. The strength of a hand is relative to stack size, board texture, player tendencies, and more. As we showed, if a player cannot have the nuts, then the best possible hand is the effective nuts. If a player does not raise 7-6 suited preflop, but raises pocket fives preflop and the board falls 5 4 3, then 5-5 is the effective nuts. Conversely, if we flip the notion on its head and we know our opponent never calls with 7-6 suited preflop and we raise with a hand like 6-6, we are called by that player, and the board falls 5 4 3, then we have an excellent chance to abuse the idea of discontinuous hand rankings in combination with rare board textures.

Rare Boards

Rare board textures often lead to exploitation, particular with lesser experienced players. For example, an early position player may always continuation bet a hand like pocket eights on the 5 4 3 board, which makes his likely checking range on the same flop extremely weak. In fact, in many games, early position preflop raisers simply check and fold 5 4 3 boards all the time. We can use the idea of blocking the effective nuts in order to construct a counter-exploitive check-calling range. In other words, for a given board, let’s continue using our 5 4 3 board, we find the nuts 7-6 suited. Secondly, we find a hand that we raise that shares cards with those nut hands. Thirdly, and often overlooked, we want a hand that cannot get value from worse hands at a high frequency. If you have been following along, then you see that 6-6 is the perfect hand for a check-call on this board texture because of the postflop blocking and unlikelihood to get value from slightly worse hands.

Postflop Blocking

Determining how to play your postflop blocking hands is a multi-step question and answer process that begins with basically any poker situation with hidden information. What is the nuts for this board? Do I have a hand that both blocks the nuts and connects with the board to beat a bluff at showdown? Is my hand too weak to get sufficient value by betting?

The reasons that these questions are important is because they exploit hidden information you have about the board. So, your opponent cannot know if you have a middling strength hand, or a hand that blocks his nut combinations. That hidden information is extremely important because when your opponent attempts to create a proper semi-bluffing distribution, you can exploit his strategy by using blockers to manipulate the ratio of value hands and bluffing hands that your opponent bets. In other words, with proper use of postflop blockers, you’ll be creating situations that an otherwise balanced player bluffs you far too often and you can profitably call! Let’s look at a simplified example.

We have checked and called the flop and turn on a 5 4 3 K board. The river is the Q and our opponent bets the size of the pot into us with a range of 7 6, 7 6, 7 6, 7 6, J 10 and 9 8, for a ratio of two value bets to one bluff. For reasons that we won’t get into in this article, we need to win one out of two times in order to make this call a break even one.

Let’s say that our hand is 8 8, then we should call and expect to lose two times for every one time we win; but we also expect to prevent our opponent from bluffing us all the time. With 8 8, we break even by calling. But, if we check-call with 6 6, not only do we protect ourselves on a lot of scary turns and rivers, but also on a 5 4 3 K Q board, we can check-call with confidence knowing that our opponent’s betting distribution has changed from 7 6, 7 6, 7 6, 7 6, J 10, and 9 8 to 7 6, 7 6, J 10, and 9 8. Without the two sixes that we hide in our hand, our opponent uses the same combinations to bluff and over-bluffs the spot, which gives us a pleasantly profitable call. Pretty cool!

Semi-Bluffing And Discontinuous Hand Values

Discontinuous hand values can be extremely telling also when you are semi-bluffing your opponent. For example, let’s say that on the turn that your opponent raises you on a 7 6 2 K board and you hold A K. Let’s say, for the sake of the example, that this player raises with the six combinations of the nut flush he plays, two combinations of king-high flushes he plays, and 16 combinations of bluffs, which, for his river bet size, should make you indifferent to calling or folding with a solid hand like A K. But, if you hold A K, then your opponent is only value-raising you 25 percent as often as he originally planned. So, your hand becomes fantastic to use to bluff catch. So, not only do you have equity against the king-high flushes on the turn when you call the raise, but you also know that if your opponent continues betting the river that you are extremely likely to see a disproportionate amount of bluffs continuing and that you may call with any piece of the board that beats your opponent’s most likely bluffs. ♠

Reid Young is a successful cash game player and poker coach. He is the founder of TransformPoker.com.