Your first poker range.

“They might have aces” names one possibility. It does not explain what else the opponent could hold, which hands your cards beat, or how often each hand takes this action. A range is a way to make those missing parts visible.

For beginners to standard 52-card no-limit Texas hold'em. Every scene is fictional, not Nolan's recorded play. Use cards, counters or paper; no wager, account or purchase is needed. This lesson follows turn and river decisions. It teaches how to describe uncertainty, not a recommended range or betting strategy.

1. A range is an account of possibilities

A range describes a collection of possible private hands. In a useful decision model it also describes their relative likelihoods. You can begin with a short list in words; you do not need a colored chart or software before you understand the idea.

Keep three layers separate. Known cards are your private cards and the shared board, plus any other genuinely exposed cards. Possible holdings are hands that do not reuse those cards. A proposed betting range is a model of which possible holdings reach this decision and choose this action. That last layer needs assumptions or evidence.

Imagine the opponent checks. That action is something you observed. “The opponent has a weak hand” is an interpretation. A player can legally check a strong hand, a medium hand or a hand that is unlikely to win. The rules do not turn a check into an exposed card.

Exercise 1: Does the check prove that your pair of kings is ahead?

No. The opponent could hold ace of clubs and ace of diamonds, making a pair of aces that beats your kings. They could instead hold queen of hearts and jack of hearts, making a high-card hand that loses to your pair. Both are physically possible on this board, and both can check.

This does not claim the two hands are equally likely. It shows why a check alone cannot prove that you lead. A useful review says which hands you consider and why they might check, rather than translating every check into “weak.” When their cards are hidden, your explanation should preserve that uncertainty.

A range is not a special ability to see hidden cards. It is a model you can examine and revise. Even a carefully reasoned range can be incomplete or wrong. Naming the assumption makes an explanation more useful than presenting a confident guess as a fact.

2. Remove impossible cards before judging plausibility

Return to your king of hearts and queen of diamonds on K♠ 9♣ 5♥ 3♦ 2♣. The king of spades is already on the board, and the king of hearts is in your hand. The opponent cannot hold either card. Those are physical exclusions, independent of how that opponent tends to play.

Consider four candidate holdings separately: K♠ A♠, K♥ J♦, A♣ A♦ and Q♥ J♥. A card code names an exact rank and suit: K♠ is the king of spades, not any king. In written study notes, the same card might be written Ks.

Exercise 2: Which two candidate holdings must be crossed out?

K♠ A♠ and K♥ J♦. The first reuses the board's king of spades. The second reuses your king of hearts. Neither is a legal opposing holding in this snapshot. A♣ A♦ and Q♥ J♥ reuse none of the known cards, so both remain physically possible.

Do not go further and call the remaining hands equally likely. Removing an impossible card is certain; deciding how often someone arrives with aces or bets queen-jack is a different question. Nor should you remove a card because you suspect a folded player had it. A guess about an unseen folded hand is not an additional known card.

Your known cards are often called blockers because they remove combinations from other players' possibilities. The label does not automatically favor your decision: a card can remove a strong opposing hand or remove a hand you hoped the opponent was bluffing with. First state what is removed; investigate the strategic consequence separately.

3. Compare four exact holdings, not four broad labels

Now use only the four holdings below as a deliberately small teaching model. Each row names one exact two-card combination. These are alternatives for the same opponent, not eight cards that opponent holds at once. Cards may appear in more than one alternative in a general range, but no individual holding may duplicate a known card.

Keep your K♥ Q♦ and the same complete board beside the four rows. Write the best five cards for each alternative before opening the answer. Saying “I have top pair” is not enough to compare it with all four.

Exercise 3: Which of the four exact holdings does your hand beat?

Only D, queen-jack of hearts. Your K-K-Q-9-5 loses to A's A-A-K-9-5, B's K-K-A-9-5 and C's 9-9-9-K-5. It beats D's K-Q-J-9-5. There are no ties in these four comparisons.

Aces are a higher pair than kings. Ace-king shares your pair of kings and wins on the first different kicker, the ace. The nines make three of a kind. Queen-jack has only a high-card hand on this board. The number of listed hands you beat is one; the probability of facing that hand has not yet been supplied.

Do not confuse these four exact holdings with the labels AA, AK, 99 and QJ. A label can represent several physical combinations. Before any cards are removed, a pocket-pair label contains six combinations; an unpaired label containing both suited and offsuit versions contains sixteen. This exercise intentionally starts smaller. The combination workshop teaches group counts after the distinction feels comfortable.

4. Equal chances are an explicit assumption

Change the action to a bet. In a fictional heads-up cash-game river decision there are 40 chips before the opponent bets 20. Both players began the river with 100 behind. You face 20 with enough chips to call. A call closes betting. Assume no fees, side pots or tournament-prize effects.

The current pot is 60. Calling adds 20 and makes 80; both players then have 80 remaining. The simple break-even share is 20 / 80 = 25%. This prices calling relative to folding now. It does not estimate your hand's equity or compare calling with a legal raise.

For this calculation only, suppose our opponent has exactly A, B, C or D at this betting decision, each with the same chance. No other holding is included. The equal likelihood applies after the observed action; we are not measuring how a real player arrives here. In this model your hand loses to A, B and C and wins against D.

Exercise 4: Is calling profitable if the four alternatives are equally likely?

It is exactly break-even relative to folding under these assumptions. You win one time out of four and never tie, giving 25% equity against this invented betting range. Receiving the final 80 one quarter of the time and paying 20 each time gives 0.25 × 80 - 20 = 0.

Equivalently, a win gains the current 60 and a loss costs the additional 20: 0.25 × 60 - 0.75 × 20 = 0. Earlier contributions are already in the pot. This says nothing about full-hand profit. Most importantly, listing four hands did not justify assigning equal chances to them. That was a supplied teaching assumption, not a conclusion about an opponent.

Here the three stronger alternatives can be treated as the model's value candidates, and D as its bluff candidate. Those labels describe this restricted betting model. A weaker made hand could bet in another model, and a real opponent can have hands we left out. Your kings are not automatically a pure bluff catcher against every possible betting range.

5. A possible bluff can appear less often

This optional step introduces a weight: a relative amount of probability assigned to a hand. Keep the same cards, same bet and same price. Assign weight 1 to each of A, B and C, but weight 0.5 to D. Those values describe the relative likelihood of the four alternatives at this betting decision, including the action history.

The weights total 3.5: 1 + 1 + 1 + 0.5. The share belonging to D is therefore 0.5 / 3.5 = 1 / 7, about 14.3%. A half-weight hand is not half of a physical card. It is a way to say that this alternative appears half as often as each full-weight alternative in the constructed model.

Exercise 5: Do you still have 25% equity because the same four hands remain on the list?

No. You now have 1 / 7 equity, about 14.3%, with no ties. D is still the only hand you beat, but it has less weight. The 25% call price did not change. In this revised chip model, the value of calling relative to folding is (1 / 7) × 80 - 20 = -60 / 7, about -8.57 chips.

This does not establish the opponent's actual bluff rate or the best action among every legal choice. It demonstrates sensitivity to one assumption. If a weight already includes reaching the river and betting, do not multiply the same action history into it again. For a more detailed construction, continue to the range-combination workshop.

Do not quietly turn “could be a bluff” into “is as common as every value hand.” Conversely, removing every bluff without evidence is also an assumption. When you cannot justify frequencies, preserve that limitation. A precise calculation conditional on uncertain inputs remains uncertain as a description of the real decision.

6. One revealed hand does not validate the whole range

Imagine the opponent eventually shows D, queen-jack of hearts. That reveals what happened in this one fictional hand. It does not reveal all the hands the opponent could have arrived with, how often they bet them, or which alternative model best described your earlier information.

Exercise 6: Does seeing queen-jack prove the equal-weight model was correct?

No. Both the equal-weight and half-weight models allow queen-jack. A single revealed result does not distinguish their frequencies. It also does not prove that your earlier call was good merely because it won, or that every future bet should be called.

Record the actual board, action and shown cards without adding a story you did not observe. Then ask a narrower study question: which other hands could take this line, and what evidence would change their relative weights? Keep other players' identifying information out of public notes. A useful review preserves what was unknown at the time instead of rewriting the decision around its ending.

Leave with a range question you can explain

Close the answers. Explain, in order: the known cards; the holdings those cards exclude; which remaining hands beat or lose to yours; the price of continuing; and the assumptions about how often each alternative appears. You can use the four exact holdings again without pretending they are a realistic complete range.

Keep a private study note with two columns, “Observed” and “Assumed.” Put the board, bet and amount to call in the first. Put the candidate range and frequencies in the second. Add one sentence about what would change your conclusion. There is no answer form here and no practice response is stored.

• If the five-card comparison was difficult, revisit kickers and ties.
• If the 20-chip call was unclear, revisit river calls.
• If exact holdings and labels became mixed together, use the combination workshop.
• If the model now makes sense, try the river Decision Lab before opening its answers.

These checks develop a way to describe a hand, not evidence of a profitable strategy or readiness to risk money. You can keep learning with fictional cards and counters. Safer-play and support resources are available without completing a lesson or opening an account.

References and limits

Read October 14, 2026: PokerStars' introduction to thinking in ranges, range overview and pot-odds lesson. These support terminology and study concepts. Broad claims that a check excludes strong hands, population range percentages or a particular action is best are not adopted here.

The card scenes, restricted four-holding model and accounting are original teaching examples. They are not Nolan's hands, observed opponent frequencies, a recommended range or solver outputs. The final-street model intentionally excludes future betting, fees, side pots and tournament payouts. External publishers may advertise gambling or paid products; no purchase is required here.

Published October 14, 2026. Prepared with AI assistance. Study before or after play, following the venue's device and assistance rules.