A 20-Minute Poker Study Session for Six-Max Cash Players

What you will have at the end. Twenty minutes from now, on paper or in a notes file:

One attempted answer — your own, written down before you checked anything.
One correction or confirmed explanation — the step you changed, or the reasoning you checked and confirmed.
One attempted variation — the same question with one input changed.
A short note saying what you can explain, what you cannot, and when you will try again.

Those four items are the outputs of the routine. They are what you produce, not a promise about what you will retain. Twenty minutes is a suggested work allocation that keeps the session small enough to actually do — it is not an optimal duration, and finishing it is not mastery.

You need a pen and this page. No paid account, no solver subscription, no hand-history import.

One decision, not a hand review

This session studies one uncertain decision. It does not find that decision for you.

Finding a recurring problem across a batch of your own hands is a different job, and Poker Study Lab's post-session worksheet is a separate 20-minute routine for it: pull about twenty hands, tag each hero decision, choose one study target, and set a baseline. That routine ends roughly where this one begins.

So do not try to stack them. Pulling hands, filling in the worksheet, reading a full guide and running this routine do not fit into twenty minutes together. That is a separate session; today, bring one decision, or use the one supplied below.

The schedule

The five allocations, in order.
Minutes	What you do	What you write
0–3	Commit to an answer	Your answer, your reasoning, and the assumptions you used
3–8	Check the reasoning	A specific correction or confirmed reasoning, in your own words
8–14	Change one input	The variation, your answer, and what changed versus what did not
14–18	Retrieve the reasoning	The reasoning again, from memory, with the explanation hidden
18–20	Leave a useful review note	What you can explain, what is still uncertain, and when you will return

Five allocations: 3 + 5 + 6 + 4 + 2 = 20 minutes.

Set a timer if it helps, but treat the boundaries as a budget rather than a rule. Running a little over on one step is fine, and skipping the correction to stay on schedule is not a good trade. What is worth avoiding is letting the whole session drift to forty minutes.

Bring one decision — or use this one

A good candidate is a spot you have actually been unsure about: a river call you keep making uncomfortably, a turn size you guess at, a preflop defence you have never checked.

If you bring your own decision, bring its explanation with it — the lesson, book, article or solver output you would check yourself against. Minutes 3–8 and 14–18 need something to read and then put away; the routine is identical, only the reference changes. The question below exists so you can run the session today with nothing else to hand.

If nothing is ready, start here instead of spending your first three minutes choosing. This is the question the worked example below follows all the way through.

Today's question In the simplified, fully polarized heads-up river model, you bet pot with 6 value combinations. How many bluff combinations balance the range?

The model behind that question — state it before you answer, because the answer is only true inside it:

Heads-up, on the river. Two players, final street, all five community cards out.
A fully polarized betting range. Only strong hands and pure bluffs — no medium-strength hands.
Bluffs lose when called. They have no showdown value against the relevant bluff-catcher.
Value hands beat the relevant bluff-catcher. When that caller calls a value bet, the caller loses.
Only call or fold. The caller cannot raise; the hand ends there. Rake and ties are ignored.
Balance means indifference. The composition is the one that makes a pure bluff-catcher equally happy calling or folding — not the one that maximises profit against a particular opponent.

This is a teaching model. It gives you a reference composition to reason from, not an instruction for every real river: real ranges hold medium-strength hands, the combinations you actually have may not divide neatly, and a hand with more betting still to come needs a fuller model than this one.

0–3 minutes — Commit to an answer

Do: work out an answer yourself before looking anything up. Write the reasoning you actually used, including any guess or uncertain step. That gives you something specific to check against the explanation.

Write: three things — your answer, the reasoning in one or two sentences, and the assumptions you used. The assumptions matter most, because an unstated assumption cannot be corrected.

If you genuinely have no belief to commit — you have never thought about this spot — write “no idea”, then your best guess and the one reason you guessed it. That is still a commitment, and it still gives the next step something to work on. What does not work is leaving the line blank and reading ahead.

Three minutes is deliberately short. It is enough to commit and not enough to hedge.

Write your answer down before you read on. The example below is someone else's attempt, and it is wrong on purpose. Once you have seen a number, you cannot un-see it.

Illustrative learner example · 0–3 minutes

A worked demonstration written for this article. It is not a real customer, a testimonial, or an observed result.

Answer: Two bluffs.
Reasoning: “A pot-sized bet is one-third bluffs, and I have six value combinations, so six multiplied by one-third is two.”
Assumptions: “Heads-up river, polarized, bluffs lose when called, no raising.”

3–8 minutes — Check the reasoning

Do: read the short explanation below, then locate the exact point where your reasoning diverged from it. Not the topic. The step. “I used the wrong denominator” is a finding you can act on; “I need to work on river ratios” is not.

Write: the specific step you corrected, or the reasoning you confirmed, in your own words. Explain why it works instead of copying the answer.

If your answer was already right, compare your reasoning and assumptions with the explanation. Record any missing step you find. If they were sound, write “reasoning confirmed” and explain why; you do not need to invent a mistake. Then try the variation to check whether you can use the same method when an input changes.

The short explanation

Write P for the pot before the bet and B for the bet. In the model above, two different numbers describe the same betting range, and they are easy to swap:

The bluff fraction — bluff combinations divided by all betting combinations. It equals B / (P + 2B). At a pot-sized bet (B = P) that is 1/3.
The bluff-to-value ratio — bluff combinations divided by the value combinations. It equals B / (P + B). At a pot-sized bet that is 1/2: one bluff for every two value combinations, written 1 : 2.

Each fraction or ratio compares combination counts. Its formula calculates the same proportion from the pot and bet amounts. The result is a proportion, not a count of hands or an amount of money.

The two are linked by one rule: a ratio of a bluffs : b value is a bluff fraction of a / (a + b). So 1 : 2 becomes 1/(1 + 2) = 1/3.

Which one you need depends on what you are starting from. Starting from a count of value combinations, you multiply by the ratio, not by the fraction. At a pot-sized bet the ratio is 1/2, so multiplying by it is the same as dividing by 2 — which is how the worked answers below are written. The fraction's denominator already includes the bluffs you have not counted yet.

For where B / (P + 2B) comes from — the caller's break-even arithmetic, and the full derivation of both formulas — see Bluff-to-Value Ratio: River Bet Sizes and Practice Questions. You do not need it to finish this session.

Show the worked correction

Three bluffs.

The ratio at a pot-sized bet is 1 bluff : 2 value. With 6 value combinations, that is 6 ÷ 2 = 3 bluffs.

Check it against the fraction: the betting range is 6 + 3 = 9 combinations, and 3 of 9 is 3/(6 + 3) = 1/3 — the one-third, now measured against the denominator it actually belongs to.

Why “6 × 1/3 = 2” is wrong. The one-third is a share of all nine betting combinations, not a share of the six value combinations. Multiplying a value count by the whole-range fraction answers a question nobody asked. Two bluffs alongside six value hands would be a range of only 2/8 = 1/4 bluffs — noticeably less bluffing than a pot-sized bet supports.

The correction to write down is not “the answer was 3”. It is: the fraction and the ratio have different denominators, and a value count has to be multiplied by the ratio.

Illustrative learner example · 3–8 minutes

The step that was wrong: “I multiplied the value count by the whole-range fraction.”
Rewritten reasoning: “One-third counts bluffs against every bet I make, including the bluffs. Six value hands is only part of that. To get from a value count to a bluff count I use the ratio, one bluff per two value, so six gives three. Then 3 out of 9 is a third, which is where my original number was supposed to come from.”
Assumptions I had left out: “That value hands beat the bluff-catcher, and that balance means that caller is indifferent. I had them in my head but never wrote them down.”

8–14 minutes — Change one input

This is the step that separates a memorised answer from a method. A number you have just read can come back correctly without your being able to say where it came from. A number you can re-derive after something changed is different.

Do: take the same question and change exactly one input. Solve it before you reveal anything. One input, not two — if you change the bet size and the combination count together, a wrong answer will not tell you which part you do not understand. Changing the bet size is the safer choice: change the value count instead and the balanced answer often stops being a whole number (nine value hands at a pot-sized bet needs 4.5 bluffs), which is a distraction rather than a lesson.

Write: the variation, your answer, and then explicitly: what changed, and what stayed the same.

Today's variation Keep the 6 value combinations, but make it a half-pot bet instead of a pot-sized one. How many bluffs balance the range now, and what fraction of the betting range is that?

Show the variation's worked answer

Two bluffs, which is 2/(6 + 2) = 2/8 = 1/4 of the betting range.

With B = P/2, the ratio B / (P + B) is (P/2) / (P + P/2) = (P/2)/(3P/2) = 1/3 — one bluff for every three value combinations, 1 : 3. With 6 value combinations: 6 ÷ 3 = 2 bluffs.

Check it against the fraction: B / (P + 2B) = (P/2) / (P + P) = 1/4. And from the combinations directly: 2 bluffs out of 2 + 6 = 8 bets is 2/8 = 1/4. Both routes agree.

What changed: the bet got smaller, so the balanced range holds fewer bluffs — 1 : 3 instead of 1 : 2, a quarter of the range instead of a third. A smaller bet offers the caller a better price, so the balanced mix holds fewer bluffs: at that composition the bluff-catcher is exactly indifferent, and any more bluffs than that would make calling profitable for them.

What stayed the same: the method, exactly. Get the ratio, multiply the value count by it, then check the result against the fraction.

One last thing worth noticing: two was the wrong answer at a pot-sized bet, and it is the right answer here — and the sum that produced it was the same sum both times. The pot-sized fraction and the half-pot ratio are both 1/3, so “six multiplied by one-third” lands on the correct answer in this variation and the wrong one in the original question. That is exactly why naming the quantity matters more than remembering the number.

Illustrative learner example · 8–14 minutes

Variation: Half-pot bet, still six value combinations.
Answer: “Ratio is 1 : 3, so 6 ÷ 3 = 2 bluffs. Check: 2/(6+2) = 1/4.”
What changed: “Smaller bet, so a smaller share of bluffs — a quarter rather than a third.”
What stayed the same: “The method. Ratio first, multiply the value count, then check against the fraction.”

14–18 minutes — Retrieve the reasoning

Do: put the explanation out of sight. Nothing on this page hides it for you — the short explanation stays open where you left it — so scroll past it to the prompt below, or look away from the screen and work on paper. The discipline is yours, and the step does nothing if you glance back up.

Treat an immediate correct answer as one successful practice attempt, not proof of lasting retention. With the explanation hidden, note what you can reconstruct today and where you need a cue. A failed attempt identifies something to revisit; it does not establish that you have learned nothing. Try again in a later session before deciding the reasoning is reliably available.

Write: the reasoning as you reproduce it. Then, and only then, compare it with the answer below and mark the parts you could not produce. Those gaps are what the note's still uncertain line is for.

Retrieval prompt Explain why “one-third of the complete betting range” and “one bluff for every two value combinations” describe the same composition. Do not restate the formulas — say what each number is divided by, and why that makes them agree.

Show the retrieval answer

They count the same bluffs. They divide by different things.

Take the balanced pot-sized range: 3 bluffs and 6 value hands, 9 combinations in total.

1 : 2 divides the bluffs by the value hands: 3 ÷ 6. It answers “how many bluffs do I add per value hand?”
1/3 divides the bluffs by every bet in the range: 3 ÷ 9. It answers “what share of my bets are bluffs?”

Nothing about the range changes between those two sentences — only the denominator does. And the two denominators are related: add the parts of the ratio, 1 + 2 = 3, and you have the fraction's denominator. That is why 1 : 2 and 1/3 are the same statement about the same nine combinations.

The practical consequence is the one worth retrieving: a value count gets multiplied by the ratio, because the fraction's denominator already includes the bluffs you are trying to find.

Illustrative learner example · 14–18 minutes

In this worked demonstration, the learner reproduced both denominators and the “add the parts” rule, but needed two attempts to say why adding the ratio's parts gives the fraction's denominator. Closing the page made a second gap obvious, one this prompt never asked about: they could not rebuild B / (P + 2B) from P and B at all. Both go into the note.

18–20 minutes — Leave a useful review note

Two minutes, and the easiest step to talk yourself out of. A session you cannot reconstruct next week was a way of spending twenty minutes, not a way of studying.

Do: write the note for the version of you who has forgotten this. Name the mistake specifically enough that you would recognise it again, and set an actual time to return.

Write: the note's last two fields — what is still uncertain, and when you intend to try again. What you can explain is already sitting above them: the correction and the variation, in your own words. Read those back and check they still make sense with this page closed. Put the return in your calendar yourself; nothing on this page will remind you.

A sensible next session is a few days out, with another about a week after that — long enough that you have to reconstruct the reasoning rather than merely recognise it. Lesson 1.2 in Poker Study Lab sets out its own review plan for this material — days 1, 4 and 10, interleaved with the minimum-defence-frequency lesson — which is a reasonable shape to copy. Treat any of these as a practical appointment, not a prescribed interval.

Illustrative learner example · the completed note

Written for this article to show what a finished note looks like.

QUESTION + ASSUMPTIONS
Pot-sized river bet, 6 value combos. Simplified model: heads-up
river, fully polarized, bluffs lose when called, value beats the
bluff-catcher, call-or-fold only, balance = caller indifferent.

MY ANSWER + REASONING
2 bluffs. Took the one-third and multiplied: 6 x 1/3 = 2.

CORRECTION OR CONFIRMED REASONING
The one-third is a share of ALL betting combos, not of the value
combos. A value count gets multiplied by the RATIO: 1 bluff per
2 value, so 6 / 2 = 3 bluffs. Check: 3/(6+3) = 1/3.

VARIATION + ANSWER
Half pot, same 6 value. Ratio 1 : 3, so 2 bluffs. 2/(6+2) = 1/4.
Method identical; only the bet size moved.

STILL UNCERTAIN
I can go from the ratio to the count now, but I cannot rebuild
the fraction B/(P+2B) from P and B without looking it up.

NEXT REVIEW (date)
Thu 17 Sep. Redo from P and B with the formulas hidden, then
try a twice-pot version.

Notice what that note does. It names the mistake — using the whole-range fraction where the ratio belongs — not the topic. It records the variation result so the next session starts from evidence. And its uncertainty line is specific enough to be the next session's opening question.

The blank template

Copy this into your notes and fill it in as you go. The page has no submission form and does not store your answers. Save your copy in your own notes.

QUESTION + ASSUMPTIONS


MY ANSWER + REASONING


CORRECTION OR CONFIRMED REASONING


VARIATION + ANSWER


STILL UNCERTAIN


NEXT REVIEW (date)

If you get stuck

You will sometimes reach minute fourteen without the correction making sense. That is a normal outcome, and there is a right way to end the session:

Write down the unresolved step, as precisely as you can. “I do not understand why the caller's break-even equity and the bluff fraction are the same number” is a usable next question. “River maths is confusing” is not.
Stop at twenty minutes anyway. If you push on to forty, check whether you are still working or just re-reading the same paragraph — and a session that routinely overruns is a harder one to sit down to next time.
Carry the unresolved step into the next session as its opening question. That is what the note is for. A question you have already written down is a much easier session to begin.
Do not count the timer as the achievement. Finishing twenty minutes is not the same as understanding the concept. The honest note — “still cannot do this” — is worth more than a tidy one.

If the same step remains unclear over several sessions, try checking a prerequisite or using a different explanation. Keep the unresolved question specific so you can judge whether that change helped.

Keep going

The routine is deliberately portable. The river ratio was only today's subject — the same five steps work on a preflop defence, a turn size, or any decision you can state precisely enough to be wrong about. Commit, correct, vary, retrieve, note.

Two habits are the ones worth keeping: writing the assumptions down before answering, and changing one input before believing you have understood something.

Sources

Poker Study Lab lesson 1.2, Value-to-bluff ratio and the bluff fraction A = B / (2B + P) — the simplified model, the half-pot and pot-sized worked examples used above, the mastery check paraphrased in the closing section, and the day 1 / 4 / 10 review plan. The lesson states the ratio value-first: its 2 : 1 at a pot-sized bet is this page's 1 : 2. Same range, opposite reading order.
Bluff-to-Value Ratio: River Bet Sizes and Practice Questions — the companion guide, for the derivation of B / (P + 2B) and B / (P + B) and the bet-size comparison this session's variation draws on.
GTO Wizard: How to solve toy games — the polarized nuts-or-air river game this session's question lives inside, with the equilibrium bluff share stated as s/(2s + 1) for a bet of s times the pot: one-third bluffs at a pot-sized bet.