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Master Poker Probability and Range Evaluation Quiz

Elevate Your Poker Odds and Range Knowledge

Difficulty: Moderate
Questions: 20
Learning OutcomesStudy Material
Colorful paper art displaying poker elements for a probability and range evaluation quiz

This poker probability and range evaluation quiz helps you practice pot odds, equity, and hand ranges so you can make better decisions at the table. Use it as a warm-up before the strategy quiz or as a quick review after the equity test.

How many combinations of pocket aces (AA) are there before the flop?
16
4
12
6
There are 4 aces in the deck and choosing any two gives C(4,2)=6 combinations. This follows basic combinatorics of two-card combinations. Suits determine the total number of combos.
What is the approximate probability of flopping a set when holding a pocket pair?
7.5%
11.8%
15.7%
5.9%
With a pocket pair there are C(2,1)*C(48,2)=2*1128=2256 favorable flop combinations out of C(50,3)=19600 total flops, which is about 11.8%. This is a standard poker probability result.
If the pot is $100 and an opponent bets $50, what are your pot odds for calling?
1 to 2
2 to 1
3 to 1
1 to 3
After a $50 bet into $100, the total pot becomes $150. You must call $50 to win $150, so the pot odds are 150:50, or 3:1. You compare this to your draw equity.
Which of these starting hands has the highest equity against a random hand preflop?
QQ
AKs
KK
AA
Pocket aces (AA) are the best possible starting hand and have the highest preflop equity versus any random hand. All other hands rank below AA in raw equity.
In poker range analysis, what does "equity" refer to?
The ratio of bet size to pot size
The fixed probability of winning the next hand
The chance the opponent folds
A player's expected share of the pot over the long run
Equity represents the percentage of the pot a player can expect to win on average given two ranges. It is calculated by simulating or using combinatorics for range matchups.
Which best describes implied odds?
The percentage chance to win a showdown
The immediate pot odds after a bet
The ratio of bet size to stack size
The ratio of expected future gains to the cost of a current call
Implied odds consider not only the current pot but also expected future bets you can win. They help inform calls when drawing by estimating additional money you might extract.
What is the break-even equity for a call when facing 3:1 pot odds?
25%
50%
33%
20%
With 3:1 pot odds, you risk 1 unit to win 3. The break-even equity is 1/(1+3)=0.25 or 25%. You need at least this equity to justify a call.
How many total unique two-card starting hand combinations (including suits) exist?
169
1326
1176
156
There are C(52,2)=1326 possible two-card combinations when suit and rank matter. This is the basis for many combinatoric calculations.
Approximately how many two-card combinations are in a top 15% starting hand range?
150
180
200
250
A 15% range of 1326 combinations is 0.15Ã-1326≈199. So we approximate to 200 combos. This helps gauge the frequency of hands in a range.
How many combinations of KQo (king-queen offsuit) are there preflop?
4
16
12
6
For offsuit KQ, there are 4 kings and 4 queens, but offsuit excludes same-suit combos, so 4Ã-4âˆ'4=12 combinations.
If the table is playing extremely tight, your opening range from late position should generally:
Widen to include more speculative hands
Switch to 100% bluffing
Remain unchanged
Tighten to only premium hands
Against tight opponents, you can widen your range to exploit low defense frequency, adding more speculative or marginal hands for value and bluffs.
Which factor does NOT influence implied odds?
Expected future bet sizes
Opponent's calling tendencies post-flop
Remaining stack sizes
Fold equity
Implied odds refer to future value you can win when you hit your hand. Fold equity is a separate concept and not part of implied odds calculations.
Which hand has higher equity versus a random hand: 98s or 65s?
Depends on suits
They have equal equity
98s
65s
98s has higher straight and broadway possibilities compared to 65s, giving it more overall equity versus a random hand.
How many pocket pair combinations are there in the range 22 - 99?
30
36
54
48
Ranks 2 through 9 are eight distinct pocket pairs; each pair has C(4,2)=6 combinations, so 8Ã-6=48 combos in total.
Which flop texture is considered dry and ideal for continuation betting?
K♣-7♦-2♠ rainbow
9♥-8♥-7♥
Jâ™ -10â™ -9â™ 
6♦-5♦-4♦
A dry rainbow flop like K-7-2 has few draws and weak coordinated hands, making it favorable to continuation bet for fold equity.
If you have only two outs after the flop, what is your approximate chance to hit one by the river?
11.8%
4.3%
8.5%
2.5%
The probability to hit one of two outs by the river is 1âˆ'C(45,2)/C(47,2)≈4.26%. This uses combinatorics over turn and river cards.
In which game condition are implied odds most significant?
Single-possession pot-limit contests
Short-stacked tournaments
When only pot odds matter
Deep-stacked situations
Deep stacks allow larger future bets, increasing the potential extra money you can win when you hit, which drives implied odds.
What defines a polarized 3-bet range preflop?
Is comprised of only small pairs for set mining
Bluffs exclusively without value hands
Contains mostly premium hands and pure bluffs, and excludes medium-strength hands
Includes all strong and medium-strength hands only
A polarized 3-bet range mixes the strongest value hands with bluffs and omits medium hands, balancing for fold equity and value extraction.
How do blockers in your hand affect your bluffing frequency when 3-betting?
Blockers only affect pot odds, not bluffs
Blockers reduce your ability to bluff since they remove outs
Blockers force you to narrow your value range
Blockers allow more frequent bluffs because they reduce opponent equity in value hands
Holding blockers to strong boards reduces the combos of opponents' strong hands, making your bluffs more credible and allowing higher bluff frequencies.
Compared to heads-up pots, multiway pots generally have which effect on implied odds and hand equity?
Have no effect on equity or implied odds
Increase implied odds but decrease equity
Decrease the equity of draws and reduce implied odds
Increase both implied odds and equity
In multiway pots, equity for drawing hands is shared among more players and future value is harder to extract, lowering both implied odds and equity.
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Learning Outcomes

  1. Analyse hand ranges to determine optimal play in varied scenarios.
  2. Evaluate pot odds and implied odds to inform decision-making.
  3. Apply combinatorics to calculate opponent hand probabilities.
  4. Identify profitable range-based strategies in preflop and postflop spots.
  5. Demonstrate proficiency in adjusting ranges based on game dynamics.

Cheat Sheet

  1. Understanding Pot Odds - Pot odds are the ratio of the current pot size to the amount you must call, helping you decide if chasing your draw makes sense. Think of it like checking the price tag before buying a candy - you only grab it if it's a sweet deal!
  2. Calculating Implied Odds - Implied odds factor in the extra chips you expect to win on future streets when your hand hits, giving you a sneak peek at deeper value. It's like banking on a bonus level in a video game: the potential reward can justify taking a small risk now.
  3. Applying Combinatorics to Hand Ranges - Combinatorics counts how many possible hand combinations your opponent might hold, so you know whether they're likely strong or just bluffing. Imagine sorting colored beads - you'll see patterns that reveal when to fold or fire back.
  4. Evaluating Opponent's Bluffing Frequency - Knowing how often foes bluff helps you avoid costly calls or get that perfect hero call. Game theory suggests matching their bluff rate to the pot odds - call 3-to-1? They should bluff about 25% of the time.
  5. Implementing Semi-Bluffs - A semi-bluff combines pressure and potential: you bet with a drawing hand that can make the best hand later, or win the pot right away if they fold. It's the ultimate two-for-one deal - like ordering a dessert that doubles as a main dish!
  6. Adjusting Ranges Based on Game Dynamics - Adapt your hand selection to the table vibe: loosen up and add bluffs against tight players; tighten up and extract value from loose opponents. It's like switching dance moves to match the tempo of the music.
  7. Understanding Morton's Theorem - Morton's Theorem warns that a third player's call can hurt your drawing equity more than it helps the caller, so multi-way pots require extra caution. Think of it as a traffic jam: more cars can slow everyone down.
  8. Utilizing Bayesian Inference for Opponent Modeling - Bayesian inference lets you update your beliefs about an opponent's style based on their actions, refining your reads with each bet and fold. It's like leveling up your detective skills - every clue counts!
  9. Incorporating Expected Value (EV) Calculations - EV crunches all outcomes and their probabilities to tell you if a play is profitable over time, separating lucky wins from smart decisions. If your long-term math is positive, you're on the right track - no superstitions needed!
  10. Recognizing the Importance of Position - Acting after your opponents gives you extra info and control over pot size, turning late position into a strategic playground. It's like having the last word in a debate - you get to fine-tune your argument with full knowledge of their stance.
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