Texas Hold’em Math Test

To succeed at the table, you need to have logical thinking and problem-solving abilities.

Among all the skills, perhaps the most important is your mathematical ability.

However, even those who are not very good at math can still grasp some fundamental poker math principles.

In today's content, we will present 10 questions to test your understanding of the core mathematical principles of the game.

After completing the test, you can compare your final score to see which famous poker player you match up with. Different score ranges will correspond to different professional players.


Question 1

The pot is $20. Suppose your opponent bets $10 on the flop. What is the cost of your call (expressed as a percentage)?

A. 20%

B. 25%

C. 33%

D. 50%

Answer: B, 25%. You need to invest $10 to compete for $30. The odds are 3:1, which is 25%. This means your winning percentage needs to be at least 25% for a call to break even.

Question 2

The board is J♠8♠7♥3♥, and your hole cards are A♠9♠. What is the of hitting a straight or flush on the river?

A. 26%

B. 33%

C. 41%

Answer: A, 26%. A9s has 12 outs (9 flush outs + 3 straight outs). Therefore, the probability of hitting your draw on the river is 26%. Using the Rule of 2 and 4, it's 12*2=24%, which is close to the actual probability.

Question 3

On the river, suppose your opponent bets the amount of the entire pot. What win percentage do you need to call to break even?

A. 25%

B. 33%

C. 50%

D. 75%

Answer: B, 33%. If your opponent bets the size of the pot, the breakeven point is calculated as: Investment ÷ (Investment + Return) = 1 ÷ (2 + 1) = 1/3, which is approximately 33%.


Question 4

Suppose you have a pocket pair. What is the approximate probability of hitting a set or better on the flop?

A. 9%

B. 12%

C. 15%

D. 17%

Answer: B, 12%. More precisely, the probability of a pocket pair hitting a set or better on the flop is 11.8%.

Question 5

On the river, you bluff by betting the amount equivalent to the pot. What is the success rate needed for your bluff to break even?

A. 33%

B. 50%

C. 75%

D. 100%

Answer: B, 50%. Because it's a bluff, your win rate when called is 0. The breakeven point for the bluff is calculated as: (Pot before the bet) ÷ (Bet amount + Pot before the bet) = 1/2 = 50%.

Question 6

Pre-flop, the button opens with a , and only the BB calls. Which player is more likely to realize their equity in this situation?

A. Button


Answer: A, Button. “Equity realization” refers to the probability that a hand will win the pot compared to its raw equity percentage.

For example, a hand's raw equity might be 45%, but due to other factors (positive or negative), the long-term realization of its equity in the pot might be higher or lower than 45%.

In this example, the pre-flop raiser on the button has a better chance of realizing their equity in the pot than the BB caller. The button's advantages in this situation include:

  1. Position
  2. A stronger and uncapped range

Question 7

In which of the following situations is your implied odds the highest?

A. Four-way pot, flop is K-Q-7 rainbow, and you hold JT with an open-ended straight draw.

B. Four-way pot, flop is 2-8-3 all of the same suit, and you have the third nut flush draw.

C. Four-way pot, flop is 6-7-9 rainbow, and you hold 45 with an open-ended straight draw.

Answer: A. Among all the options, holding JT on a K-Q-7 rainbow flop with an open-ended straight draw has the highest implied odds. You have 8 outs (all 9s and As), and if you hit, you make the nut straight. In options B and C, opponents might have stronger flushes in B or stronger straights in C, and even if you hit, it's harder to get paid by weaker hands.


Question 8

Pre-flop, you open-raise with TT from the button, and the BB 3-bets. Assuming your opponent 3-bets with hands JJ+ only, how many combinations of these hands are there?

A. 4 combinations

B. 16 combinations

C. 24 combinations

D. 32 combinations

Answer: C, 24 combinations. Generally, there are 16 combinations for non-pair (12 offsuit + 4 suited) and 6 combinations for pocket pairs. Since JJ+ includes JJ, QQ, KK, and AA, that's 4 pocket pairs × 6 combinations each = 24 combinations.

Question 9

Suppose you call with a flush draw on the turn. What is the approximate probability of hitting your flush on the river?

A. 12%

B. 15%

C. 20%

D. 25%

Answer: C, 20%. With a flush draw, you have 9 outs. On the turn, using the Rule of 2, you calculate 9 outs × 2 = 18%, so the probability of hitting your flush is approximately 20%.

Question 10

The pot is $100. Suppose your opponent bets $100 on the river. You estimate you have the best hand 40% of the time when you call. What is the EV () of your call?

A. -$20

B. $20

C. $80

D. $100

Answer: B, $20. There are two outcomes when you call: ① Winning $200 with a 40% probability; ② Losing $100 with a 60% probability.

So, EV = 0.4 × 200 + 0.6 × -100 = 80 – 60 = $20.


Score Assessment

01 Answered 1-2 questions correctly

Matched Player: Guy Laliberté. This businessman lost over $31 million online between 2006-2012 (less than 3% of his net worth), playing under seven or eight different accounts. The players who won this money include Phil Ivey, Tom Dwan, the Dang brothers, Phil Galfond, and Patrik Antonius. So, if your score matches this businessman, you still have some work to do.

02 Answered 3-5 questions correctly

Matched Player: Mike Matusow. Nicknamed “The Mouth,” Mike had a significant impact in the early part of his career, but in recent years… it seems like he has burned out.

03 Answered 6-8 questions correctly

Matched Player: Patrik Antonius. The Finnish poker legend had his golden years from 2003-2010.

04 Answered 9-10 questions correctly

Matched Player: Phil Ivey. Does this man even need an introduction?!

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