# Poker Math Quiz Answers and Explanations

Here are the answers and explanations for our poker math quiz.

## Question #1

Suppose your opponent bets \$10 on the flop into a \$20 pot. What is your price to call (expressed as a percentage)?

A – 20%
B – 25%
C – 33%
D – 50%

You are being laid 3 to 1 to call in this scenario (calling 10 to win 30), which equates to 25%. This means you must win the pot at least 25% of the time for your call to break even.

## Question #2

You have A♠️ 9♠️ on a J♠️ 8♠️ 7♥️ 3♥️ board. What is the approximate likelihood you will improve to a straight or flush on the river?

A – 26%
B – 33%
C – 41%

With 3 outs to improve to a straight and another 9 outs for a flush, you have a 25% chance of hitting a strong 5-card hand on the river. A good rule of thumb is to multiply your number of outs (12 in this case) by 2. That’s the approximate likelihood you’ll hit one of your outs on the next card.

It’s worth noting that if hitting an Ace on the river would give you the best hand as well, you actually have a ~41% chance of improving to the best hand on the river.

## Question #3

If we are on the river and facing a pot-sized bet from our opponent, what percentage equity does our hand need to have to be a break-even call?

A – 25%
B – 33%
C – 50%
D – 75%

Facing a pot-sized bet, we need 33% equity to call on the river to break even. (1 pot-sized bet to call)/(2 pot sized bets already in the pot after our opponent bets) + (1 pot sized bet to call). This simplifies to ⅓, which equals 33%.

## Question #4

If we have a pocket pair in our hand, what is roughly the percentage chance we make a set or better on the flop?

A – 9%
B – 12%
C – 15%
D – 17%

We have exactly an 11.8% chance of flopping a set or better with a pocket pair in our hand.

## Question #5

If we are bluffing for a pot-sized bet on the river, what percentage of the time does our bluff need to work to break even?

A – 33%
B – 50%
C – 75%
D – 100%

When betting pot with zero equity when called, we are getting 1:2 on our bet, or 50%. We can calculate how much a bluff needs to work to break even by using the following formula:

(Pot size before our bet) + (Our bet) / (Total pot after our bet)

(1)+(1)/ (2)= 50%

## Question #6

If a player on the Button raises preflop and is called by the Big Blind, which player is more likely to over-realize their equity?

A – Button
B – Big Blind

Equity realization’ is a term in poker used to describe how hands may over or under-perform compared to their absolute equity. One player might have 45% equity in a hand, for example, but other factors could either negatively or positively affect whether or not that player actually is able to win 45% of the pot share on average.

In this example, the Button raiser is more likely to over-realize their equity than the Big Blind.

The Button, in this case, has 2 major advantages:

1. Position
2. An uncapped range of premium hands like JJ+ that can be leveraged postflop against Big Blind’s capped range

## Question #7

In which of these scenarios do you have the best implied odds?

A – Flopping an open-ended straight draw with JT on a K-Q-7 rainbow in a 4-way pot
B – Flopping the 3rd nut flush draw in a 4-way pot on 2-8-3 flush draw
C – Flopping an open-ended straight draw with 45 on 6-7-9 rainbow in a 4-way pot

Out of all these scenarios, having JT on K-Q-7 rainbow has the best implied odds. JT, in this case, has 8 clean outs that complete the nut straight (9 or A). In options B and C, by contrast, completing your draw allows other opponents to improve to better flushes or straights that beat you. Plus, in example C, hitting an 8 would give you a straight on a four-to-a-straight board, so it will be difficult to get paid off by worse hands.

## Question #8

If you open the Button with TT and the Big Blind 3-bets you, how many combinations of JJ+ could our opponent have?

A – 4 combinations
B – 16 combinations
C – 24 combinations
D – 32 combinations

There are 24 potential combinations for any unpaired starting hand (12 unsuited at 4 suited) and 6 potential combos for any pocket pair. Only the pocket pair combinations are relevant here.

This translates to 6 JJ+ 6 QQ + 6 KK + 6 AA= 24 combos

## Question #9

After calling a bet on the turn with a flush draw, about what percentage of the time will you make your flush on the river?

A – 12%
B – 15%
C – 20%
D – 25%

After the turn, there are 9 flush completing cards left in the remaining 46 cards in the deck. 9/46= 19.57% -> rounded to 20% for the quiz.

## Question #10

Suppose your opponent bets \$100 on the river into a pot of \$100. You estimate that you will have the best hand 40% of the time when you call. What is the expected value (EV) of calling expressed in dollars?

A) -\$20
B) \$20
C) \$80
D) \$100

Consider the two potential outcomes of your call and their likelihood:

• 60% of the time you will call and lose \$100
• 40% of the time you will call and win \$200

To calculate the exact expected value, multiply the likelihood of each result by the monetary outcome, then add those two results together.

CALL AND WIN: 0.40 * \$200 = \$80

CALL AND LOSE: 0.60 * -\$100 = -\$60

EV OF CALL: -\$60 + \$80 = \$20