Math

Question 1

What are Pot odds? What are we looking to achieve with this calculation?

How do we calculate Pot odds? Ratio Method & Percentage Method?

There is $80 in the pot and your opponent bets $20, what are our pot odds as a ratio?

Our opponent has bet $30 into a $60 pot, what are our pot odds as a percentage (equity).

Answer 1

Pot odds involves using the odds or likelihood of winning when on a DRAWING hand to decide whether or not to call a bet or a raise.

The odds / equity we are getting in the hand

Ratio Method:

Amount in the Pot : Amount we have to call

$100:$20
5:1
we are getting 5:1 odds

Percentage Method:

1 / 1 + (Amount in the Pot : Amount we have to call)

1 / 1 + ($90:$30)
1 / 1 + (3:1)
1 / 1+3
1 / 4
25%
we are getting 25% equity

If we call and win 25% of the time, then calling is profitable.

Question 2

What are Card Odds/Card Equity? What are we looking to achieve with this calculation?

How do we calculate Card odds/Card Equity? Ratio Method & Percentage Method?

We hold Ah 8h — flop is 2h-7s-Jh, what are our Card Odds as a ratio?

We hold 7s 9d — flop is 6h-8c-Ad, what is our card equity as a percentage?

Answer 2

This is the equity we need to continue in the hand.

Ratio Method:
47 cards (amount remaining in the deck) - the amount of cards we need that makes our hand (flush or straight) : the amount of cards we need that makes or hand (flush or straight)
(47 - 9) : 9
38 : 9
4:1 
we need roughly 4:1 odds to continue

Percentage Method:
Rule of 4&2 -
Flop - multiply outs by 2 + 1% if 5-13 outs
multiply outs by 2 + 2% if more than 13 outs

Turn - multiply outs by 2 + 1% if 5-13 outs
multiply outs by 2 + 2% if more than 13 outs

Opponent is all in on the flop - multiply outs by 4

8*2 = 16

We need roughly 16% to continue

** Also try your outs divided by the number of unseen cards -

9/47 = 19%
8/47 = 17%

This calculation is a lot closer

Question 3

How do Pot Odds and Card Odds/Card Equity interact.

Answer 3

Pot odds percentage - what you are getting / percentage of the time you will win

Cards equity - what you need

Cards Equity > Pot Odds/Ratio

You need your pot odds percentage (the odds we are getting to continue), to be less than the Card Odds/Card Equity (the odds/equity we will need to continue and try to hit our draw) in order to make a profitable call.

I know I will win 35% of the time and I only need to win 33% of the time. Since 35% is greater than 33%, I have a profitable call.

When we are getting = pot odds
We need to realize = card odds

Question 4

What are Implied Odds? What are we looking to achieve with this calculation?

How do we calculate Implied Odds, as a ratio?

If someone raises to 2.5bbs out of a 75bb effective stack,
we are calling 2.5bbs to potentially win a pot of 7.5bbs plus 72.5bbs remaining in the stacks, what are our implied odds.

Answer 4

Implied odds are an extension of pot odds.

Help us decide whether or not a drawing hand is worth calling in the face of a raise. Essentially, the implied odds of a hand tells us how much we expect to win after we make our draw.

If we expect to win a lot of chips from our opponents after making our draw, then we have good implied odds.

If we anticipate we will not be able to get any more chips from our opponent on future rounds, then we have little or no implied odds.

Implied odds indicate the amount of money that we expect to win after completing our draw.

Effective stack is the stack amount that matters.

Ratio Method:
(Amount Remaining in Stacks + Pot) / Call Amount : 1

(72.5 +7.5) / 2.5
80 / 2.5
32:1

Question 5

What Implied Odds do we need to continue when we are holding:

Small Pair
Suited Connector
Suited Ace

Answer 5

We want to get at least:

Small Pair - 10:1 implied odds with small pairs.

Suited Connector - 20:1 implied odds with suited connectors.

Suited Ace - 20:1 implied odds with suited aces.

Question 6

What is Minimum Defense Frequency? What are we looking to achieve with this calculation?

How do we calculate it?

You raise to 3bbs from UTG+1 and the lojack 3-bets to 10bbs. What is your MDF?

Answer 6

Mathematical percentage that we must defend to keep our opponent from blindly profiting from pure aggression.

How often we should defend at the least.

AKA: how to prevent from getting run over by bluffs.

MDF = 100% - (opponent’s bet / (opponent’s bet + pot))

100% - (10 / (10 + 3 + .5 + 1 + 1))
100% - (10 / 15.5)
100% - 64.52
35.48%

we need to defend roughly 35% of the time

If opponent were bluffing, we would have to force a fold at least 65% of the time to make a profit.

Question 7

What is Stack to Pot Ratio? What are we looking to achieve with this calculation?

How do we calculate it?

Answer 7

Compares smallest stack size in play to the size of the pot to help evaluate
strategy & risk.

SPR informs which starting hands you play with, and how you play them.

SPR = Effective Stack / Money in Pot

AKA - risk / reward

SPR 0-3 = Low
SPR 3-6 = Medium
SPR 6+ = High

Question 8

How many total possible hand combinations are there in poker?

Answer 8

Hand Combinations - 1326

Question 9

How many combinations of pocket pairs are there for any rank?

How many combinations of pocket pairs are there in a deck?

Answer 9

Any rank - 6 different ways to make a pocket pair

In a deck - 78 combinations of pocket pairs

Question 10

How do we calculate the number of combinations of Pocket Pairs (PP) in a players range?

Answer 10

(x * (x - 1)) / 2

Where x is the number of available cards remaining in the deck

Question 11

How many combinations of unpaired hands are there?

How many suited combinations of unpaired hands are there?

How many off-suit combinations of unpaired hands are there?

Answer 11

Total unpaired hands: 16 ways to make an unpaired hand
4 suited AK
12 off-suit AK
and any other unpaired hand

Suited: 78 of any suit, 312 total

Off-suit:

Question 12

How do we calculate the number of combinations of unpaired hands in a players range?

Answer 12

(x * y)

Where x and y are the number of available cards remaining in the deck for each rank.

Question 13

How to quickly divide by 4?

How to quickly divide by 5?

How to quickly divide by 6?

How to quickly divide by 8?

How to quickly divide by 9?

Answer 13

4 - divide by 2 twice (half and half)

5 - multiply by 2 then divide by 10

6 - divide by 3 then divide in half (by 2)

8 - divide by 2 three times (half and half and half)

9 - divide by 3 two times (1/3 and 1/3)

Question 14

How often will we profit if we steal the pot with a pot sized bet?

Answer 14

If we bet the size of the pot, we immediately profit if we steal the pot at least 1 / (1+1) = 50% of the time.

Question 15

How often will we profit if we steal the pot with a 67% pot sized bet?

Answer 15

If we bet 67% pot, we immediately profit if we steal the pot at least 0.67 / (0.67+1) = 40% of the time.

Question 16

How often will we profit if we steal the pot with a 50% pot sized bet?

Answer 16

If we bet 50% pot, we immediately profit if we steal the pot at least 0.50 / (0.50+1) = 33% of the time.

Question 17

How often will we profit if we steal the pot with a 33% pot sized bet?

Answer 17

If we bet 33% pot, we immediately profit if we steal the pot at least 0.33 / (0.33+1) = 25% of the time.

Question 18

How often will we profit if we steal the pot with a 25% pot sized bet?

Answer 18

If we bet 25% pot, we immediately profit if we steal the pot at least 0.25 / (0.25+1) = 20% of the time.

Question 19

How often will we profit if we steal the pot with a 150% pot sized bet?

Answer 19

If we bet 150% pot, we immediately profit if we steal the pot at least 1.5 / (1.5+1) = 60% of the time.

Question 20

How often will we profit if we steal the pot with a 200% pot sized bet?

Answer 20

If we bet 200% pot, we immediately profit if we steal the pot at least 2.0 / (2.0+1) = 67% of the time.

Question 21

How often do we have to defend when our opponent bets pot?

Answer 21

we have to defend with 50% of our range.

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

Question 22

How often do we have to defend when our opponent bets 67% pot?

Answer 22

we have to defend with 60% of our range.

0.67 / (0.67+1) = 40%
1 - 40% = 60%

Question 23

How often do we have to defend when our opponent bets 50% pot?

Answer 23

we have to defend with 67% of our range.

0.50 / (0.50+1) = 33%
1 - 33% = 67%

Question 24

How often do we have to defend when our opponent bets 33% pot?

Answer 24

we have to defend with 75% of our range.

0.33 / (0.33+1) = 25%
1 - 25% = 75%

Question 25

How often do we have to defend when our opponent bets 25% pot?

Answer 25

we have to defend with 80% of our range.

0.25 / (0.25+1) = 20%
1 - 20% = 80%

Question 26

How often do we have to defend when our opponent bets 150% pot?

Answer 26

we have to defend with 40% of our range.

1.5 / (1.5+1) = 60%
1 - 60% = 40%

Question 27

How often do we have to defend when our opponent bets 200% pot?

Answer 27

we have to defend with 33% of our range.

2.0 / (2.0+1) = 67%
1 - 67% = 33%

Question 28

What is the calculation to determine the equity needed/required to make a call?

Ex: we are facing a river bet of $50 into a $100 pot

Answer 28

Pot odds calculation.

150:50
3:1
25%

We need 25% equity. We need more than 25% equity to call.

So if our opponent is betting a hand stronger than ours less than 75% of the time, we should call because we are either making money or breaking even.

If our opponent has a stronger hand than ours more than 75% of the time, we should fold.

If our opponent has a better hand exactly 75% of the time, we are breaking even.

Question 29

How do we calculate Expected Value (EV)?

Answer 29

(Win% x (Total Pot - Our Bet)) - (Lose% x Our Bet)

Where win% is our equity, and lose% is our opponent’s equity

Question 30

How do we calculate Required Bluff Success Rate?

Ex: bet of $50 into a $100 pot

Answer 30

Bet / (Bet + Pot)

Which means that a bluff of 50% needs to succeed on the river 33% of the time to be profitable.

Said another way, if our opponent folds more than 33% of the time, we immediately profits. This means our opponent must call or raise 67% of the time.