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Poker Math: Every Decision is based on Pot Odds

This is a very important lesson and can

also be quite intimidating 💶 to a lot of people as we are going to discuss Poker Math!

But there is no need for you 💶 to be intimidated, Poker Maths is very simple and we will

show you a very simple method in this lesson. 💶 You won’t need to carry a calculator

around with you or perform any complex mathematical calculations.

What is Poker

Math?

As daunting 💶 as it sounds, it is simply a tool that we use during the decision

making process to calculate the Pot 💶 Odds in Poker and the chances of us winning the

pot.

Remember, Poker is not based on pure luck, it is 💶 a game of probabilities, there

are a certain number of cards in the deck and a certain probability that outcomes 💶 will

occur. So we can use this in our decision making process.

Every time we make a decision

in Poker it 💶 is a mathematical gamble, what we have to make sure is that we only take

the gamble when the odds 💶 are on in our favour. As long as we do this, in the long term

we will always come out 💶 on top.

When to Use Poker Maths

Poker Maths is mainly used when

we need to hit a card in order to 💶 make our hand into a winning hand, and we have to

decide whether it is worth carrying on and chasing 💶 that card.

To make this decision we

consider two elements:

How many “Outs” we have (Cards that will make us a winning 💶 hand)

and how likely it is that an Out will be dealt. What are our “Pot Odds” – How much

💶 money will we win in return for us taking the gamble that our Out will be dealt

We then

compare the 💶 likelihood of us hitting one of our Outs against the Pot Odds we are

getting for our bet and see 💶 if mathematically it is a good bet.

The best way to

understand and explain this is by using a hand walk 💶 through, looking at each element

individually first, then we’ll bring it all together in order to make a decision on

💶 whether we should call the bet.

Consider the following situation where you hold A 8 in

the big blind. Before the 💶 flop everyone folds round to the small blind who calls the

extra 5c, to make the Total pot before the 💶 Flop 20c (2 players x 10c). The flop comes

down K 9 4 and your opponent bets 10c. Let’s use 💶 Poker Math to make the decision on

whether to call or not.

Poker Outs

When we are counting the number of “Outs” 💶 we have,

we are looking at how many cards still remain in the deck that could come on the turn

💶 or river which we think will make our hand into the winning hand.

In our example hand

you have a flush 💶 draw needing only one more Club to make the Nut Flush (highest

possible). You also hold an overcard, meaning that 💶 if you pair your Ace then you would

beat anyone who has already hit a single pair on the flop.

From 💶 the looks of that flop

we can confidently assume that if you complete your Flush or Pair your Ace then 💶 you

will hold the leading hand. So how many cards are left in the deck that can turn our

hand 💶 into the leading hand?

Flush – There are a total of 13 clubs in the deck, of which

we can see 💶 4 clubs already (2 in our hand and 2 on the flop) that means there are a

further 9 club 💶 cards that we cannot see, so we have 9 Outs here.

– There are a total of

13 clubs in the 💶 deck, of which we can see 4 clubs already (2 in our hand and 2 on the

flop) that means 💶 there are a further 9 club cards that we cannot see, so we have 9 Outs

here. Ace Pair – 💶 There are 4 Ace’s in the deck of which we are holding one in our hand,

so that leaves a 💶 further 3 Aces that we haven’t seen yet, so this creates a further 3

Outs.

So we have 9 outs that 💶 will give us a flush and a further 3 outs that will give

us Top Pair, so we have a 💶 total of 12 outs that we think will give us the winning

hand.

So what is the likelihood of one of 💶 those 12 outs coming on the Turn or

River?

Professor’s Rule of 4 and 2

An easy and quick way to calculate 💶 this is by using

the Professor’s rule of 4 and 2. This way we can forget about complex calculations and

💶 quickly calculate the probability of hitting one of our outs.

The Professor’s Rule of 4

and 2 After the Flop (2 💶 cards still to come… Turn + River)

Probability we will hit our

Outs = Number of Outs x 4

Probability we will 💶 hit our Outs = Number of Outs x 4 After

the Turn (1 card to come.. River)

Probability we will hit 💶 our Outs – Number of Outs x

So after the flop we have 12 outs which using the Rule of 💶 4 and 2 we can calculate

very quickly that the probability of hitting one of our outs is 12 x 💶 4 = 48%. The exact

% actually works out to 46.7%, but the rule of 4 and 2 gives us 💶 a close enough answer

for the purposes we need it for.

If we don’t hit one of our Outs on the 💶 Turn then with

only the River left to come the probability that we will hit one of our 12 Outs 💶 drops

to 12 x 2 = 24% (again the exact % works out at 27.3%)

To compare this to the exact

💶 percentages lets take a look at our poker outs chart:

After the Flop (2 Cards to Come)

After the Turn (1 💶 Card to Come) Outs Rule of 4 Exact % Outs Rule of 2 Exact % 1 4 % 4.5

% 💶 1 2 % 2.3 % 2 8 % 8.8 % 2 4 % 4.5 % 3 12 % 13.0 % 💶 3 6 % 6.8 % 4 16 % 17.2 % 4 8 % 9.1

% 5 20 % 21.2 % 💶 5 10 % 11.4 % 6 24 % 25.2 % 6 12 % 13.6 % 7 28 % 29.0 % 💶 7 14 % 15.9 % 8

32 % 32.7 % 8 16 % 18.2 % 9 36 % 36.4 % 💶 9 18 % 20.5 % 10 40 % 39.9 % 10 20 % 22.7 % 11

44 % 43.3 % 💶 11 22 % 25.0 % 12 48 % 46.7 % 12 24 % 27.3 % 13 52 % 49.9 % 💶 13 26 % 29.5 %

14 56 % 53.0 % 14 28 % 31.8 % 15 60 % 56.1 % 💶 15 30 % 34.1 % 16 64 % 59.0 % 16 32 % 36.4

% 17 68 % 61.8 % 💶 17 34 % 38.6 %

As you can see the Rule of 4 and 2 does not give us the

exact 💶 %, but it is pretty close and a nice quick and easy way to do the math in your

head.

Now 💶 lets summarise what we have calculated so far:

We estimate that to win the

hand you have 12 Outs

We have calculated 💶 that after the flop with 2 cards still to come

there is approximately a 48% chance you will hit one 💶 of your outs.

Now we know the Odds

of us winning, we need to look at the return we will get 💶 for our gamble, or in other

words the Pot Odds.

Pot Odds

When we calculate the Pot Odds we are simply looking 💶 to

see how much money we will win in return for our bet. Again it’s a very simple

calculation…

Pot Odds 💶 Formula Pot Odds = Total Pot divided by the Bet I would have to

call

What are the pot odds after 💶 the flop with our opponent having bet 10c?

Total Pot =

20c + 10c bet = 30 cents

Total Bet I would 💶 have to make = 10 cents

Therefore the pot

odds are 30 cents divided by 10 cents or 3 to 1.

What 💶 does this mean? It means that in

order to break even we would need to win once for every 3 💶 times we lose. The amount we

would win would be the Total Pot + the bet we make = 30 💶 cents + 10 cents = 40

cents.

Bet number Outcome Stake Winnings 1 LOSE 10 cents Nil 2 LOSE 10 cents 💶 Nil 3 LOSE

10 cents Nil 4 WIN 10 cents 40 cents TOTAL BREAKEVEN 40 cents 40 cents

Break Even

Percentage

Now 💶 that we have worked out the Pot Odds we need to convert this into a

Break Even Percentage so that 💶 we can use it to make our decision. Again it’s another

simple calculation that you can do in your head.

Break 💶 Even Percentage Break Even

Percentage = 100% divided by (Pot odds added together)

Let me explain a bit further.

Pot Odds 💶 added together means replace the “to” with a plus sign eg: 3 to 1 becomes 3+1

= 4. So in 💶 the example above our pot odds are 3 to 1 so our Break Even Percentage =

100% divided by 4 💶 = 25%

Note – This only works if you express your pot odds against a

factor of 1 eg: “3 to 💶 1” or “5 to 1” etc. It will not work if you express the pot odds

as any other factor 💶 eg: 3 to 2 etc.

So… Should You call?

So lets bring the two elements

together in our example hand and see 💶 how we can use the new poker math techniques you

have learned to arrive at a decision of whether to 💶 continue in the hand or whether to

fold.

To do this we compare the percentage probability that we are going to 💶 hit one of

our Outs and win the hand, with the Break Even Percentage.

Should I Call? Call if……

Probability of 💶 Hitting an Out is greater than Pot Odds Break Even Percentage

Fold if……

Probability of Hitting an Out is less than 💶 Pot Odds Break Even Percentage

Our

calculations above were as follows:

Probability of Hitting an Out = 48%

Break Even

Percentage = 25%

If 💶 our Probability of hitting an out is higher than the Break Even

percentage then this represents a good bet – 💶 the odds are in our favour. Why? Because

what we are saying above is that we are going to get 💶 the winning hand 48% of the time,

yet in order to break even we only need to hit the winning 💶 hand 25% of the time, so

over the long run making this bet will be profitable because we will win 💶 the hand more

times that we need to in order to just break even.

Hand Walk Through #2

Lets look at

another 💶 hand example to see poker mathematics in action again.

Before the Flop:

Blinds:

5 cents / 10 cents

Your Position: Big Blind

Your Hand: 💶 K 10

10 Before Flop Action:

Everyone folds to the dealer who calls and the small blind calls, you check.

Two people

💶 have called and per the Starting hand chart you should just check here, so the Total

Pot before the flop 💶 = 30 cents.

Flop comes down Q J 6 and the Dealer bets 10c, the

small blind folds.

Do we call? Lets 💶 go through the thought process:

How has the Flop

helped my hand?

It hasn’t but we do have some draws as we 💶 have an open ended straight

draw (any Ace or 9 will give us a straight) We also have an overcard 💶 with the King.

How

has the Flop helped my opponent?

The Dealer did not raise before the flop so it is

unlikely 💶 he is holding a really strong hand. He may have limped in with high cards or

suited connectors. At this 💶 stage our best guess is to assume that he has hit top pair

and holds a pair of Queens. It’s 💶 possible that he hit 2 pair with Q J or he holds a

small pair like 6’s and now has 💶 a set, but we come to the conclusion that this is

unlikely.

How many Outs do we have?

So we conclude that 💶 we are facing top pair, in

which case we need to hit our straight or a King to make top 💶 pair to hold the winning

hand.

Open Ended Straight Draw = 8 Outs (4 Aces and 4 Nines)

King Top Pair = 💶 3 Outs (4

Kings less the King in our hand)

Total Outs = 11 Probability of Winning = 11 x 4 💶 =

44%

What are the Pot Odds?

Total Pot is now 40 cents and we are asked to call 10 cents

so 💶 our Pot odds are 4 to 1 and our break even % = 100% divided by 5 = 20%.

Decision

now 💶 we have quickly run the numbers it is clear that this is a good bet for us (44% vs

20%), 💶 and we make the call – Total Pot now equals 50 cents.

Turn Card

Turn Card = 3 and

our opponent makes 💶 a bet of 25 cents.

After the Turn Card

This card has not helped us

and it is unlikely that it has 💶 helped our opponent, so at this point we still estimate

that our opponent is still in the lead with top 💶 pair.

Outs

We still need to hit one of

our 11 Outs and now with only the River card to come our 💶 Probability of Winning has

reduced and is now = 11 x 2 = 22%

Pot Odds

The Total Pot is now 75 💶 cents and our Pot

odds are 75 divided by 25 = 3 to 1. This makes our Break Even percentage 💶 = 100% divided

by 4 = 25%

Decision

So now we have the situation where our probability of winning is

less than 💶 the break even percentage and so at this point we would fold, even though it

is a close call.

Summary

Well that 💶 was a very heavy lesson, but I hope you can see how

Poker Maths doesn’t have to be intimidating, and 💶 really they are just some simple

calculations that you can do in your head. The numbers never lie, and you 💶 can use them

to make decisions very easy in Poker.

You’ve learnt some important new skills and it’s

time to practise 💶 them and get back to the tables with the next stage of the Poker

Bankroll Challenge.

Poker Bankroll Challenge: Stage 3 💶 Stakes:R$0.02/$0.04

Buy In:R$3

(75 x BB)

Starting Bankroll:R$34

Target:R$9 (3 x Buy In)

Finishing

Bankroll:R$43

Estimated Sessions: 3 Use this exercise to start to consider 💶 your Outs

and Pot Odds in your decision making process, and add this tool to the other tools you

have 💶 already put into practice such as the starting hands chart.

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