# Pot Odds and Outs

If you haven't hit anything yet on the flop or you don't expect to have the best hand with it
(i.e. Bottom-Pair), then it's useful to know how high your chances are for a better hand.

With the help of Outs you can calculate this probability, whereas calculating the Pot Odds will tell you if it's
worth to call in a certain pot and with given Odds.

## Pot Odds

Basically Pot Odds represent nothing else than the relationship between the available jackpot and
the necessary bet. If for example there is a potsize bet, meaning that a player bets the exact sum
in the pot against us, then the Pot Odds have a value of 2.

**Pot-Odds = ( Pot + adversarial Bet ) : your own call = 2**

We receive (provided that we win ;)) double the amount of our betted money back, thus the Pot-Odds are **2 to 1**.

To continuously win in such situations our chances of winning have to amount to at least 50%.
In the section *Outs and Odds* we'll explain how to achieve this value.

**Important:** The higher the Pot Odds, the less the required chances of winning.

**Example:** If there are $180 in the pot and the opponent bets 60$ we need a chance of winning of at least 25% (1/4) to justify our call mathematically.

*Pot-Odds = ($180 + $60) : $60 = 4 *

Since we get back the quadruple amount of our 60$ (provided that we win), the Pot Odds are 4:1.

## Outs und Odds

It's truly not always easy to calculate our chances of winning without knowing the hand of our opponent.
Here several factors are taken into consideration to help us in our decision. Firstly, you could already
have collected some information on your opponent which give away which hand he could have. Secondly, we
know our cards and the cards on the board. From this, we can determine how many future helpcards we would
need to improve our hand. The number of these *helpcards* is called **Outs**.

If, for example, you hold a 9♣ and 10♣ and the board brings 4♥, 7♣, 8♣,
then we have 21 Outs, which can improve our hand slightly bis significantly.

9 cards (the other ♣ - cards for a flush or straight flush)

+ 6 cards for a straight (four 6es + four jacks - 6♣ - J♣)

+ 6 cards for the high pair

===========

**21 outs**

## From the Outs, how do you now calculate the Odds, so the probability?

Examining the Outs really only becomes interesting after the flop. Let's say we see 3 cards on the board
plus 2 cards in our hand, 47 cards are hidden from us. We have 2 hearts in our hand and in the flop are 2
more hearts. Thus we are only missing one heart for a flush. Altogether there are 13 hearts, minus the 4
hearts (in the flop and in our hand) leaves 9 Outs. Of the 47 hidden cards there are now 9 "good ones"
and 38 "bad ones". We now create the ratio of good cards to bad cards to calculate the Odds.

*38 : 9* → 4.22 : 1 ≈ **4 : 1**

This value means that in 1 out of 5(!) cases we hit upon a "good" card, meaning a heart.

At this point let's go back to the *Pot Odds*. They help us decide when we should call such a "chance".
If, as in the above example, only 1 out of 5 hands will win, then in the case that we win, the pot
should yield 5 times as much as we bet, since we assume that we have previously lost a pot with an
identical bet 4 times.

**Example:**

The flop lies open and we count 9 Outs, there are another 5 players in the pot, which already consists of $120.
You are *"on the button"* (meaning you're the last one to act) and *"under the gun"* (UTG), meaning the first player,
bets $40, 3 players fold and one calls. Now it's your turn: by now the pot amounts to $200 and the required bet is $40.

We start with the Pot Odds: $200 / $40 = 5, thus the Pot Odds are 5:1. Since we've already counted our Outs, we know that our
chance of hitting a "good" card is 4:1. A call is justified if the Pot Odds (5:1) are higher than the Odds (4.22:1).