• Probability
  Probability tells us how many times an event will happen.
  For example, we know that pocket pairs are dealt to a player about once every 17
  hands or 5.9% of the time.
  
  
• Odds
  Odds tell us how many times an event will not happen.
  Example:
  The odds for being dealt a pocket pair are 16 : 1 against.
  
  
• Pot Odds
  Pot Odds is the relationship between the current pot and the bet you have to make.
  
  
• Out
  An out is a single card which improve your hand. The number of outs is very important
  for calculting your Odds and EV.
  Example:
  You hold and the board is     rainbow, so you have an open ended straight draw.
  Your outs are now all 4 queens and all four sevens, as they give you the nut straight in
  each case.
  
  
• Counterfeited Outs
  An out is counterfeited when a card improves your hand, but giving an opponent an
  even better hand.
  Example:
  You hold and the board is     , so you have an open ended
  straight draw. But this time there is a flush draw on the board.
  When you have more than two callers here, is very probably that one of them has
  a flush draw. You still have 8 outs, but the and the are counterfeited now, as
  they give you a straight, but also one of your oppenent a flush beating you.
  
  
• Discounted Outs
  Counterfeited outs should be discounted. In the example above we would now count
  only 6 outs for your straight draw and not eight as usual.

For example you are playing a $1/$2 limit game. On the flop are $10 in the pot. One player before
is betting $1 and you are to act. Your pot odds are now 11 : 1, because the pot is $10 + $1 = $11
and you have $1 to pay.

Here are some other examples, the pot is always $10.

 

 

Draw Odds

In the beginner section here we give you a chart where you see the odds for certain types of draws.
The mathematics behind are simple. On the flop you have seen 5 cards, your two pocket cards and the
three cards on the flop. The deck has 52 cards, so 47 cards are now unseen. When you are on a flush
draw you have four cards for the flush and nine other cards of the same colour are in the deck. The odds
to hit one with the next card are 38 to 9 or better 4.2 to 1.

Example:

You hold   and the board is   7 
The deck has 52 cards. You know now 5 cards.
To make your flush you need one of the following cards on the turn or the river:

            

These are your outs. When you hit one of these cards on the turn or the river, you will
win the hand in most of the cases.
38 cards are bad for you and 9 cards are good for you. So the odds are 38 : 9 or 4.2 to 1.

Here is a table with general odds for common draws.

 

 

Explanations:

Weak draws = 4 outs or less
Strong draws = 8 outs or more

• 2 outs / Pocketpair
  When you play a small pocket pair you need to hit a set on the flop to win.
  If you don't hit the set on the flop you need a very big pot to justify a call
  
• 3 outs / Aces with small kicker
  When you play an Ace with a small kicker you are often dominated by
  an Ace with a higher kicker. So you have to make two pair to win.
  
• 4 outs / Gut-Shot Straight Draw or Full House Draw
  You will often have Gut-shots and you need 11 : 1 pot odds or more to justify a call.
  When you have two pair and there is much resistance, you might be against a set
  or better. Then you need to make a full-house to win. The outs and odds are
  then the same like for a gut-shot.
  
• 5 outs / Middle pair against Top pair
  Here you want to hit a set or two pair.
  
• 6 outs / Two Overcards
  Already a good draw. When you hit you will have top pair with good kicker.
  
• 8 outs / Open ended straight draw
  Here the strong draws start. You want almost always see the River.
  Of course depending on bet you have to pay.
  
• 9 outs / Flush Draw
  If there are already 2 players in the pot before you, you should raise for value
  on the flop when you have a flush draw.
  
• 12/14 outs / Flush Draw with Overcards
  You will always go to the River. Often you should raise for Value to get maximum profit.
  

How to calculate Pot Odds and Drawing Odds?

1. Determine your Pot Odds
   (see above)
   
2. Determine your Outs
   (don't forget discounting outs with a dangerous board)
   
3. Depending on your Outs determine your Drawing Odds
   
4. Compare Pot Odds with Drawing Odds
   ( The Pot Odds must always be higher)
   

Examples:

$1/$2 Limit game, 10 players

You are the button and you hold  

5 players see the Flop of      

The SB bets $1, 2 players call and the pot is now $5.50 and you have $1 to bet.

Pot odds = 5.5 : 1
Outs = 9
Drawing odds = 4 : 1 (according to our table)

Your action: We recommend to raise here.

You have excellent odds to hit your flush
and so more money in the pot means more profit for you.


$1/$2 Limit game, 10 players

You are in the Big Blind and you hold    

 

5 player see the flop of      

 

You check, 1 player bets and all are calling.
The Turn is

You check. The bettor bets again and 1 player calls.
The pot is now $14 and you have $2 to bet.

Pot odds = 7 : 1
Outs = 4
Drawing Odds = 11 : 1

Your action: Fold

Why?

When you play such hands 12 times a day, you will lose 11 times and win one time.
Your pot odds give you 7 : 1
So you loose 11 times $2 = $22 and you win one time $7.
So calling here has a negative Expected value of -$15 (when you repeat the same hand
type with 4 outs and the same pot odds).

When you always have better pot odds than drawing odds you will have a positive EV and
you will be long-term winner.