Pot Odds and Implied Odds

Pot odds and implied odds are major concepts in the math of poker.  It is crucial to know when the odds are in your favor, and when they are against you.  Then, you can make informed decisions on when to call, bet, fold, raise, re-raise or go all-in. 
Note: For the examples in this section, round numbers will used (whenever possible).  It is easier to learn a concept in black and white.  The real world runs in shades of gray.  Consequently, at the poker tables you will need to approximate.  

Pot Odds
Pot odds are the ratio of the current size of the pot to the cost of a contemplated call. 
For example, if there is $7,500 in a pot and villain (an opponent) bets $2,500.  There is now $10,000 in the pot.  It will cost you $2,500 to win a potential $10,000.  If you bet there will be $12,500 in the pot. 

Your pot odds are 20% ($2,500/$12,500).  You must win 1 out of 5 pots to break even.  This can be expressed as 1:4.   That is to say, you must win one pot and can lose four pots to break even.  If you win more than that, you will make money.   

When the odds of drawing a card that wins the pot are higher than the pot odds, the call has a positive expectation.  In other words, on average, you will win more money than the cost of the bet.

Conversely, if the odds of drawing a winning card are numerically lower than the pot odds, the call has a negative expectation.  On average, you will win less money than the cost of the bet.

To explain this concept further let’s review a flush draw.  Sometimes this is called chasing a flush.

Example #1: Getting Pot Odds on a Flush Draw

• You have Ace 8 suited (hearts). 
• The flop has 3 different cards with two hearts.
• After the flop villain bets $1,500 into a $8,500 pot.  The pot is now $10,000.
• You must put in $1,500 to call the bet (making the pot $11,500).
• You have a 19% probability to make a flush on the next card.
• You have pot odds of 13% ($1,500/$11,500).  This gives you an  expectation of  +6% (19% - 13%) over the long run. Also, you have good implied odds which will be covered next. 
• This is a good bet mathematically (assuming you aren’t short stacked and/or have other considerations that will encourage you to fold).   

Implied Odds
Implied odds are your potential winnings by the end of the hand compared with the amount of money required to make a call.  They are different than pot odds because they account for possible future betting.

Implied odds are calculated in situations where you have a draw.  You expect to make money on additional bets if your draw is made.  And, you can fold to a bet on the next card if the pot and implied odds are unfavorable.

Since you expect to gain additional money in a later round, or rounds (if your draw is made, and not be committed to lose additional bets when your draw is missed), the extra money you expect to gain is added to the current pot size. 

What you may gain is only an estimate depending on your read of the other player.  It isn’t an exact science. 

Example #2: Getting Implied Odds on a Flush Draw

• You again have Ace 8 suited (hearts).  
• The flop has 3 different cards with two hearts.
• Villain bets $3,500 into a $6,500 pot.  The pot is now $10,000.

• You must put in $3,500 to call the bet (making the pot $13,500).
• You have a 19% probability to make a flush on the next card.
• You have pot odds of 26% ($3,500/$13,500).   This gives you an expectation of  -7% (19% - 26%) over the long run.
• However, you consider making the call since you have good Implied odds.
  • Implied odds are important if you think you can get more money from your opponent(s) if you hit your flush on the following round/rounds of betting (assuming you aren’t short stacked or have other considerations).  This is especially true in this example because you have the potential for a nut flush.
    
    

 Example #3: Not Getting Pot Odds on a Flush Draw

• You again have an Ace 8 suited (hearts).  
• The flop has 3 different cards with two hearts.
• Villain bets $6,000 into a $4,000 pot.  The pot is now $10,000.
• You must put in $6,000 to call the bet (making the pot $16,000). 
• You have a 19% probability to make a flush on the next card.

• You have pot odds of: 38% ($6,000/$16,000).    You are getting a potential 19% for a cost of 38%.  This gives you an expectation of -19% (19% - 38%) over the long run.

• Mathematically, this is a bad deal and you should consider folding.

To learn more please go to the: Mastering Poker Math Book

Copyright 2021
Charles W. Clayton
All Rights Reserved