Poker - Odds and Outs

[KillJoy]

Every now and then you find yourself in a situation where your opponent is betting on the flop and you are on a draw (flush or straight) or you just have small pocket pair and are wondering what are the odds for hitting your monster hand on the next card or is it profitable to call the raise from your opponent. To answer this questions we will have to look at outs, odds and pot odds.

First, a quick definition of this terms:
- Outs – card(s) that can improve the strength of your hand so you can win the showdown
- Odds – probability that one of your outs shows up in the community cards
- Pot Odds – ratio between the amount you can win vs. the amount you have to invest into the pot to stay in the current hand. It is reward versus risk ratio


Outs – Counting the Cards that can Help you Win the Hand

Let’s look at an example so we can better understand it.

First example
You have 56 (both spade) and the flop is 78K (rainbow, no spade)

Cards that complete your straight draw are fours and nines thus enabling you to win the showdown. There are 4 fours and 4 nines in the deck which is a total of eight outs.

Now, let’s look at another example.

Second example
You have 56 (both spade) and the flop is 7 (hearts) 8K (both spades)

In this example, besides the straight draw we also have a possibility for a flush (we have 2 spades + 2 spades on the board). So, how many outs do we have now? There are still 9 spades in the deck that can improve our hand plus the outs for the straight which makes a total of 15 outs.
What? 15? Not 17?
Nope, don’t forget we already counted in four of spades and nine of spades when we were calculating the outs for the flush. Duh!

Third example
In the example you are holding 3(diamond) 3(hearts) and the flop is 8JA(rainbow, one heart). Your opponent has A(diamonds) 6(hearts).

In this example you have only 2 outs. The two threes.

So now I know how to count the outs, big deal, it’s useless!
Not if you use this information to calculate your odds of hitting a straight or a draw.


Odds – Chances of Hitting that Straight or Flush

We’ll be using the second example in our next calculations.
We calculate odds using this formula:

Odds = number of useless cards / number of useful cards,

and we use this formula for calculating the number of useless cards:

useless cards = number of cards in the deck and in our opponents hands – number of useful cards

So in our case the calculation would be :
number of useless cards = 47 cards in – 15 useful cards = 32
Odds = 17 / 15 = 1.133 or approximately 1:1

This odds read as following: you will hit your straight or flush in 1 of two cases, or simply put, you have 50% chance to make your straight or a flush.

Great! So if my chances are 50 or more percent then I call?
It depends on the amount of money you have to pay to see the next card, and here pot odds come into play.

Let’s just calculate odds for the first and third example before we move onto pot odds.
Outs for our first example:
Odds for getting a straight on the turn = 39 / 8 = 4.875 which is around 5:1 odds.

Outs for our third example:
Odds for hitting a set on the turn = 45/2 = 22.5


Pot Odds – To Call or Not to Call

We’ll continue using the hand from the second example with the assumption that we are playing No Limit Hold’em. To calculate pot odds we need the following information:
1. The size of the pot before the raise: $200
2. The amount raised: $40
3. Your possible winnings: $240
4. The amount you must wager to stay in the hand: $40

We calculate pot odds using the next formula:
Pot Odds = possible winnings / amount needed to call

So, our pot odds are:
Pot Odds = 240 / 40 = 6 or 6:1

When we put this number next to the odds of getting our straight we can tell is it profitable or not to call the raise.
General rule of thumb is: if the pot odds are bigger than odds against you it is profitable to call otherwise you will lose money in the long run.

In our case pot odds are 6:1 and odds against us are 5:1, 6 is greater than 5 (Duh!) which means we should call. But if our opponent raised the pot for $80, then the pot odds would be 3.5 which would make it a bad call, at least in the long run.

Regarding our third example, the pot odds should be bigger than 22.5 to justify the call.

Great! Now I’m ready!
Not quite, almost there!

Sometimes you need to modify the number of your outs because in some situations the cards you may consider to be helpful to you can help your opponent to make a stronger hand.

Fourth Example:
You have 78 (both spade) and the flop is 56 (both heart) K (diamond), and let’s presume your opponent has 2 hearts (eg. AQ).

If turn card is nine or four of hearts you would make your straight but your opponent would make the flush which is as we know it stronger than your straight, so you would loose the showdown. Because of this we should discard the four and nine of hearts when calculating the total number of our outs and adjust our odds accordingly. When to discard some cards from the total of your outs depends on your read on an opponent.

Next you should read is an article regarding implied odds.

[KillJoy]

(03-10-2009 07:13 AM)AZDuffman Wrote:  Good posts on odds above, but at the table you are excited and not doing complex math well so a few "shortcuts." As the saying goes, they are not perfect but close enough for government work. (And maybe better considering the government doesn't even read what it is spending $800MMM of our money on, but I digress.)

I won't go into counting outs again. But say post-flop you have 5. Simply take the number "5" and multiply it by 4 to see your odds of getting what you need on either 4th or 5th street. Thus you have a 20% chance post-flop. So you need 5:1 to make it worth the odds.

Now, with only the river card to come you do the same but multiply by 2. So it is a 10% chance of "rivering" the other guy and picking up that card you need.

For math geeks out there I know these are not "exact" percentages. But at the table multiplication by 2 or 4 is a lot simpler than doing long division in your head.