poker

Poker Strategy V - How to Calculate the odds in Hold'em

How to Calculate the odds in poker: 

Basic concept -  what are the odds of getting an Ace or any card you need..

When you sit down to play Hold'em, every one wants to start with great cards. Very few players ever truly understand the  reality of the odds in poker. So let's start with a basic concept: What are the odds of getting an Ace (or any other card). There are 52 cards in the deck, and there are exactly (you hope) four Aces so the odds of getting an Ace are 4/52 = 1/13 = .0769 or 7.7%. 

Now - In order to get a Pair of Aces, you need to draw one of the three remaining Aces. You haven't seen any other cards so since there are 51 cards left in the deck, you base your odds on 51 cards (3/51) or about 5.9% 

Simply stated: The odds of getting a pocket pair is approximately 5.9% - The odds of getting a specific pair is that 5.9% divided by 13 or just about 0.45% of the time

Okay - let's say you have pocket Aces: 

What's my chance of getting an Ace on the turn?

We know there are 2 more Aces. Even though there are other players, and a burn card you don't know what they are so you can only calculate odds based on the  five cards you have seen already. The answer is 2/47, or .0426, close to 4.3%. If a player flashes a card adjust your calculations accordingly.

What are the chances of getting an Ace on the river?

There are still 2 Aces left. You have seen 6 cards from the deck bringing the grand total to 46. What's 2/46? That's .0434, which is also close to 4.3%. 

Remember, everyone is playing the common cards. What is the best possible hand? What cards would you need to make that hand? If you are playing for a third Ace on the turn or the river, then your odds are 2/47 + 2/46 

What are the chances of getting both Aces?

Now you are calculating the odds of drawing one Ace on the turn AND one Ace on the river. 

Just multiply the probability of each event happening. The probability of getting that first Ace on the turn was about 4.3% (.0426).

And the chance of getting a second Ace on the river would drop to 1/46, because there'll is now only one Ace left in the deck which is about .0217, or 2.2%

  

So 2.2% of the time that you have a three Aces, you will draw the fourth Ace on the river. 
So if you have pocket aces, you will draw to four Aces about 9 times out of 10,000.

What are the chances of getting an Ace on the flop?
There are two ways you can calculate this. Either  "think in reverse"  and calculate the odds of Not Getting an Ace on the flop. On the first card you have a 48/50 chance (48 non-Ace cards left, 50 cards left in the deck), second card is 47/49, third card is 46/48. If you multiply those probabilities (.96 x .959 x .958) you will get .882, or an 88.2% chance of NOT getting any Aces on the flop. Invert it to figure out what your chances really are and you get .118 or 11.8%. This will be your chance to get one or two Aces

In review: 

The odds of getting one ace or a specific card is 7.7%. 
The odds of pairing that card and having a pocket pair is 5.9%
The odds of having a specific pair (Aces, Kings, Etc.) is approximately .45%
If you have a pocket pair, the odds of getting a set (three) is 11.8% on the flop and 4.3% on the turn and river. 

Here is a quick chart to give you some basic odds: 

 
What is the probability that ...

 (%) 

The odds against it are...
You will hold a Pair before the Flop 5.88 16 to 1
You will hold suited cards before the Flop 23.53 3.25 to 1
You will hold 2 Kings or 2 Aces before the Flop 0.90 110 to 1
You will hold Ace-King before the Flop 1.21 81.9 to 1
You will hold at least 1 Ace before the Flop 14.93 5.70 to 1
If you have four parts of a Flush after
the Flop, you will make it
34.97 1.86 to 1
If you have four parts of an Open-end Straight-Flush after the Flop, you will make a Straight-Flush 8.4310.9 to 1
If you have four parts of an Open-end Straight Flush after the Flop, you will make at least a Straight 54.12 0.85 to 1
If you have Two-Pair after the Flop, you will make a Full House or better (this includes the weaker full house - be careful)16.74 4.97 to 1
If you have Three-of-a-kind after the Flop, you will make a Full House or better* 33.401.99 to 1
If you have a Pair after the Flop at least one more of that kind will turn up (on the last two cards) 8.4310.9 to 1
If you have a pocket pair - that one or more of that kind will hit on the flop (a set or quads)11.767.51 to 1
If you don't have a pair (Hopefully you are playing A,K or are suited) that you will pair at least one of your cards on the flop.32.432.08 to 1
If you hold two suited cards - that two or more of those cards will hit on the flop giving you four to a flush or a flush.11.87.47 to 1 
If you hold two suited cards (about 23.5% of the time) the odds of catching a flush if you stay to the river is - 5.77 16.3 to 1
If you have a pocket pair (5.88%) and stay through the river, what are the odds that at least one more of your kind will turn up (a set or quads)19.18 4.21 to