Hand Probabilities

For the most part, the hand probabilities should determine your action in a hand and act as a guide to what your next play should be.

For example:

1. What are your chances of finishing a flush or open ended straight draw?
2. What percentage of the time are you going to flop a set to match your pocket pair?
3. What are the chances of hitting the full house?

These are all important questions that must be asked. This is even more important in online games because of the lack of physical tells.

Here are three important terms needed when talking about poker odds:

Outs – The number of cards left in the deck that will improve your hand.

Pot Odds – The odds that are present in regards to the size of the pot vs. how much
it costs you to call.

Implied Odds – The assumed result of betting for later hands.

Examples:

A Pocket Pair:

You are Dealt:

King Clubs

King Spades

 

With a Flop of:

9 Clubs

5 Spades

Jack Diamonds

Question 1: What are my chances of getting another K?

Well, there are two cards left, but your chances will improve with every card that comes out that isn’t a King. There are two Kings left in the deck and 52 (total cards)-2(your cards)-3(the flop) = 47 cards left in the deck. The probability of you catching the K on the turn is 2/47 = .0426, approximately 4.3%. If you miss the K on the turn, the chances you will catch it on the river is 2/46 = .434, again approximately 4.3%.

Question 2: What about quads?

What are the chances that the only two K’s left in the deck get dealt on the turn AND the river? First the simple answer… “slim to none.” Now the mathmatical answer: The probability of first catching a K on the turn, 2/47 = 4.34% and catching the next K, 1/46 = 2.17% because now there is only one K left in the deck. So the combined chance is equal to 4.34% * 2.17% = .0009%. Less than 1/10 of 1 percent!

Question 3: What were your chances of getting dealt K’s in the first place?

After being dealt the first card, there will be 3 similar cards left and 51 cards in the deck. 3/51 is .059 or 5.9%. The chances that it’ll be K, well, there are 13 different cards in a suit. So, .059/13 is about .0045%. There is less than half a percent chance that you will get a specific pair.

Question 4: What were the chances of flopping a K?

First we must work backwards and figure out the chance of NOT getting the K. On the first card of the flop you have a 48/50 chance (48 non-K’s left out of 50 cards left), second card is 47/49, and third card is 46/48. Those come out to .96, .959, and .958 respectively. Multiply them and you get .882, or an 88.2% chance of NOT getting any K’s on the flop. Subtract this chance from 100% and you get 11.8%. That is your chance of flopping a King.

The Straight Draw:

You are Dealt:

8 Diamonds

9 Diamonds

 

With a Flop of:

6 Hearts

7 Clubs

Jack Spades

You have an open ended straight draw.

Question 1: What are the chances of you making the straight on the next card?

A ten or a five will complete your hand and there are presumably four of each left in the deck. You have 8 outs. The chance of getting one of them on the turn is 8/47, (47 cards left in the deck.) That comes out to about .170, or around 17%.

Turn:

3 Clubs

Question 2: Now what are my chances?

There are still 8 cards that complete your straight. Now there are only 46 cards left in the deck. That’s 8/46. Your chances actually improve to .174 =17.4%.

Question 3: What are the chances before seeing the turn?

Once again you will have to calculate the chances of a ten or five NOT appearing. So we can do it like the last problem. In this case, it is {39/47} * {38/46}). You have a .170 chance on the turn, and a .174 on the river. By subtracting them from 1 you get .830 and .826. Multiply and you get .686. That’s your chance of NOT hitting the cards at all. Subtract this from 1 and you get.314, or 31.4% catching the card on the turn or river.

Top Two Pair:

Dealt:

Ace Clubs

10 Diamonds

 

With a flop of:

Ace Hearts

10 Spades

7 Clubs

Question 1: What are your chances of getting a full house on the turn?

Presumably there are 4 outs left in the deck, 2 aces and 2 tens.. After the flop there are always 47 unaccounted cards. 4/47 is around .085 or an 8.5% chance of catching the boat.

Question 2: What are your chances of getting a full house on the river?

If you miss the full house on the turn, your chances improve slightly that you will hit it on the river. There are still 4 outs and now 46 unknown cards. 4/46 is about .087 or around an 8.7% chance of hitting it on the river. OK, not a BIG improvement.

Question 3: What are the chances of hitting full house if I take it to the river?

Again with must start with the probability of NOT getting it. On the turn it will NOT happen 43/47 times. On the river it will NOT happen 42/46 times. 43/47 is .915, and 42/46 is .913. Multiply them and get .835, or 83.5% chance of it NOT happening. Subtract from 1 and you get a 16.5% of getting at least a full house by the showdown.

Question 4: What are your chances of a four of a kind?

It doesn’t matter which two cards gives you the quads, you must first hit a full house on the turn and according to calculations, the chance of that happening is .085. The chance of getting the same card we got on the turn is 1/46. Since there is only one left out of the four and 46 unseen cards. 1/46 is around .022, or 2.2%. Multiply the two probabilities (.022 * .085) and get .002.

Pot Odds

Bt definition above, pot odds are the odds that are present in regards to the size of the pot vs. how much it costs you to call. To be able to calculate your pot odds you need to always be aware of the pot size. Of course with online poker this is easy since the pot is displayed on the screen.

When you know how to calculate your pot odds, you need to start applying the information and connect the pot odds to the value of your hand. The key is to calculate your chances of making a better hand than your opponents.

In the open ended straight draw above we calculated that with 8 outs we had a 17.4% chance of catching that sraight on the turn. That is about 5:1 odds. So in calculating the pot odds we need to get 5:1 money on our call.

Example: (NOT considering rake)

We are playing a $1/$2 ring game and in late position get dealt:

8 Diamonds

9 Diamonds

3 people limp before us, we call and Big Blind see’s for free. $5.50 in the pot (with blinds)

A Flop of:

6 Hearts

7 Clubs

Jack Spades

2 players check and the player to our right bets. What do we do?

There is $5.50 in the pot + $1 from player’s bet so we have to call $1 for a $6.50 pot, getting 6.5:1 on a 5:1 chance……we call.

In the same scenerio above but 1 player bets, one raises and one re-raises when it gets to us, Now what?

There is $5.50 + $1 (bet) + $2 (raise) + $3 (re-raise)= $11.50 in the pot. Now though we have to call $3 for the $11.50 pot for a 3.8:1 pot odds on a 5:1 chance of hitting and it turns into a fold.

Though this is a simple example, I hope it helps explain how the probabilities of a hand improving and pot odds should go hand in hand.