Pot Odds & Hand Probabilities

The Math Behind Pot Odds/Hand Probabilities

Your Poker Strategy must include a good understanding of pot odds versus the probability of making your hand, in order to be a winning player. Without being able to calculate your hand probabilities, it is impossible to make the best decision possible while at the tables. I am going to share a lot of math here, but it’s all simple math. I will show you how to calculate your hand probabilities, as well as pot odds.

Before we get started with Texas Hold’em Pot Odds and Hand Probabilities, let’s briefly talk about hand frequency. Does it seem that you are dealt some hands more than others? That’s because you are. We will only discuss a couple, and we will discuss more in a later session.

There are six ways of being dealt any particular pair. Let’s take Queens as an example.

• Qh, Qd,
• Qs, Qc
• Qc/Qh
• Qd/Qs
• Qh/Qc
• Qd-QC

What is the probability that you will be dealt pocket Queens or any specific pocket pair? It’s 0.45% or odds of 221 to 1. The probability of being dealt any random pocket pair is 6% or 16 to 1.

There are 12 ways you can get AK -but only 4 ways to get AKs. You will get dealt AK, suited or unsuited, 1.20% of the time, or about once every 82 hands. AK suited probability is 0.30% or once every 333 hands. Here is a chart that will help you to understand the probabilities of being dealt specific hands.

Pre-Flop Poker Strategy – Hand Probabilities

Here is another way to view Hand Frequency. Just to demonstrate how to read this chart, let’s look at pairs that are listed in the center of the chart. It starts with AA at the top of the pyramid and lists each possible pair in declining order. You will note in the Column Frequency row that this adds up to 13, as it should. Notwithstanding “suitedness”, there are only 13 cards in the deck. The line below “Hand Frequency” says 6, so 6 ways to make each pocket pair. Then, the total frequency is 78, so there are a possible 78 versions of pocket pairs. The process is the same for the balance of the pyramid.

Poker Strategy – Let’s Look At The Probabilities In Action

Let’s play a hand.

You are UTG+2 and are dealt 8c7c. You have a flush draw and a straight draw. Lucky you, right? You have 6 players to act after you, pre-flop and we don’t yet know how many after the flop. Is 8c7c a great hand in this spot? Let’s see.

Just for a second, we will say that 8,7 isn’t suited. Your probability of making a straight is 9% or 10.11 to 1 odds. But, it is suited, so you are 15%, 5.67 to 1 odds to make either a straight or a flush. What about flopping a pair? Well, that’s 24% or 3.17 to 1 odds But, do you want to continue in the hand with say a flopped pair of 8’s and a 7-kicker, with 6 players behind you? So what about two pairs? That’s 2% probability, 49 to 1 odds. Don’t hold your breath on that one.

For this discussion, I’m not going to get into who bet what. We’ll cover that in the Pot Odds discussion after this. For now, we’re just going to focus on hand probability.

Remember, all the stats above are Pre-Flop. The Flop can change the world, right? So let’s see the Flop.

Here comes the FLOP – Probabilities Brought To Life

Flop is 10c,9d,3d. You flopped an open-ended straight draw and a backdoor flush draw. In a good spot, or are we? We have 9 clubs, 4 Jacks, and 4 sixes that will complete our hand. But, one of those Jacks and one of those sixes is a club, so we can’t count them twice, which gives us 15 outs (9+3+3).

That means we have a 32%, 2.13 to 1 odds, of completing our straight on the Turn. If we miss the Turn, we now have a 35%, 2.07 to 1 chance to make it on the River. Damn, that’s 54%, 0.85 to 1 of making the hand. That means we are more likely than not to complete the hand by the River.

Before we continue, I want to backtrack and ask a couple of questions. Remember your position is UTG+2, should you have even been in the hand with 8c7c, from that position? From any position? What if UTG+1 had raised? Would you call? What if there is a Pre-Flop raise behind you? Are you calling that? I can’t answer, because all things poker are situational, who raised, who called, etc. I can tell you the math says no, you don’t even smooth call Pre-Flop. It’s a solid fold.

Now The Pot Odds

So here we are. We have 8c,7c UTG+2, not sure how we got here, but. Maybe we called in the dark, or perhaps we just had a complete moment of insanity and threw our money into the pot. Somehow, no one raised Pre-Flop, and now we have 7 players seeing the Flop, the SB, and the UTG +1 folded Pre-Flop. Just a reminder, the Flop is 10c, 9d, 3d.

Blinds are $2/$5. Seven players went to the Flop, so we have a pot of $35. The BB checks, UTG checks, and now it’s on you. What to do? You still have 4 players to act behind you, and you really have exactly no information about their hands. Everyone limped in Pre-Flop. For all you know, one of them limped a pair of Jacks, expecting an overcard on the Flop. No over card, to Jacks, Queens, or Kings, on the board. Maybe one has JQ, the nut straight draw. Did someone limp with pocket threes and hit a set?

To Bet Or Check?

If you check, and someone bets, now what? So, you decided to bet. This gives you the lead in the hand and an opportunity to gather information, or maybe your bet takes down the pot right there. So now, how much to bet? You decide on $25, about 70% of the pot. Now the pot is $60, giving the next player 2.4 to 1 Pot Odds. Not really good for most hands. Lojack folds, Hijack Folds, Cut Off Calls, Button Folds, BB Calls, UTG+1 Folds.

Three players left: BB, you, and the Cut Off. The pot is now $110. The Turn is the Jc. The board now reads, 10c, 9d, 3d, Jc. You’ve made the straight, and have a backdoor flush draw. Life is wonderful. BB checks. You have a made hand, a vulnerable made hand at that. Why is it vulnerable? Because you have the bottom end of the straight. You have an 8 high flush draw. And you have 2 opponents. They see the board too, and I doubt they called you with nothing.

Pot Odds/Hand Probability

The pot is $110, so you bet $90 in an effort to protect your hand. The pot is now $200. This gives the Cut Off about 2.2 to 1 pot odds. Cut Off Folds, the BB calls. The pot is now $290 and you are heads up with the BB. The River card is the 3c. Now the board reads, 10c, 9d, 3s, Jc, 3c. Wow, well you have the flush you wanted, and the straight, on a paired board.

The BB bets $150 into the $290 pot. The pot is now $440. Pot odds no longer matter now. What does matter is you have to call $150 to win $440, getting almost 3 to 1 on your money.

Could he have also made a flush? Sure, the odds of him also having two clubs is about 35%. The odds of him having a club higher than your 8, is 28%. Plus, the board is paired, and he has let you do the betting, till now.

We will leave that hand sitting there for now. Do you see the problems playing a hand like suited 8,7 can cause, especially from an early position?

Poker Strategy – Some More On Pot Odds

How do you calculate pot odds versus hand odds while at the table? Here’s an easy method.

Let’s say you have Jh,10s. The flop is Kd,9h,3c. You have an inside straight draw, in order to have a made hand, you need a Queen and a Queen only. There are 4 Queens left in the deck (we hope) and 47 unseen cards. You have the Turn and River to come. There are those that would say you are 5 to 1, or 17% chance to make the hand by the river. They would be correct, but taking into account pot odds, it doesn’t work that way.

There are 2 cards to come. I can’t speak for your world, but in mine, it’s doubtful I will get to draw at a hand, twice, for free. So what are my real odds?

Calculate Hand & Pot Odds For Turn & River

On the turn, you are 9% or 10.75 to 1 to hit a Queen. So let’s say the pot is $50 and loose Leroy bets $35. Now the pot is $85. You have to call $35, which gives you Pot Odds of 2.42 to 1. Now your chance of hitting the hand on the turn and for this bet, is 10.75 to 1 or slightly more than 4 times less than what you are getting on Pot Odds. Easy fold.

You would take that $85 and divide it by $35 to get your pot odds. $85/$35=2.42 For your hand odds, you have 4 outs. There are 47 unseen cards. 4 of those complete your hand, the other 43 are worthless to you. You take the 43 cards that are worthless and divide that by the 4 cards you love. 43/4 = 10.75 Then you compare your odds of making the hand, in this case, 10.75 to 1 in relationship to the pot odds you are getting, 2.42 to 1 and you can see, easy fold.

Below is an “outs” calculation chart. This shows you the probability and odds based on outs for both the Turn and River, as well as your total.

Know Your Hand Probability At All Times

The Math Behind Pot Odds/Hand Probabilities

In our next session, I will talk about Implied Odds, Hand Equity, Expected Value, and Fold Equity. Check back in often, as we are in a constant state of adding additional data.

You may also want to take a look at our Cash Game Strategy Page, for more information regarding Texas Hold’em Pot Odds and Hand Probabilities. It has lots of links to other articles. Also, don’t forget to sign up on our Contact Page. You will receive our Newsletter, and updates as we continue to add articles to Pokerrailbird.com.