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Poker Odds

Every hand of every variant of poker has the best players weighing up probability and poker odds in different ways. There’s the most intuitive angle of working out the probability that your hand will rank highly compared to what’s already been dealt, and just on the value of the cards. Then, there are more in-depth poker odds to consider.

Counting your outs, understanding how pot odds work, assessing equity, using implied and reverse implied odds, and getting to grips with pre-flop probabilities can all make you a much better poker player.

Here, we’re looking at all of these key areas of poker odds, why they matter, and how to add these calculations to your arsenal.

Table of Contents:

The Importance of Math and Probability

Probability and poker go hand-in-hand. To work out if you have any kind of advantage, you need to work out the probability of the other players at the table having a hand that’s as good as your hand. In some poker formats, you’ll also need to weigh the probability of improving your hand through discards.

With each game of poker only featuring one deck of 52 cards and one of each card, you can assess the probability of success. This increases as the deck dwindles and you have more information about what’s been dealt so far.

Just as is the case in blackjack games, using math to work out probability and poker odds can give you the edge.

Risk vs Reward

Establishing probability only shows you the most favourable course of action. Rarely does the math give you a guaranteed path to victory in any given hand. Working out the probability is all about putting a figure on the risk of betting and if that risk is worth it for the potential reward, be it in competitive poker or casino poker.

The Basics of Poker Odds – Counting Your “Outs”

Counting your outs is a way of establishing your poker odds of getting a card that you need to improve your probability of winning the round.

What are “Outs” in Poker?

Outs is a term that describes any card from the deck that would improve your hand. Thus, if it comes out, your hand will improve your odds of winning the round.

How to Count Your Outs

These are some common scenarios where you’re counting your outs. Each example will assume a fresh deck and the first round of a game. For later rounds, you need to keep a running count in your head of the cards that you’ve already seen. Naturally, with people folding face-down and burned cards, counting your odds isn’t an exact science.

Flush Draw

Let’s say you get dealt enough cards or your opening hand and two of the community cards – depending on the poker variant – to give you four of the same suit. This means you have a flush draw and just need one more suit. So, you’d have nine outs at the most in the rest of the deck.

Open-Ended Straight Draw

You’ll have an open-ended straight draw if your hand cards and the community cards allow you to get a straight with either a high card or a low card on either side of your numbers. In this case, with four of the high and four of the low being left, you have up to eight outs.

Inside Straight Draw

Between your hand and the flop, you’ve got four of the five cards needed for the straight, with the one missing being one of the middle values. This is the gunshot or inside straight draw and only gives you four potential outs.

Two Pair Drawing to a Full House

To see your two pair hand level up to a full house, you’ll need one more of the same card that makes up your two pair. With two of each already in play, this gives you four potential out cards.

Three of a Kind drawing to a Full House or Quads

Taking the game of Texas hold’em here, if you have three of a kind, that leaves two others after the flop. So, to climb to a full house from three of a kind, you have up to six possible out cards, as each of those other two just needs one more to become a pair. For a quad from threes, you only have one out card.

The Monster Draw (Straight and Flush Draw)

Named the “monster draw” for good reason, this opening hand offers you a gluttony of outs to land high-scoring hands. With a nine and ten of the same suit, with an eight and a jack of the same suit on the table, you need either nine outs to get the flush or eight of the cards on either side of your straight to complete that run. Combining these and factoring in the cards that crossover for both hands, you get 15 outs.

Converting Outs to Equity

Hand equity is about how much your hand is worth and how likely it is to win against the others at the table. Pre-flop, this is about the value of your hand cards. Post-flop, you add in the increased equity of your hand with the community cards and the likelihood of improving the hand through your number of potential outs.

So, until you complete the round, your hand equity will be directly impacted by the number of outs left. The more outs possible for you to hit a better hand, the greater your chances of improving your hand equity. Hand equity can then be converted into a percentage chance of winning, and that can be your poker odds of winning the pot.

The In-Game Shortcuts

To help you to quickly convert outs into equity values and understandable poker odds, you can use the Rule of 4 and Rule of 2 principles.

These are straightforward methods for you to calculate equity based on the number of outs you have from a drawing hand. It’s not perfectly accurate, but it does offer a quick way of getting poker odds.

Rule of 4

First, you apply the Rule of 4 to convert your outs into poker odds. On the flop, you multiply your number of outs by four to see your equity as a percentage. So, if an open-ended straight draw gives you eight outs, you have 32 percent equity.

Rule of 2

The next step comes on the turn with the Rule of 2. If you still have eight outs with your open-ended straight draw, for example, your equity is multiplied by two, giving you 16 percent equity.

Understanding Pot Odds

When it comes to probability and poker calculations, after working out baseline poker odds, you need to convert them to a monetary value. This is because you want to know the value of your hand and the cost of your options in relation to the pot, as, ultimately, poker’s a game of winning money.

What are Pot Odds?

The pot is the total sum of all of the bets placed in the current round. The pot odds show you the ratio between the pot with the size of the bet that you’re currently deliberating.

How to Calculate Pot Odds

Let’s say that the pot has reached $30 and your opponent has just called with $10. Now it’s your turn, and with $10 being the call to get into what is presently a $40 pot. This makes the pot odds 4:1 as you need to bet one-quarter of the pot.

Put into a percentage, you have pot odds of 20 percent due to your bet making up one-fifth of what will be the pot should the bet be placed. With this as a percentage value, you can then weigh your pot odds against your equity odds to assess whether or not you should make a call.

Combining Equity and Pot Odds

This is where all of the calculations for your probability and poker odds come together. If you have a hand equity value that’s in excess of the calculated pot odds, it’ll be profitable to make the call.

Here’s a look at this with an example from one of the hands explained above in the context of Texas hold’em poker after the flop:

  • You get a flush draw of a 3H and 6H in hand with a QH and 9H on the table, giving you nine outs.
  • At this point, you can apply Rule of 4 to give yourself hand equity of 36 percent.
  • As the betting comes around, the pot’s at $3 and your opponent has just bet $3, totalling $6.
  • This puts to pot odds at 2:1, with your $3 call giving pot odds of 33.3 percent on the $9 pot.
  • Your hand equity of 36 percent is higher than the pot odds, making the call the correct call, on paper.
  • After the turn, still needing one heart for the flush, you apply Rule of 2 to get hand equity of 18 percent.
  • So, any call that would make your bet a fifth (20%) or more of the pot odds would be a poor call.

Implied Odds and Reverse Implied Odds

Both reverse implied odds and implied odds can be considered when you have a draw hand detailed above, such as an open-ended straight draw or a three of a kind. Here’s how they work:

The Concept of Implied Odds Explained

Where pot odds apply to your current pot size and bet, implied odds concern your potential return if you improve your hand during the round. To do this, you add your expected win to the pot size before weighing it against your current bet, giving you a higher bar for calling. As an example, if the pot’s at $50 and you need to call a $25 bet, the pot odds would be 3:1.

Expecting to win from your draw hand, you’d say that you can expect to win at least $75. So, you add the $50 to the $75 expected win to make $125 and then divide that by this current bet of $25. Here, you get 5:1 implied odds or 20 percent to beat with your hand equity calculation.

The Concept of Reverse Implied Odds Explained

Where implied odds offer a new bar to estimate your probability and poker odds against, with an eye on winning, reverse implied odds consider the loss if you lose. The calculation works as a useful counter to better ground your call after also considering the implied odds. It’s particularly important if you could get a winning hand with a card that may also give others a strong hand. Here, assess the chances of other winning hands being better than yours.

Pre-Flop Odds and Probabilities

While we’ve focused on your own hands here for the most part, assessing poker odds is also about working out the probabilities your opponents may have. So, these are some common probabilities and poker matchups that you should keep in mind.

Common Pre-Flop Matchups

Pocket Pair vs Two Over-Cards

Having a pocket pair against two over-cards – two cards that are higher than the pair – only gives the pocket pair hand an advantage of around 56 percent to 44 percent.

Pocket Pair vs Two Under-Cards

Against two unpaired under-cards, a pocket pair can assume an advantage of around 82 percent to 18 percent.

Pocket Pair vs Higher Pocket Pair

If your pocket pair is up against a pocket pair of a higher value, your hand will only have a 20 percent shot at beating the higher value pair hand.

Dominated Hands

Dominated hands are hands that are relying on three or fewer out cards to beat a hand that’s similar but better, such as when you have pocket fives and face a player with pocket sixes or better. It’s all about having fewer shots at getting those out cards than the opposing hand.

Useful Probabilities to Know

Odds of Being Dealt a Specific Pocket Pair

The odds of any player being dealt a specific pocket pair in Texas hold’em poker is 0.45 percent or 220:1.

Odds of Hitting a Set on the Flop When Holding a Pocket Pair

When holding a pocket pair, you then hit a set on the flop when a third of the same card value comes up on that first reveal of community cards. The odds of this happening is 11.76 percent or 7.5:1.

Odds of a Flop Being All One Suit

Assuming that your hand has two cards of the same suit, thus you want three more to show on the flop, you’d have a 0.8 percent or 118:1 shot of the flop being all the same suit as your hand.