Poker Odds & Probability


Figuring out poker odds and probabilities can seem like an overwhelming task. However, with a little research and memorization, this seemingly dense topic can be made much simpler. Once you understand basic situations, such as the likelihood of being dealt certain hands, hand versus hand scenarios, how your odds change with each new card, pot odds and implied odds, you will have the kind of primer you need to become a more effective player.

How Come I Never Get Dealt Pocket Aces?

One of the most common complaints, especially among inexperienced players, is that they never get good cards. Sometimes that just comes down to a common misconception. Televised poker has the advantage of being edited down to where only the most interesting hands and the biggest pots are shown, so you are more likely to see players with pocket aces or ace-king suited than a 2-7 off-suit.

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Televised poker highlights the best and most interesting hand. Your chances of being dealt pocket Aces in a game are not nearly as high.

In reality, however, your chances of being dealt any specific pair in a game of Texas Hold ‘Em are 220:1. And since most games you play at a casino will only deal about 30-45 hands an hour, even with professional dealers, you can’t expect a never-ending string of aces and kings.

Hand vs. Hand

This type of scenario comes into play most often in tournaments. And since there are so many basic scenarios that can be applied across a number of different types of match-ups, it’s mainly about memorizing those basic odds.

For instance, when you have a pocket pair and are facing only one opponent with a lower pocket pair, you are about a 4.5:1 favorite, meaning that for every eleven times the hand plays out you are likely to win nine. Another frequently seen scenario would be a pocket pair versus two over cards, e.g., pocket queens versus ace-king. In that case, which is often referred to as a race, the pocket pair is about a 1.2:1 favorite, essentially a coin flip.

Here are some odds for other basic hand-to-hand match-ups in Texas Hold ‘Em:

  • Pair vs. 2 Under Cards – 4.9:1
  • Pair vs. 1 Over Card, 1 Under Card – 2.5:1
  • 2 Over Cards vs. 2 Under Cards – 1.7:1

In-Hand Odds

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This is where poker odds begin to get more complicated. No matter what kind of game you’re playing, as the hand progresses, more cards get dealt and bets get made, the odds change accordingly. In Hold ‘Em, just because you have the best hand on the flop doesn’t mean you’re the projected favorite to win once all the cards are dealt. Top pair on the flop may seem sweet, but if there are possible flush and straight draws, you may just be putting money into what will eventually become someone else’s pot.

One way to simplify the complexity of post-flop betting is to look at the odds certain types of draws face. That way you can decide whether it is worth it to draw against a better hand, or how much you need to bet to protect your hand. Like head-to-head odds, there are a few basic scenarios, and if you memorize the odds inherent in them, they can be applied as a rule of thumb. They will also help you better understand more difficult concepts like pot and implied odds.

For in-hand odds you need to know how many outs a certain hand has, e.g., in Hold ‘Em, a flush draw has nine outs – you have two of the suit in your hand and there are two on the board, meaning there are nine of that suit left that would give you a flush. Then it’s a matter of knowing what the chances are one of those outs will come on the turn and/or river.

Here are some odds for common post-flop scenarios in Hold ‘Em:

  • Inside Straight Draw (4 outs) – 10.8:1 on the turn, 5.07:1 turn or river
  • Open-Ended Straight Draw (8 outs) – 4.88:1 on turn, 2.18:1 on turn or river
  • Flush Draw (9 outs) – 4.22:1 on turn, 1.86:1 on turn or river

Pot and Implied Odds

This final category of odds involves a little more subjectivity than the previous ones, and even invites a little bit of artistry on the player’s part. Pot odds are fairly simple. You look at the situation, i.e., you have a flush draw after the flop, and calculate how much money is in the pot and what it will cost you to call a bet. Then you figure out whether the potential payoff makes it worth calling to see another card.

In Hold ‘Em, with a flush draw on the flop you are likely to make your hand a little more than 1 out of every three times if you see the turn and river. But on the turn only the odds of hitting your flush are slightly worse than 4:1. So if there is already $120 in the pot and your opponent bets $40, you would be calling $40 to win $160 (the previous pot plus his bet), meaning you have 4:1 pot odds, since you would win four times the amount you are putting in.

In this particular scenario, the pot odds line up almost exactly: 4:1 on your money, approximately 4:1 that you hit on the next card. This is where experience and intuition would come into play. Analyze the situation, your opponent and your feeling about the likely direction of the hand to make a decision.

Implied odds are where you factor in the amount of money you think is likely to be added to the pot later in the hand by your opponent(s) after your bet or call. In that scenario, you may think your opponent will call even if you make your flush. That means, not only are you calling to win the $160, you think you’ll be able to get another x amount of dollars out of him on the turn or river.

Once you understand how to factor odds into your betting equation you will come to the table with far more tools and information at your disposal – and in poker, the more tricks and knowledge you have, the better your odds of winning.