Probabilities, Odds and Outs - PokerTraining.org

Probabilities, Odds and Outs
Much more simple than it looks!

- your chances of winning are 50-50 against two over-cards (e.g. KQ).

In case you don´t hold a pair (e.g. KQ),

- you are ahead by 70-30 against any hand that is built of one of your cards and a less valuable second card (e.g. KT or QT);

- you are behind by 30-70 against any hand that is built of one of your cards and a more valuable second card (e.g. AK or AQ);

- you are ahead by around 60-40 against any under-card combo (e.g. JT);

- you are behind by around 40-60 against a combo containing an over-card (e.g. AJ);

- your chances of winning are 50-50 against any under-pair (e.g. 99);

- you are behind by 20-80 against any over-pair (e.g. AA).

Odds and Outs:

After dealing with the pre-flop probabilities, let us turn our attention to the post-flop action. If you know a little bit about Poker, you may have heard the phrase that somebody is “counting his outs” or that someone couldn´t call because he didn´t have the “odds” to do so. Now, what exactly is an “out”? An “out” is a future card that improves your hand to be the best hand on the table. As you know, a flush beats top-pair. In case you´re drawing to a flush with maybe 4 hearts, and assuming you´re actually trailing the top-pair, every additional heart would give you the advantage. There are 13 hearts in the deck and 4 that you know of, giving you 9 outs to beat your opponent.

The ratio of the total pot size in comparison to the amount of chips you have to use in order to call a bet is referred to as “pot odds”. Assuming the pot size is 100 in chips and your sole opponent still being involved in the pot bets 50, you have to invest 50 of your chips in order to stay in the pot. Your call is worth 50 chips, with the total pot climbing to 200 chips (100+50+50), meaning your pot odds are 25 % or 1/4.

However, the more important aspect is how you can implement this knowledge into your game in order to improve your performance and avoid making rookie mistakes. The answer is pretty simple; only call someone else´s bet with a weaker hand if your probability of winning the hand (determined by the amount of outs) is higher than your pot odds.

To compare these two numbers, you have to use a little trick in order to transform the outs you counted into your winning %:

Following the flop, you multiply your outs by 4; following the turn you multiply your outs by 2. The number you get is your chance hitting an out and therefore winning the pot.

Now, let´s move on to a vivid example:

Assuming you hold Jh Th and the flop shows Qs 9c 2d and you have a feeling that your sole opponent have hit the top-pair. The pot size amounts to 100 in chips and your opponent bets 50. What do you do now?

1)      You count your outs! Assuming your opponent has a pair of queens, a jack or a ten would be of no use to you. But with QJT9 you´re holding an open ended straight draw, meaning every 8 and every K completes your straight. There are still four eights and four kings in the deck, accumulating to 8 outs.

2)     You calculate your chances of winning the pot! You have 8 outs and turn and river are still to be shown, meaning your chance of winning the pot is 32 % (8x4).

3)      You calculate your pot odds! Your opponent bet 50 in a pot of 100, meaning you have to pay 50 in order to stay in the pot. Your pot odds are 25 % (50/200 = 1/4 = 25 %).

4)      You compare pot odds and your chance of winning! Your chance of winning is higher than your pot odds (32 % > 25 %): You call!

After you called, the turn shows a 3 of hearts so nothing really changed so far. The pot size now amounts to 200 and your opponent bets 200. What do you do now?

1)      You count your outs! Nothing has changed so far, you still have 8 outs.

2)      You calculate your chances of winning the pot! You have 8 outs and only the river is still to be shown, meaning your chance of winning the pot is 16 % (8x2).

3)      You calculate your pot odds! Your opponent bet 200 in a pot of 200, meaning you have to pay 200 in order to stay in the pot. Your pot odds are 33 % (200/600 = 1/3 = 33 %).

4)      You compare pot odds and your chance of winning! Your chance of winning is lower than your pot odds (16 % < 33 %): You fold!

Of course, counting your outs is not restricted to open ended straight draws or flush draws. Any card that improves your hand to the best hand on the table is considered an out. Another scenario you´re able to see very often is the situation of two over-cards (e.g. AK) going against a pair (e.g. JJ). When facing such circumstances, the player holding AK is behind but he still has 6 outs. Every king and every ace would give him a higher pair. His chance of winning would be 24 % (6x4) after the flop and 12 % (6x2) after the turn.

You have to gain experience by practicing those habits in order to successfully count your outs and therefore calculating your chances of winning the pot. Additionally, accumulating information about your opponents is crucial. If you identify a certain player to play in ultra-tight fashion, you cannot give yourself as many outs as if you´re facing off against a total maniac or other loose-aggressive players.

Especially when you´re playing no limit Hold´em, avoid as many rookie mistakes as possible! A lot of bad players don´t care about odds and outs and call everything if they see a chance to improve their hands. Let me get this straight, in the long term you lose money if you call your opponent´s bets when your chance of winning the pot is lower than your pot odds and that includes every possible suck-out.

Another mistake to avoid is that some players don´t distinguish between situations after the flop and after the turn. Like described in the example before, just because you called on the flop doesn´t imply that you have to call on the turn if your situation turns out to be worse.

When looking at this article, one can easily see the options players have in the game of no limit Hold´em. Think about it, if you correctly assume that you´re currently ahead and that your opponent is on a flush-draw, you can manipulate his pot odds by betting more than you would usually do. By doing that, you not only protect your hand by making every future card extraordinary expensive, but in addition to that, you increase your estimated value in case your opponent calls your bet. The problem with a lot of bad players is that they have absolutely no clue about the mechanics of Poker. Those players are scared of a potential flush and only bet the minimum or just a little bit more. Such a behavior leaves the door wide open for draws of any kind because they decide to not manipulate the pot odds and leaving their hands unprotected.

Speaking of options in the game of NLHE, don´t forget that you might sit on a draw that is so good, that you´re able to combine different draws and increase your outs. Assuming you hold Kh Qh and the flop shows: Jh Th 2s; not only do you now hold an open ended straight draw (open ended straight flush draw to be more precise) but also a flush draw accumulating to a total of 15 outs. In case you assume that you´re winning in case you hit one of your over-cards (KQ), you can give yourself even more outs.

On the flipside, a lot of beginners have the tendency to give themselves more outs than they really have. Let me get this straight, counting your outs is a “tool” that will help you to play more efficiently; it is not meant to be manipulated in order to justify crazy decisions! Assuming you hold 2h 2s and the flop shows Jh Th 9h and three opponents are getting heavily involved before it´s your turn to make a move. Of course, you have a flush-draw, but it´s the weakest one you can have. In case you assume that no one already completed his flush, probability is that someone of your 3 opponents also holds a “heart” and therefore owns a higher flush-draw. Despite having a flush-draw, you simply cannot give you any out regarding an additional “heart”. The only scenario you can hope for is that no one else already completed a straight and that you still have two outs (2c and 2d) left, giving you a winning chance of 8 % at max instead of 44 %.

To complete this article I would like to express that properly counting your outs and calculating your pot odds takes some time and even more experience, but in the end it´ll be totally worth it. The winning percentages being mentioned here are mostly rule of thumb estimations designed in order to help you making quick decisions when the heat is on. In case you are interested in the true % figures, check out our odds-calculator and you´ll see that the estimated figures come really close to the true numbers.

Click here to see the Odds and Outs table

Back to top