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Texas Hold'em - Outs

The outs are those cards from the deck that will complete your hand or improve it, potentially turning it into the best hand at the table, or at least into what you believe is the best hand at the table. Knowing your number of outs is extremely important, as this piece of information is the basis of almost all mathematics involved in the game.

On one hand, your number of outs can give you the odds of your making the hand you’re looking for, on the other hand, when you compare these odds to your pot odds, you will get a clear mathematical indication as to whether you should fold, call or raise.
Remember that all these “mathematical” guidelines do not take the psychological factor into account, so in a situation in which mathematics suggests you should make a given choice, you may want to go down a different road based on decisions you make taking other factors into account.

Let’s take things one step at a time though and take a close look at how your number of outs determine the odds of your hand being “filled up”. 

Let’s consider an easy example: you have 4-card flush on the flop. At his point, you decide to determine the odds of a flush coming about on the turn, based on the total number of unseen cards and those amongst them that will make your flush happen.

Because there are 5 cards you can see on the table (the 2 in your hand and the 3 community cards on the table), the total number of unseen cards will be 52 (the number of cards in a deck) – 5 (the cards you can see) = 47. The number of cards that will help your flush is 9. That’s because there are 4 sets of 13 same suited cards in every deck, and out of those 13 cards you can already see 4. 13-4=9, that is your number of outs.

Because out of the 47 cards 38 will not help you, and 9 will, you may a well say that your odds of making your flush are 38 to 9 against.  Divide that equation by 9 and you’ll get the base result of 4.22-1.

One can make such calculations for every hand taking the number of outs as a starting point. In this respect, one can compile a chart detailing the odds in percentages (to make it easier to assess for most people).

For our above example, 4.22-1 against could be translated as: out of a total of 5.22 cards, 1 will help you make your flush, and 4.22 will not. If all 5.22 cards would help you, you’d have 100% chances. Therefore:

X = 1X100/5.22 = 19.157

You will make a flush in the above mentioned situation 19.157% of the time. You need to keep in sight that the above detailed calculus is valid only for your turn card, but – provided it misses you, you’ll get one more shot with similar odds on the river. That means your overall % chance to make your flush on the turn OR on the river is 19.15X2=38.3% (this is not the correct mathematical way of calculating the chances of making a flush on the turn OR on the river, but it is easy-to-calculate and a good approximation).

You can choose to learn such odds charts by heart for all numbers of outs, but there’s a simpler way that will give you a good approximation of the above detailed odds. Just take your number of outs and multiply it by 2 if there’s only one more card to come or by 4 if there are 2 cards to come. Note that this will not give you an accurate result but it will give you a close enough one to make a decision on.

For our above example (9 outs) the odds with one card to come are 9X2= 18 (pretty close to 19.157%). With two cards to come it’s 9X4=36 (again, pretty close to the real number of 38.3%).
One mistake that players often make when determining the odds for their hands using the number of outs is that they fail to take extra outs into consideration. While you may be looking for a flush, remember that under certain circumstances you may also be hit by outs for a straight a set or two pairs, hands that could also become pot winners. 

Determining your course of action based on the odds of making a winning hand
The odds calculus presented above carries a special significance: it holds the key to the ever present question: should I call, fold or raise?

By comparing your pot odds with the odds of making your hand you’ll gain a definite mathematical answer to that question.
Let’s say you’re on the flop holding a 4-card flush (like in the above example), there’s a $50 pot and you’re faced with a $10 raise. What do you do?

First, you take a look at your pot odds. It takes you $10 to take a whack at a $50 pot, right? That means you get 5-1 payout for your money, in conclusion, your pot odds are 5-1. Making the above presented calculus, you arrive to the result that the odds of making your flush on the turn are 4.22-1 against. Since those odds are better than the pot odds you get, you should definitely make the call – speaking from a mathematical perspective.

Making a $10 raise is not mathematically justified, because it ruins your pot odds making them 5-2, or 2.5-1. 4.22-1 against is worse than the 2.5-1 pot odds, and therefore such a move is not justified.

When you make your decisions based on such mathematical tricks, always remember that the result you get is only valid for the turn. On the river, the odds on your hand remain the same, but the pot odds can change a lot. The odds for the turn and the river are called Effective Odds and cannot be accurately calculated since the human factor has a decisive role in them.

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