Outs and Odds
When you are holding a hand that is a draw, it is important to know how many cards in the deck will improve your hand. Those are called your outs. When you count your outs, there are two things that you have to bear in mind. First, you cannot know whether one of the other players may hold one of the cards you are looking for. A player may have folded that card, but you cannot know that. That means you count as an out any card that may still be in the deck.
Second, you have to consider the possibility that what you believe is an out is actually not. Either one or several of the cards you are waiting for will improve your hand, but they will improve your opponents hand even more and you still lose. Example: You have a flush draw against an opponent who flopped a set. Some of the cards of the suit you think are outs would pair the board, giving the other guy a full house.
Or you are already so far behind that your outs will not make your hand a winner. Example: You hold AT offsuit, the flop comes A-K-6 rainbow and you are up against AK. Even if you hit your kicker on the turn, you still have the second best hand.
Some typical hands and their outs
- One overcard to the board - 3 outs
- Two overcards to the board - 6 outs
- A pocket pair looking to make a set - 2 outs
- Two pair looking to make a full house - 4 outs
- An open ended straight draw (you hold T9, flop is Q83) - 8 outs
- A flush draw - 9 outs
How to calculate your odds
Let's assume all your outs are live. Let's also assume that if you improve, your opponent's hand will not improve to beat you on a later street. This, of course, can happen, but at this point, it does not enter our calculation. Now after the flop, you have to calculate the the probability of the turn and/or river card improving your holdings to best hand. There are 52 cards in the deck, and you know 5 of them (your hole cards and the 3 cards on the flop). That leaves 47 cards in the deck on the flop, and 46 on the turn. Divide your outs by 47 and you have the percentage, or probability, of your chance of winning.
For example, with two overcards and thus 6 outs on the flop, your chance of making top pair on the turn is 6 divided by 47, which is app. 12,7%. If you want to know what your chances are to hit either on the turn or river, you have to divide 6 by 46, which is app. 13%, and add the two percentages, giving you a total chance of app. 26%.
Obviously, that is a bit of a long shot. But let's assume you have a flush draw, with 9 outs. Then your chances on the turn and river combined are roughly 39% - much better. Now that still does not mean that you always should call with 9 outs and fold with 6 or less outs.
What is the price to see the next card?
The next step before you decide to call is to look at the price you would have to pay to see the next card versus the current pot size. Example: The current pot size is $10, you have a flush draw and 9 outs. Your opponent bets $3. Your price is 30% of the pot, and your chance is app. 18,5% to find the magic card on the turn. Looks like a clear fold, right? But wait a second...
What are implied odds?
You probably already guessed what this means. If I improve to a flush, I will probably win more money on later streets, right? That is correct, although it is not guaranteed. The implied odds make the abovementioned $3 call profitable, if your opponent bets the flop, and will not go on betting aggressively after the turn. To calculate this effect is next to impossible because you can never tell how the hand will turn out, but at least you have an idea.
Whether you actually have implied odds depends on a number of factors. First, it is questionable if your opponent will keep betting into you (or calling your bets and raises) in case your draws turns into a winner at some point. So, how well hidden is your draw? If you are drawing to a flush because there are two cards of the same suit on the flop, and the turn brings another card of the same suit, then the other guy will certainly be wary and may not be willing to invest more money. This willingness will also depend on the strength of his hand, obviously.
Straight draws may be very well hidden (like you hold 89, and the flop comes 7TA) and the other guy will pay you out on the turn and river with AQ or AK or AT. And with a pocket pair like 99 and a flop like 3KJ, your chances of spiking a 9 may be very thin, but the payout should be good in case you do hit. Also, there is a chance that 99 is still the best hand.
While doing all this, your position is important too. Let's say a player acting before you bets into your draw, and there are more players to act after you. Those players may improve the situation if they just call once you do (because they put more money in the pot). But they can also completely destroy your calculation by raising and killing your pot odds in the process.
As you can see, the considerations are quite complex. But after a while, you will not have to calculate that much during a hand. You will be able to see the situation and have an idea of whether it is profitable to call or not.