Some say poker is a game of luck, while others defend it as a sport. We say you can play poker as a game of luck and lose a lot of money, or apply your intellect to it and start reaping pots like never before. By applying the laws of probability to your poker game you will make more educated decisions and gain an indisputable edge over players who see poker as mere "gambling."
For those completely unfamiliar with odds, let's take this from the very top. Imagine a standard coin with the usual two sides: heads and tails. In terms of odds the chance of you tossing tails is "two to one" - spelled 2: 1 - since there are TWO options available (heads and tails) and ONE way you can get your desired income (heads.) Piece of cake? Indeed! Now think of a standard 6-sided dice, and calculate the odds of throwing a 5. If you said 6 to 1 you were absolutely right! Now for a tad of math: if you want a percentage all you have to do is divide the small number by the large one and multiply by 100. In the case of the coin you have odds of 2: 1, so divide 1 by 2 (Calculator allowed) and you'll get 0.5. Multiply by 100 and you get 50, which means that odds are 50% that you'll toss heads. Use the same procedure for the die and you will get odds of 16.6% (or 17% if you're in a hurry.) Are you ready to advance to the next level?
Our thing is poker, so let's start talking about cards. If you have a well shuffled deck, what are the odds of picking the Ace of Spades? Well, since there is just one Ace of Spades out of a total of 52 cards, the odds are 52: 1, or less than 2%. What about the odds of picking any Ace? Well, since there are 4 Aces in the deck the odds would be 52: 4, but since odds always have to be "something to 1" what you do is divide the first number by the second to get 13: 1. To get percentage odds you divide 4 by 52, which will give you 7.6% (8% is fine too.) And for one last example, what about the odds of picking any Spade? There are 13 Spades in total, so the odds are 52:13 - or rather, 4: 1 - for a 25% chance.
Let's summarize what we know so far: the odds of something happening are
THE TOTAL NUMBER OF OPTIONS YOU HAVE: THE NUMBER OF WAYS IT CAN HAPPEN
Now let's see how we can apply this powerful mathematical tool to poker!
Simple Hand odds:
Hand odds are the odds of making a hand in the flop, turn or river, to make the most of your hole cards. This can get complicated, so let's start with a very simple example: you have two spades in your hand, there are two more in the flop, and a flush would just make your day. What are the odds of that happening in the turn? Let's start by counting the remaining spades: since 4 are already out in plain view it follows that 9 must remain in the deck, so you have 9 "outs," which are the 9 ways in which you can complete your flush. Now let's count the number of cards that are still unseen: since you can see 5 cards (your hole cards and the flop) then 47 cards remain unseen, since you have a whole deck of 52 minus the 5 you can see. Now we can apply the Universal Formula of Odds we just learned, and get odds of 47: 9, which any calculator will tell you equals 5.2: 1, or a percentage of 19.1%. What if you did not catch your flush in the turn? Let's calculate it for the river: you have 9 outs, and now only 46 cards remain unseen (because you can see the turn card now) so the odds are now 5.1: 1 or 19.6%.
In general, hand odds for the turn or river will be calculated like this:
NUMBER OF UNSEEN CARDS REMAINING: NUMBER OF OUTS
This is good for calculating odds a card at a time, but experts agree that if you want to go all-in you should only do it after considering the combined odds for both turn and river. How is this done? Unfortunately it is not as easy as the previous ones, but we will break it down for you, and teach you some tricks as well. But first, let's talk about outs.
Let's take the simple scenario: you have a pocket pair, and you are hoping for a set. How many outs do you have? Well, if you are holding 2 Aces then it follows that 2 more remain unseen in the deck. You have 2 outs to hit that third Ace.
That was easy, was not it? Let's try a slightly more difficult case - after the flop you have 2 pair, and are now aiming for a boat. For the sake of the example let's say you have a pair of 6 and a pair of Kings. Since either a 6 or a king will complete your full house, you have 4 outs: the two remaining sixes and the two remaining Kings. Of course you would prefer a King, but beggars can not be choosers and we are only counting outs anyway. If you have two pairs, you have 4 outs for making a full boat.
Let's think of straights now, shall we? There are those nasty little inside straights that keep you on the edge of your chair for the whole hand; Let's say 7, 9, 10, J for this example. All you need to be happy is an 8, and there are 4 of those in every normal deck, which leaves you with 4 outs. On the other hand, if you have a friendlier open-ended straight such as 8, 9, 10, J you could complete your hand with either a 7 or a Q. Every deck is provided to have 4 of each of those, which leaves You sitting pretty with 8 outs.
Flushes are very generous when it comes to odds. If after the flop you find yourself with 4 cards of the same suit, lady Luck could well be smiling at you: since there are 13 cards of each suit, and 4 are already out there, the remaining 9 must be still in the deck trying To find their way to you. If you hold 4 to the flush, you have a whopping 9 outs, which is not bad at all.
But odds-wise, possibly the best hand you can hold is an open straight flush draw, the one that is open for almost everything, say 7, 8, 9, 10 all Hearts. Your flush draw has 9 outs, as we just found out, and an open straight draw has 8. However, we must take into account that the 6 and Jack of Hearts have been counted twice: once as part of all remaining Hearts (for the Flush) and once as outs for the straight. So the total number of outs for an open straight flush draw is 9 + 8 - 2 = 15 outs.
On the second part of this series you will learn how to calculate combined odds and pot odds, and how to apply these ratios to your decision-making process. Use your brains at the tables and become a shark in no time!