### How are poker odds calculated?

There are many ways to calculate Pot Odds but here's a simple one. Rather than using a formula, poker players around the globe use the Rule of 2 and 4. The rule says that if you have two cards to come, you can multiply the number of outs you have by four and you'll come to an approximate percentage of making your hand.

Another method of converting percentage into odds is to divide the percentage chance when you don't hit by the percentage when you do hit. For example, with a 20% chance of hitting (such as in a flush draw) we would do the following; 80% / 20% = 4, thus 4-to-1.

### How do you calculate flop odds?

To work out this probability we simply multiply the probability of 3 individual cards being dealt.

1. (random card) * (random card) * (random card)
2.

3. (1/52) * (1/51) * (1/50) = 132,600 possible flops.
4.

### How are card odds calculated?

Mathematicians measure probability by counting and using some very basic math, like addition and division. For example, you can add up the number of spades in a complete deck (13) and divide this by the total number of cards in the deck (52) to get the probability of randomly drawing a spade: 13 in 52, or 25 percent.

### Calculation of Odds in Poker

Strategy in poker is based on and revolves around odds. Given its importance in the game, mastering the calculation of probabilities is essential to win in a sustained way.

But the odds are expressed in percentages and in poker it is more practical to talk about ratios. For this reason, the first probabilistic concept that should be known and understood is that of “odds”.

### What are Odds?

Odds are the odds against an event occurring. Or put another way, it is the ratio between the probability of winning and that of losing.

I will illustrate it with a simple example. When we flip a coin, the chances of it coming up heads are 50%. So we have a one in two chance that it will come out expensive. In this case, the odds of the coin coming up heads are 1 to 1; a possibility that it comes out expensive versus a possibility that it does not.

Another example. We roll a dice. The odds of a 6 rolling are 5 to 1 (usually 5: 1). There are five ways that a 6 does not come out, which are that a 5 comes out, that a 4 comes out, a 3, a 2 and a 1. And there is one way that a 6 comes out, which is, logically, that a 6 comes out. So if someone offered us a bet that he would pay us \$ 60 for each roll of a 6 and we would pay him \$ 10 for each no, we should accept immediately. Let's do the math: on average, for every six times we roll the dice, one would roll a 6 and our bettor would pay us \$ 60. The other five times the 6 would not come out, and we would pay him a total of \$ 50. As you can see, every six times we roll the dice we would earn an average of \$ 10. With such favorable odds, it is a business I would immediately sign up for.

In a moment you will know why instead of probabilities in poker it is more convenient to talk about odds.

### Applying Odds in Poker

Calculating odds is an essential part of an optimal playing strategy in poker. Through it we find out when it is not profitable to continue in a hand and therefore we must fold, and when we can continue in it because our play has a positive expectation.

Suppose we have J-Q in a Texas Hold'em hand. The flop came 10-K-3. We may make a straight on the next card, but we don't have a move yet. One of our opponents bets and we deduce that he must have a pair of K's. Therefore, at the moment we are losing, but we think that if we draw the straight we will win the hand.

To complete our play, an Ace or a 9 must come to us. Thus, among the cards that remain to come out there are eight that are good for us out of the forty-seven that remain in the deck. To calculate the odds, the total number of cards that remain to be seen, forty-seven, is divided by the number of those cards that are good for us to complete our play, eight, and, leaving the decimals aside, the result is six ( 47/8 = 6), which means that in the present situation for every time we get a ladder, five times we won't get it. The odds, therefore, are 5 to 1.

If, as I say, a player who has a pair of K's has bet, should we go? To find out, we must compare the size of the bet that we must place, with the money in the pot (including the money of our opponent's bet). If the relationship is beneficial to us, we will go. The situation is the same as with the dice example. If we have to bet \$ 10 and there is \$ 60 in the pot, we should call, because the odds of hitting a straight are 5: 1 and the pot is 6: 1. This move would have a positive long-term expectation for us. If we played it a hundred times, we would almost certainly win money (only a streak of devilish bad luck could stop us). Now, if there were only \$ 30 in the pot, it would be offering us 3: 1 odds and it would not pay us to call, so we should withdraw from the hand. The implied odds, however, could change this, but I'll talk about them below.

### Plays and Odds

The cards that go well for us to complete a play are called “outs”. Below I put a sample of the most common plays and the number of outs that each one of them has.

• Open straight + a card for a flush = 15 outs
•

• Three of a kind to become a poker or full house = 10
•

• A letter for color = 9
•

• Open stair = 8
•

• Two high cards to get a pair = 6
•

• Internal stair = 4
•

• Double pair to become a full house = 4
•

• Hand pair to become a trio = 2
•

There are a couple of considerations to keep in mind when calculating odds and deciding what our next move will be. First, we should have a high degree of certainty that if we hit the card that completes our hand, we will win the pot. In the example I have given, it is almost certain that we will do it if we get a 9 or an Ace, but sometimes it is not so obvious.

### False Odds

Suppose that in one hand we have 9♥ J♥ and on the table there are 3♥ A♣ 5♥ 8♠. If a heart comes out on the fifth card, we will have a flush, but it is possible that another player also has two hearts and one of them is higher than our Jack. Therefore, in this case, part of our odds would have to be discounted. Instead of 4: 1 we could count on our odds to be 5: 1. That is, I was still more demanding when deciding whether to continue in the hand.

Suppose that in another hand we have 9-J and the flop came 8-10-A. To complete our straight, a 7 or a Q would serve us. A 7 would be perfect because it would give us the highest straight, but if a Q came up, a player who had J-K would beat us by making a higher straight. In no-limit games it would be rare for this to happen because players would not stay in the hand with a straight draw (unless the pot odds were high, or the player with JK was the one to initiate betting with that semi-bluff hand), but in limit games we should take that possibility more into account. Therefore, we would have to discount part of our odds.

So, let's keep in mind that not every time you improve you win, and let's analyze each play based on our opponents and the cards they may have. If there is a chance that a card that suits us will do better for another player, we must be conservative in our estimation of the odds.

### Implicit Odds

In many cases, when we hit our play we will win more money in the next betting turn. The possibility of this happening is called “implied odds”. There are times when we will go to a hand without having the odds in our favor just because we think that if the card that suits us comes up, we will win much more money in the next betting turn.

This will largely depend on how our opponents are. If they are good, it is very possible that they will fold when realizing that we have made our move. But weak players are more reluctant to fold once they have put money into the pot. So in games where there are weak players it will be beneficial to go to more hands than would be wise with level players.

### Texas Hold'em Odds Chart

Below you can see the odds table for the fourth Texas Hold'em card (the Turn). For the fifth card (the River) the odds vary slightly, since instead of 47 cards, there are 46 to be seen. But the difference is small and when you are starting out in this game it is not worth worrying about.

In the left column, under the heading OUTS, the number of cards that go well to improve or complete our play is expressed. To calculate the odds we must consult the odds that we have according to the number of cards that serve us, and multiply it by the amount of the bet that we must make. If the result is less than the amount of money in the pot, including the bets that have been made in the current betting turn, we have positive odds and must go to the hand.

Practical example: In the pot there is \$ 14 and if we want to see the fourth card we must put \$ 2. Since we have an open straight, there are eight cards that suit us (8 outs). We see from the table that the odds are 4.9: 1. We multiply 4.9 x \$ 2 and it gives us \$ 9.8. Since there is \$ 14 in the pot, an amount that is greater than \$ 9.8, we must call.

OUTS ODDS
16 1,9
15 2,1
14 2,4
13 2,6
12 2,9
11 3,3
10 3,7
9 4,2
8 4,9
7 5,7
6 6,8
5 8,4
4 10,7
3 14,6
2 22,5

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