Getting to grips with poker maths part two

Find out whether you should play a particular hand or not.

In the last article, we looked at how to calculate pot odds. Now we're going to find out how to calculate the odds of you winning the actual hand.

In poker, we generally use the ratio method for expressing the odds. We compare the number of successful outcomes to the number of unsuccessful outcomes. 

Let’s imagine you’re going to draw a card from a standard 52-card deck, and you want to draw the ace of spades. 

When drawing a card from the 52 cards, there are 52 possible outcomes. Out of these 52 outcomes, 1 is a success (drawing the ace of spades) and 51 are unsuccessful (drawing any other card). 

So we have 1 possible success against 51 possible unsuccessful events. 

This would put the odds at 51-to-1 against us. We would notate these odds as 51/1, 51-1 or 51:1. 

Now you may ask, why do we use this method of notating odds? Why not use percentages or decimals? Well, we use this method because it makes it easier to compare the odds of winning the hand to the pot odds. 

Let’s try a poker example: 

We’re playing with 7♥ 8♥ and after the flop, the board reads: A♠ 9♥ 3♥. 

What are the odds of getting another heart card and hitting your flush on the turn? (In other words, you'll have five hearts.)

To solve this problem, we need to compare the positive number of outcomes (a heart coming out on the turn) to the number of negative outcomes (any other suit hitting the turn.) 

Counting outs 

To find out what our odds are, we need to count our “outs” - the number of cards that will give us a flush. ('Hit our hand' in the jargon.)

There are 52 cards in the deck. At this point, 5 of these cards are known to us (our 2 hole cards and the 3 cards on the board). That leaves 47 unknown cards; any of these unknowns could hit on the turn. 

In a deck, there are 13 cards of each suit. Since we have 2 hearts in our hand, and there are 2 hearts on the board, there are still 9 hearts left in the deck. These 9 cards are our “outs”. 

So, on the turn, there are 47 possible outcomes. 9 will make our flush (positive outcome) and 38 will not (negative outcome). In odds, we would express this as 38/9, which roughly translates into 4/1 odds against us. 

This means, every five times we see the turn, we will hit our flush once and miss it four times.

Let’s look at another example: 

Again, we have 7♥ 8♥, and on the turn, the board reads: 9♠ K♣ 6♦ 3♥ 

What are the odds of hitting our straight on the river? 

At this point, out of the 52-card deck, 6 cards are known to us, leaving 46 possible cards which could come out on the river. 

To make our straight, we need a 5 or a T (ten). There are four 5s left in the deck, as well as four Ts, giving as a total of eight outs. 

So, out of 46 possible outcomes on the river, 8 would be a success and 38 would be unsuccessful. This would put our odds of making the straight at 38/8, which leads to 4.8/1 odds against us. So, roughly speaking, for every six times we see the river, we will miss our straight about five times and hit it only once. 

So we now know how to calculate the pot odds as well as the odds of winning a hand. But how do we put these two pieces of information together and find out if we're in a profitable spot or not?

Simple, we compare the two ratios.

Here's the golden rule: When the pot odds are greater than the odds of winning the hand, you're in a winning situation. In other words, you should call.

Let's go back to the example when we were hoping to draw (get) a straight.

We play the 7♥ and 8♥.

On the turn, there are four cards on the board: 9♠, King♣, 6♦, and 3♥.

The pot is $3000 and we face only one opponent. He bets $1500.

Should we make the call or not? Let's do the maths:

1. Our pot-odds are 4500 to 1500 or 3/1.

2. Our odds of hitting the straight are 4.8/1.

3. The pot-odds are smaller than the odds of hitting the flush, so it's not a profitable call. We'll sit this one out. 

In the next article, we'll look at a crucial concept that will help you become profit-making poker machine.