Poker Odds Tips: one simple magic poker odds formula

Hate maths? You’re in luck. Paul Phua reveals the magic formula poker players use to make calculating poker odds simple

On my poker odds page, I explained why knowing the odds is vital to being a money-making poker player. Here I will show you how to calculate those poker odds.
Let’s take the example from my last blog: you have a “gutshot” draw, where there is only one card that will complete your straight – for instance, you have 6-9, and the flop is A-5-8, so you have to hit a 7. I said that would only work 1 in 6 times.
How do I know this? And how can you work out the odds in any poker situation? There’s an easy way, involving a simple “magic” formula; and there’s a harder way, which means relearning some maths you’ve forgotten since school. The easy way is all you need for basic poker; but if you’re more mathematically inclined, read on to the second way.

Step 1. First calculate your “outs”

“Outs” is the term used by poker players for the cards that will help you win. In the above example, only a 7 will help you win. Since there are four 7s in a deck of cards (one of each suit), you have four “outs”.

Step 2. Now apply the magic formula

If you don’t want to be bothered with the detailed mathematics of probability, just follow this simple formula:
* To find the percentage chance of hitting your card on the turn, multiply the number of outs by two
* To find the percentage chance of hitting your card on the turn or the river, multiply the number of outs by four
Is it really that simple? Yes, it is. It’s not absolutely accurate, but it’s very close.
As an example, let’s apply this magic formula to our gutshot draw. We have four outs, so to find out our chances of hitting one of them by the river we multiply 4 x 4, getting 16. So that’s 16% — or to put it another way, 16/100, which some quick mental arithmetic will tell you is roughly 1 in 6. Simple, unless you have no idea what fractions or percentages are, in which case I’m afraid that’s beyond the scope of this blog!
My next blog will explain how you can use these odds in poker to decide whether a bet is worth calling. And that’s it for now. Unless you want to know more about probability, in which case, read on…

Calculating probability the hard way

First, let’s look at probability in general before looking at poker. To find the chance of any particular outcome, you divide the number of desired outcomes into the total number of possible outcomes. Let’s take rolling a die as an example: if you need to roll a 6, your chance of doing so is 1 in 6. That’s one desired outcome divided into the six possible outcomes (since it’s possible to roll any one of six numbers: a 1, 2, 3, 4, 5 or 6). And if what you need to roll is a 5 or a 6, that’s two possible outcomes, so you divide 2 into 6, giving you a 1 in 3 chance.
Now let’s apply this to poker. There are 52 cards, so there are 52 possible outcomes when you turn a card over. On the flop, you know what your two hole cards are, as well as the three cards face-up on the flop, so actually there are only 47 cards left that might contain your outs.
In the gutshot draw example above, there are four 7s that will help, so to get your odds, you divide 4 into 47. We don’t all have a calculator in our heads, so when you’re at the poker table, make sums easier by rounding them up. In this case, 4 into 47 is nearly the same as 4 into 48. So, we now know we have a roughly 1 in 12 chance of hitting a 7 on the turn.
This isn’t too hard, but it gets trickier when calculating several rolls of a die, or turns of a card. When you are dealing with probabilities over multiple attempts, you actually first have to calculate the chance of something not happening, rather than the chance of it happening.
The chance of not hitting a 7 on the turn is 43 out of 47: 43/47. The chance then of not hitting a 7 on the river is very slightly different, since there are now only 46 cards left that might include your hoped-for 7. So the chance of not hitting on the river is 42 out of 46: 42/46.
To find the chance of not getting a 7 by the river, you must multiply these two fractions. (Remember, with fractions you have to multiply the tops and bottoms separately.) From this we get: 43/47 x 42/46 = 1806/2162.
To make this complex figure understandable and useful, we need to express it as a percentage. To do that, we want to turn the number under the fraction bar (mathematicians call this the “denominator”) into 100, and find out what that does to the number above the bar (the “numerator”).
If we divide the denominator of 2162 by 2162, it becomes 1. Multiply it again by 100, and it becomes 100. So now we do the same action to the numerator (we do need a calculator for this). 1806 divided by 2162 is 0.84. Multiply that by 100 and we get 84. So now we can see that 1806/2162 is the same thing as 84/100 – 84%, in other words.
Remember, the figure of 84% we just calculated is the chance of not hitting our hoped-for card. So our chances of hitting our card will be 16% — or to put it another way, 16/100, which is about 1 in 6.
If this all sounds a bit tricky, well, it is! But don’t worry: you always have the magic formula to fall back on.
Read the next article in my mini series on how to play a flush draw.