How To Calculate Odds in Poker

How To Calculate Poker Odds In Your Head

Knowing the odds that you will hit the cards you need to win the hand is very important to making money when playing online poker games.
If you know the odds it can help you determine the right move to make to maximize your expected value for a hand.
However, sometimes it can be difficult to figure out the exact odds that certain cards will come, this might discourage you from doing the math and relying on your poker intuition to know if a call or raise is the right play.
Luckily there is an easy poker odds calculating trick that will let you quickly determine your odds for hitting your hand and winning the pot and in this article Internet Gambling Sites will teach you how to do that.

The Rule Of 4

The only thing you have to remember to calculate odds in texas holdem after the flop is two numbers, 4 and 2.
On the flop, for every out that you have to make your hand, there is an approximately 4% chance that the card will come on the turn or the river.
If the turn comes and misses, now you have a 2% chance for every out that you have to make your hand.

This makes figuring out odds in poker incredibly simple.
If you have 2 spades in your hand and 2 spades hit the board on the flop you can quickly calculate the odds of hitting your flush.
There are 13 spades total, 4 are already out, which means that there are 9 spades left in the deck. 9 spades * 4% means that there is an estimated 36% chance of hitting your flush.
This is almost exactly correct.
The exact odds of hitting the flush are 34.9%.
As you can see, a quick multiplication gives extremely good knowledge of your odds.

So Why Does The Rule Of 4 Work?

In texas holdem, after the flop 5 cards are known to you.
You can see the 2 in your hand, and the 3 on the board.
That means that there are 47 unknown cards in the deck. (You treat your opponents cards as unknown, because even though he can see them, you can’t.
If you have an exact read on your opponent and know his exact cards you can assume you have 45 unknown cards, but that is unlikely and does not change the answer significantly.)

Once you know you have 47 unknowns out there, you count the number of your outs.
Let’s assume you have 1 out.
On the turn, the odds of you hitting your one cards are

1 / 47 = 2.13 %

If you miss that card, then there will know be 46 unknown cards to you, and you will have one more chance to hit it on the river so

1 / 46 = 2.17 %

Adding 2.13 + 2.17 = 4.3% Rounding gives us 4%, and hence the rule of 4.
Since 4% is the odd for a single card, you can scale that up to find the odds for any number of cards.
Multiply the 4% by the number of cards you can hit to win to get your answer. ( After the turn, you can see that you lose half you chances to hit your cards so you should multiply by 2%)

Rounding 4.3% Down To 4. Clean Outs And Redraws

Rounding 4.3% down to 4 % is a smart move for several reasons.
The first is it is much easier to remember the rule of 4 and implement integer multiplication than to try to remember extra decimals that aren’t very important. Secondly, it makes your solution a little more accurate for real life scenarios as most of the time your outs aren’t clean outs.
Your opponent may be holding a hand that has one or more of the outs you think you have dead to you.
If you have an ace high flush draw, you may think that you can win the hand by hitting your flush draw, or by hitting your ace.
But if your opponent is holding a set, you can only win with your flush draw, so your odds are slightly worse than you may think.
Finally, rounding 4.3% down to 4% is a good estimator of the odds you lose to your opponents redraws.

If, for instance, you have the J-10 of hearts, and your opponent had the Ace-hearts, K-spades.
The board could come King, 7, 3 with 2 hearts.
You know your opponent has a king, and think that a heart flush will win it for you. You know that the odds of hitting your flush are 38.7% since you can see 4 hearts. The problem is that approximately 3% of the time you will get two hearts hitting the turn and the river, not just one.
This ability to “redraw” against you, i.e. for your opponent to draw at his flush on the river after you hit your flush on the turn, hurts your odds somewhat.
If You Are A Stickler For Math

The strategy outlined above doesn’t actually give the odds that a card will come, but it gives a very good estimate of those odds at lower number of cards (anything less than 15).
Instead of calculating the odds of hitting your outs by multiplying by 4%, you are actually calculating the number of outs that will come.
This is an important distinction for big numbers of outs, but unimportant for small numbers of outs.
To demonstrate, if you have 25 outs ( perhaps a straight flush draw with two overcards ), and multiply by 4%, you think you have a 100% chance of hitting your cards, when there is clearly some chance that you won’t.
What you calculated is that on average, 1 card will come every time.
But balancing out the times that no cards come, is the time that two of your outs will come in the same hand.
In actual fact, if you have 25 outs the odds of hitting at least one of them are 25/47 + (25/46 * (1-25/47)) = 78.6 %

The Bottom Line

Using the rule of 4 is a great and easy to way figure out your poker odds in a hand.
You can use it frequently to your advantage to figure out if the math is on your side and help determine what you should do when you are playing poker online at the different gambling sites.

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