# Poker Math & Odds Strategy

## Using Pot Odds When Playing a Drawing Hand

So, in essence, you are doing the calculations as if you were the only person at the table - in that case, there are 9 spades left in the deck. When calculating outs, it's also important not to overcount your odds. An example would be a flush draw in addition to an open straight draw.

In addition to this, sometimes an out for you isn't really a true out. Let's say that you are chasing an open ended straight draw with two of one suit on the table. In this situation, you would normally have 8 total outs to hit your straight, but 2 of those outs will result in three to a suit on the table.

This makes a possible flush for your opponents. As a result, you really only have 6 outs for a nut straight draw. Another more complex situation follows:. Once you know how to correctly count the number of outs you have for a hand, you can use that to calculate what percentage of the time you will hit your hand by the river.

Probability can be calculated easily for a single event, like the flipping of the River card from the Turn. This would simply be: This can be calculated as shown below:.

Even though there might not technically be 47 cards remaining, we do calculations assuming we are the only players in the game. To illustrate, here is a two-overcard draw, which has 3 outs for each overcard, giving a total of 6 outs for a top-pair draw:.

However, most of the time we want to see this in hand odds, which will be explained after you read about pot odds. To change a percentage to odds, the formula is:. Now that you've learned the proper way of calculating hand odds in Texas Hold'em, there is a shortcut that makes it much easier to calculate odds:.

After you find the number of outs you have, multiply by 4 and you will get a close estimate to the percentage of hitting that hand from the Flop. Multiply by 2 instead to get a percentage estimate from the Turn. You can see these figures for yourself below:. As you can see, this is a much easier method of finding your percentage odds. But what about ratio odds? This is still done using this formula:. We minus 1 from that and get a rough estimate of our odds at about 3: Let's try this all the way through with an example:.

If the 1 out of 5 doesn't make a ton of sense to you, think about the 1: Now that you know how to calculate poker odds in terms of hand odds, you're probably wondering "what am I going to need it for? Pot odds are simply the ratio of the amount of money in the pot to how much money it costs to call. The higher the ratio, the better your pot odds are.

Pot odds ratios are a very useful tool to see how often you need to win the hand to break even. The thinking goes along the lines of: The usefulness of hand odds and pot odds becomes very apparent when you start comparing the two. As we now know, in a flush draw, your hand odds for making your flush are 1. Your answer should be: This means that, in order to break even, you must win 1 out of every 5 times. However, with your flush draw, your odds of winning are 1 out of every 3 times!

You should quickly realize that not only are you breaking even, but you're making a nice profit on this in the long run. Let's calculate the profit margin on this by theoretically playing this hand times from the flop, which is then checked to the river. As you can see, you have a great reason to play this flush draw, because you'll be making moneyin the long run according to your hand odds and pot odds.

The most fundamental point to take from this is:. If your Pot Odds are greater than your poker hand odds, then you are making a profit in the long run. Even though you may be faced with a gut shot straight draw at times - which is a terrible draw at 5 to 1 hand odds - it can be worth it to call if you are getting pot odds greater than 5 to 1.

Other times, if you have an excellent draw such as the flush draw, but someone has just raised a large amount so that your pot odds are 1: In this situation, a fold or semi-bluff is your only solution, unless you know there will be callers behind you that improve your pot odds to better than break-even. Your ability to memorize or calculate your hand odds as well as calculate pot odds will lead you to make many of the right decisions in the future - just be sure to remember that fundamental principle of profitably playing drawing hands requires that your pot odds are greater than your hand odds.

An important note I have to make is that many players who understand Hold'em odds tend to forget is that much of the theoretical odds calculations from the flop to the river assume there is no betting on the turn. This first one does not require math, just use the handy chart below:. The odds are slightly better from the turn to the river, and much better when you have both cards still to come.

It should come in very handy. There are a couple of ways to do the math. One is complete and totally accurate and the other, a short cut which is close enough.

The odds against hitting your flush from the flop to the river is 1. How do we get to this number? With 9 hearts remaining there would be 36 combinations of getting 2 hearts and making your flush with 5 hearts. This is calculated as follows:.

This is the probability of 2 running hearts when you only need 1 but this has to be figured. Of the 47 unknown remaining cards, 38 of them can combine with any of the 9 remaining hearts:. So we then add the two combinations that can make you your flush:. This number can be rounded to. And voila, this is how we reach 1. If that made you dizzy, here is the short hand method because you do not need to know it to 7 decimal points. A much easier way of calculating poker odds is the 4 and 2 method, which states you multiply your outs by 4 when you have both the turn and river to come — and with one card to go i.

What about with just one card to come? As for calculating your odds…. Tom has been writing about poker since and has played across the USA for over 40 years, playing every game in almost every card room in Atlantic City, California and Las Vegas. PokerTracker Director Steve McLoughlin explains the true value of hand-tracking software and why heads-up displays Play Poker Best Poker Sites. Find the best poker sites to start your online poker quest. Our in-depth reviews make it easy to pick the right poker site.

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