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POKER ODDS
Hand Odds and Poker Odds
To calculate your hand odds, you first need to know how many outs your hand has. Outs are defined as a card in the deck that help you make your hand. So if you hold AK of spades and have two spades on the flop, that leaves 9 more spades in the deck, since there are 13 cards of each suit. This means you have 9 outs to complete your flush - but not necessarily the best hand! Usually you want your outs to count toward a nut draw, but this is not always possible. The quick amongst you might be wondering "But what if someone else is holding a spade, doesn't that decrease my outs?". The answer is yes and no. If you know for sure that someone else is holding a spade, then you will have to count that against your total odds. However, in most situations when you do not know what your opponents hold, you can only do calculations with the knowledge that is available to you. That knowledge is your pocket cards and the cards on the table. So, in essence, you are doing the calculations as if you were the only person at the table, which in 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 really isn't a true out. An example would be chasing an open ended straight draw when two of another suit are on the table. In this regard, where you would normally have 8 total outs to hit your straight, 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 is as follows:
How to calculate hand odds (the longer way):
Once you know how to correctly count the number of outs you have on a hand, you can use that to calculate
what percent 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:
Total Outs / Remaining Cards. For two cards
however, like from the Flop to the River, it's a bit more tricky. This is calculated by figuring the probability
of your cards not hitting twice in a row. This can be calculated as shown below:
The number 47 represents the remaining cards left in the deck after the flop (52 total cards, minus
2 in our hand and 3 on the flop = 47 remaining cards). 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 percent to odds, the formula is:
How to calculate hand odds (the shorter way):
Now that you've learned the proper way of calculating hand odds, there is a shortcut that will makes it
much easier to calculate odds. The shortcut is, 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 the formula: Odds = ( 1 / Percentage ) - 1
However, we can rephrase this math equation so that your brain might process it a bit easier:
Using 100 divided by the whole percentage number, such as 24%, we can easily see that 100/24 is
equal to about 4. We minus 1 from that and get a rough estimate of our odds at about 3:1.
Let's try this all the way through with an example:
Pot Odds and Poker Odds:
Now that you know how to calculate poker odds in terms of hand odds, you're probably wondering
what you're going to need it for? That's a good question. This is where pot odds come into play.
Pot odds is simply a ratio of the amount of money in the pot compared with how much money
it takes to call. If there is $100 in the pot and it takes $10 to call, your pot odds are
100:10, or 10:1. If there is $50 in the pot and it takes $10 to call, then your pot odds are
50:10 or 5:1. 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.
If there is $100 in the pot and it takes $10 to call, you must win this hand
1 out of 11 times in order to break even. The thinking goes along the lines of: If you play 11 times,
it'll cost you $110, but when you win, you get $110 ($100 + your $10 call).
Poker Odds from the Flop to Turn and Turn to River
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. So while it's true that for a flush draw, the odds are 1.9 to 1 that the flush will complete,
you can only call a 1.9 to 1 pot on the flop if your opponent will let you see both the turn and
river cards for one call. Unfortunately, most of the time, this will not be the case, so
you should not calculate pot odds from the flop to the river and instead calculate them one
card at a time.
Example of Correct Pot Odds Math
As you can see from these example calculations, calling a flush draw with 2 to 1 pot odds
on the flop can lead to a long term loss, if there is additional betting past the flop. Most
of the time however, there is a concept called Implied Value (which we'll get to next) that
is able to help flush draws and open-ended straight draws still remain profitable even with
seemingly 'bad' odds. The draws that you want to worry about the most are your long shot draws:
overcards, gutshots and two outers (hoping to make a set with your pocket pair). If you draw
these hands using incorrect odds (such as flop to river odds), you will be severely punished
in the long run.
Implied Value
Implied Value is a pretty cool concept that takes into account future betting. Like the above
section, where you have to worry about your opponent betting on the turn, implied value most often
is used to anticipate your opponent calling on the river. So for example, let's say you have
yet another flush draw and are being offered a 3 to 1 pot odds on the turn. Knowing that you
need 4 to 1 pot odds to make this a profitable call, you decide to fold.
Aha, but wait! Here is where implied value comes into play. So, even though you're getting 3 to 1
pot odds on the turn, you can likely anticipate your opponent calling you on the river if you do
hit your flush draw. This means that even though you're only getting 3 to 1 pot odds, since you
anticipate your opponent calling a bet on the river, you are anticipating 4 to 1 pot odds - so
you are able to make this call on the turn.
So in the most practical standpoint, implied value usually means that you can minus one bet off
your drawing odds on the turn, as it anticipate your opponents calling at least one bet. In
some more advanced areas, you can use implied odds as a means of making some draws
that might not be profitable for a majority of the time, but stand to make big payouts when they
do hit. Some examples of this would be having a tight image and drawing to a gutshot vs another
tight player. Even though this is a horribly bad play (and hopefully you don't have to pay much
for it), it can possibly be a positive play if you know your opponent will pay you off if you
hit your draw - namely because he won't believe you played a gutshot draw. For many reasons,
I do not recommend fancy implied odds plays like these, but mentioned it more so that
you can recognize some players who pull these 'tricky' plays on you as well.
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