poker school
lesson 11: hand odds for texas hold'em
Glad to see you all back for the next lesson. This lesson and the next one are very important for you and your success at the tables. The preceding lessons have taught you how you figure out how good your hand is and what the mathematical chances are of hitting your hand and winning the pot. Let's get right to it.
In Texas Hold'em, as a player you will commonly use outs and pot odds the most while you are figuring out your chances of hitting your aspired hand. Hand odds are defined as the chances you have of making a hand in Texas Hold'em. For example, if your pocket cards are two spades and two spades arrive on the flop, you now have hand odds for making a flush at 2 to 1. This means that approximately every 3 times you decide to play this hand you will hit your flush one of those times. If you have hand odds of 3 to 1, then that means you would hit your hand 1 out of every 4 times.
X to 1 odds = you hit your hand 1 out of (X + 1) times
X to 1 odds = 1/(X + 1) = % chance to hit your hand
(For example 3 to 1 odds = 1/4 = 25% chance to hit your hand)
The first step for you to figure out your hand odds you first need to find out how many outs your hand has. Outs are defined as the number of cards that remain in the deck that are required to make a hand. For instance, your pocket cards are the J
10 and two clubs fall on the flop, that means there are 9 clubs remaining in the deck (remember that there are 13 cards of each suit in a deck). Therefore, you have will have 9 outs to complete your flush.
how to calculate the odds
The numerator will represent the number of outs you have to complete your hand. The denominator will represent the number of cards that remain that we have not seen. This will leave us with the percentage chance of making one of those outs. Therefore, there will be math involved, but don't worry it won't be too complex if it is a weakness for you. The most math you'll be doing will be dividing small numbers by 50(pre-flop), 47 (after the flop), or 46 (after the turn). Let's take a look at a couple of examples.
In the first scenario, you are dealt pocket tens. Now the flop comes and it does not help out your hand as it does not contain another ten. So now you will need to figure out what your chances are of hitting your ten on the turn.
So, remember first off you need to figure out the number of outs your hand contains. Once you have figured out your total outs you will proceed to divide the outs by the number of cards in the deck. You know that there are two more tens remaining. There are 47 more cards since we have already seen five cards. That leaves us with an answer of 2/47, or .0426, close to 4.3%.
If you didn't get lucky and get your ten on the turn, let's see what your chances are of you getting your ten on the river. There are still 2 tens remaining, but now there is one card less in the deck so that leaves us with 46 cards. We know that the answer is 2/46 and that is .0434, which is also close to 4.3%. Your chances of getting the ten on the turn did not change much from your chances of getting the ten on the turn.
Let's see what your chances were of hitting a ten on the flop. Let's first figure out the chances of not getting a ten on each successive flip. On the first card there is a 48/50 chance (48 non-ten cards left, 50 cards left in the deck), the second card gives us 47/49 and the third card leaves you with 46/48. These figures come out to .96, .959, and .958. The next step would be to multiply those three numbers and you get .882, or an 88.2% chance of not getting any tens on the flop. Therefore, this means you would have an 11.8% chance of getting a ten on the flop.
This gives you some insight on how odds can help you when you are playing and it will make your decisions on whether or not to go for it. Let's take a look at our second example.
Now we are going to look at the chances you have of hitting a straight draw. The dealer distributes your cards and you receive a 9
8. Now you see the flop and it arrives with a 104
7. As a result of the flop you now have a straight draw.
First off we will look at finding out what your chances are of hitting your straight on the turn card. We know that a Jack or a six will complete your drawing hand. We can also assume that there are four of each left in the deck since we do not know what cards your opponents have. With that information in front of you, we can now figure out that you have 8 possible outs. We have figured out that the chance of getting one of your needed cards on the turn is 8/47, because there 8 outs and there are 47 cards remaining in the deck. This will leave you with a 17% (.170) chance of finishing off your straight on the turn.
Okay, assuming we did not get the needed card on the turn, we will now figure out what our chances now are of getting the much needed card. We know that there are still 8 cards remaining in the deck that can potentially help out our hand, and there are now a total of 46 cards left in the deck. That leaves us with 8/46. Our chance of getting this card has improved to 17.4% (.174), which is obviously not a big change from the turn card.
Let's now take a look at what the odds would have been if we tried to figure out our chances of getting one of our needed cards on the turn or river. First off, we will begin by calculating the chances of not getting a Jack or a six, so we can do it like the way we did in our first example (which would be, {39/47} X {38/46}). Also, since we have already figured out our chances in the previous scenarios, we will just invert the probabilities and multiply them. On the turn we figured out that there was a .170 chance, and the river gave us a chance of .174. To invert the probabilities we will subtract the numbers from one (which looks like this, 1 - .170 and 1 - .174). Now we are left with .830 and .826. We will now multiply these numbers and we get .686. This number is our chance of NOT hitting our card at all. So to figure out our chances of hitting our much needed card we invert this number (1 - .686) and we get .314, or 31.4%.
Those are two examples of how to try and figure out your chances of hitting your cards at the opportune time. If you are interested in finding out the odds from a percentage all you have to do is follow this formula:
Odds = (1 / Percentage) - 1
A lot of you might be wondering why we did not factor in your opponents' cards or burn cards when we are determining how many cards are remaining in the deck. The reason being is that if you saw what the burn cards happened to be, or an opponent for some reason showed you his hand, you would know that those cards are not going to be drawn and you could use that information to process your percentages further. We typically do not know what our opponents have, so we don't even think about it when figuring out the odds.
We hope this lesson has helped you out and trust us when we say this information will help you out with your approach to playing poker. This is important information so make sure you understand it before moving on. Well that's all for lesson eleven and we'll see you at the next class.
good luck and enjoy your experiences at the poker tables
