Tonybet Poker and its players continue to provide strategy material to all of you who are interested in Open Face Chinese poker and are eager to learn more about it. Today we would like to talk about one of the most important things in poker – the math behind the game. Poker mathematics is no doubt one of the most important aspects of the game. With a little experience and the knowledge of poker math you can become a very successful OFC player.
When playing with the regulars, other players often wonder how come it seems that when the professionals are about to foul their hand, they always manage to pull it off? While the amateurs with the lack of poker math knowledge are trying to figure it out, the professionals are always aware of their % after every street
Let’s get started with a simple example.
When we’re done placing these cards there will be only one street of cards left in the deck, so before making the decision we should know whether it’s going to be profitable in a long term. In this scenario our bottom hand is already completed. There’s no question about the nine going to the middle. However, the queen is trickier. Should we take this risk and put it on top even though there are only two kings left? It’s actually a very common situation and in most cases we don’t even have the pair of nines. So let’s discuss it a bit more.
First question: How many outs do we have?
The outs are all live cards which will prevent our hand from fouling.
If we put the Q up top, we will need to improve the middle to something better than a pair of queens. The only cards that can help us improve are the two kings and a five, since all nines are already gone. Although we have counted 3 outs, let’s not forget the fact that our opponents have discarded two cards each. Usually the cards like Aces, kings and queens are never discarded because of their strength. However, a five could have easily been discarded.
Let’s think that we have somewhere between 2 and 3 outs. What should be our next move? First of we should calculate the possibility of receiving the cards we need. Most players would say that 2-3 outs is nothing, but let’s not judge too quickly.
How many cards do we have in the deck?
There’s a total of 52 cards in the deck, so both of our opponents have placed 9 cards and discarded 2. In this case we will have 11 cards placed and 3 discarded after making our move. So there will be 29 visible and 7 discarded cards. In other words we have 16 cards left.
What is our %? The easiest way to calculate it is by applying the following formula:
1: (A/Z) x (A/Z) x (A/Z)
A: Cards we don’t want
Z: All the other cards left in the deck
With 16 cards left, Z equals 16.
Unfortunately with all nines gone, we only have two live kings and a five which could save us and make our hand go to fantasy land. So by subtracting 3 from 16 we get that A = 13. Let’s not forget that this needs to be multiplied three times, as we will receive not one but three more cards. Let’s try and put these numbers into the formula.
1: (13/16) x (12/15) x (11/14)
The first time we have divided 13/16, but with the second card we will have one card less so we’re dividing 12/15 and then we go with 11/14 for the third card.
Let’s try and get our percentage. For all those of you who are not too good with math, you could easily use one of the free online calculators, like: http://calculator.tutorvista.com/multiplying-3-fractions-calculator.html
1: (13/16) x (12/15) x (11/14) = 0.489 = ~49%
So after calculating all the remaining cards and the cards that can help us improve, we get our chances of drawing one of the three outs. In this case we have a 49% probability of drawing a king or a five and not fouling.
To help you improve your game in the future, we’re adding a simple table. Please note that the % will vary depending on your position at the table. The better position you have, and the less cards are in the deck, the higher your chances of drawing the cards you need will be.
Our example: First Position, 16 cards left
1 out: 18.7%
2 outs: 35%
3 outs: 49%
4 outs: 60.7%
5 outs: 70%
6 outs: 78.6%
Middle position, 13 cards left
1 out: 23.1%
2 outs: 42.3%
3 outs: 58%
4 outs: 70.6%
5 outs: 80.4%
6 outs: 87.8%
Late position: Button, 11 cards left
1 out: 33.6%
2 outs: 53.33%
3 outs: 70.83%
4 outs: 83.33%
5 outs: 91.66%
6 outs: 96.60%
This is a great way to get yourself familiar with the OFC poker math. In our next article we will look even deeper into the hands and try to explain a lot more about one of the most important things in poker, the math.