3.2 Poker Math - Texas Holdem Pot Odds
This is a very important section and can also be quite intimidating to a lot of people as we are going to discuss Poker Math! But there is no need for you to be intimidated, Poker Math is very simple and we will show you a very simple method in this section. You won’t need to carry a calculator around with you or perform any complex mathematical calculations.
So what is Poker Math? As daunting as it sounds, it is simply a tool that we use during the decision making process to calculate the pot odds in texas holdem and the chances of us winning the pot.
Every time we make a decision in Poker it is a mathematical gamble, what we have to make sure is that we only take the gamble when the odds are on in our favour. As long as we do this, in the long term we will always come out on top.
Poker Math is mainly used when we need to hit a card in order to make our hand into a winning hand, and we have to decide whether it is worth carrying on and chasing that card.
To make this decision we consider two elements:
- How many “Outs” we have – Cards that will make us a winning hand
- What are our “Pot Odds” – How much money will we win in return for our bet
We then compare the likelihood of us hitting one of our Outs against the Pot Odds we are getting for our bet and see if mathematically it is a good bet.
Lets look at each element individually first, then we’ll bring it all together.
Number of Outs
When we are counting the number of “Outs” we have, we are looking at how many cards still remain in the deck that could come on the turn or river that we think will make our hand the winning hand.
The best way to understand this is through an illustration.
We hold A 8 and the flop comes down K 9 4
Now here we have a flush draw needing only one more Club to make our Nut (highest possible) Flush. We also hold an overcard, meaning that if we pair our Ace then we would beat anyone who has already hit a single pair on the flop.
From the looks of that flop we can confidently assume that if we complete our Flush or Pair our Ace then we will hold the leading hand. So how many cards are left in the deck that can turn our hand into the leading hand?
Flush – There are a total of 13 clubs in the deck, of which we can see 4 clubs already (2 in our hand and 2 on the flop) that means there are a further 9 club cards that we cannot see, so we have 9 Outs here.
Ace Pair – There are 4 Ace’s in the deck of which we are holding one in our hand, so that leaves a further 3 Aces that we haven’t seen yet, so this creates a further 3 Outs.
So we have 9 outs that will give us a flush and a further 3 outs that will give us Top Pair, so we have a total of 12 outs that we think will give us the winning hand.
So what is the likelihood of one of those 12 outs coming on the Turn or River?
To calculate this we use the rule of 4 and 2. By using this shortcut we can calculate the probability of hitting one of our outs without any detailed and complex calculations.
|RULE OF 4 AND 2|
|Number of Cards still to come||% probability we will hit our Outs|
|After the Flop – 2 cards to come (Turn + River)||Number of Outs times 4|
|After the Turn – 1 card to come (River)||Number of Outs times 2|
So after the flop we have 12 outs which using the Rule of 4 and 2 we can calculate very quickly that the probability of hitting one of our outs is 12 x 4 = 48%. The exact % actually works out to 46.7%, but the rule of 4 and 2 gives us a close enough answer for the purposes we need it for.
If we don’t hit one of our Outs on the Turn then with only the River left to come the probability that we will hit one of our 12 Outs drops to 12 x 2 = 24% (again the exact % works out at 27.3%)
|After the Flop (2 Cards to Come)||After the Turn (1 Card to Come)|
|Outs||Rule of 4||Exact %||Outs||Rule of 2||Exact %|
|1||4 %||4.5 %||1||2 %||2.3 %|
|2||8 %||8.8 %||2||4 %||4.5 %|
|3||12 %||13.0 %||3||6 %||6.8 %|
|4||16 %||17.2 %||4||8 %||9.1 %|
|5||20 %||21.2 %||5||10 %||11.4 %|
|6||24 %||25.2 %||6||12 %||13.6 %|
|7||28 %||29.0 %||7||14 %||15.9 %|
|8||32 %||32.7 %||8||16 %||18.2 %|
|9||36 %||36.4 %||9||18 %||20.5 %|
|10||40 %||39.9 %||10||20 %||22.7 %|
|11||44 %||43.3 %||11||22 %||25.0 %|
|12||48 %||46.7 %||12||24 %||27.3 %|
|13||52 %||49.9 %||13||26 %||29.5 %|
|14||56 %||53.0 %||14||28 %||31.8 %|
|15||60 %||56.1 %||15||30 %||34.1 %|
|16||64 %||59.0 %||16||32 %||36.4 %|
|17||68 %||61.8 %||17||34 %||38.6 %|
As you can see the Rule of 4 and 2 does not give us the exact %, but it is a very quick and simple way of getting to our % and is close enough for the purposes we need it for.
Now lets look at what we have learnt in our example situation:
- We estimate that to win the hand we have 12 Outs
- We have calculated that after the flop with 2 cards still to come there is approximately a 48% chance we will hit one of our outs.
Now we know the Odds of us winning, we need to look at the return we will get for our gamble - The Pot Odds.
Continue to next section - 3.2 Poker Odds continued