One of the most important lessons in poker is knowing and being able to calculate Outs and Odds (it is important to distinguish between Hand Odds and Pot Odds). For people new to poker I first want to explain these terms:
Refers to the amount of cards that can improve our current hand.
- You are playing Texas Hold’em and receive 67 as your pocket cards. The flop shows 45J. If a 3 or an 8 shows you will complete your straight. There are 4 3s and 4 8s in the deck which means you have 8 outs.
These are defined by the total amount of cards that are still unknown to you compared to your outs.
In our example from above:
- We have 5 known cards (our pocket cards and the 3 community cards at the flop) so there remain 47 unknown cards. 8 of them are our outs. Thus the odds are (47 – 8) : 8 = 39:8. For reasons of simplicity we will round this to 40:8 and then divide it by 8 to bring it to 5:1. So our hand odds are 5:1 meaning that if we play this very hand 6 times we will statistically finish our straight exactly 1 of these times.
This is the ratio of existing pot to money needed to call. The higher this ratio (the smaller the amount of money needed to call in comparison to the actual pot) the better.
- The pot is at €70 and you are required to pay €10 for a call – this would put the pot odds to 70:10 or 7:1 – this means that if you can win this hand exactly 1 out of 8 times you will break even.
Mathematics in the Game of Poker
Many players are discouraged to deal with odds because it seems you have to be really good at mathematics. In fact it is much easier than it looks at first (keep reading to the end and you will find some nice trick to quickly appraise your odds without having to run complicated formulas through your head or using our poker odds calculator) and while many successful players insist that their decisions are based on “gut feelings” most professionals constantly have the odds in their heads and play accordingly. Also those gut feeling players usually have learned to evaluate a situation based on their experience and while maybe not having actual numbers in their heads basically know when the law of chances favours them – otherwise they won’t be successful for long.
It is a fact that poker is not simply a game of luck – yes, luck plays its part, no question, but there is a reason why we will find the same players ending on top again and again. Why? Because they master the game of chances, probabilities and odds better than their opponents. And because they act when hand odds and pot odds are in their favour.
So what is the importance of pot odds and hand odds? And in which relation are they with each other? Do I even have to know both odds? Well, in order to answer these questions we will have to go back to the somewhat boring theory part again for a moment. Poker is – as previously mentioned – not merely a game of luck, it is a game of probabilities and chances. In order to play winning poker in the long run you will have to make sure to have the probabilities on your side. Once you can do that on a constant basis you will end up winning more often than not. Simply because a lot of players never cared to get their heads into the concept of odds and outs.
Let’s take another look at our previously mentioned example and combine hand odds and poker odds:
- So we have hand odds of 39:8 or roughly 5:1. Our pot odds are at 7:1. What to do? Well, according to the law of probabilities we should actually “risk” a call as long as our hand odds are below out pot odds. Why? Well, statistically speaking we will lose 5 times and win once but once we do win we will get 8 times our money’s worth. So in theory we could even afford 2 “unlucky” losses in our case and still break even. Thus the probabilities are on our side.
Eventually Mathematics Will Always Beat Luck
In our theory we assume that the hand odds and pot odds as well as the actual amount of the money in play will always be the same which of course is not going to happen in general. Nonetheless with this theory you will end up playing winning poker if you stick to it. You will have to be aware that in our example you will lose 5 times out of 6 strictly statistically speaking. If you end up calling and losing your €10 5 times in a row and therefore shy away from calling the next time around the strategy will not work. Even if you are so unlucky as to lose 10 or even 20 times in a row… you will have to clench your teeth and understand that the chances are in your favour and will eventually beat the crap out of your bad luck.
Important: Please be aware that for reasons of simplicity we have so far neglected the fact that you will have two chances to get one of your outs after seeing the flop instead of just one – namely once at the turn and then again at the river! The correct formula to calculate our actual hand odds is as follows:
We approach the whole matter from the opposite point of view and subtract the chances of not hitting an out on turn or river from 100%. The formula for that is:
1 – [((47 – Outs) / 47) x ((46 – Outs) / 46)]
For our example:
1 – [(39 / 47) x (38 / 46)] = 1 – [0.830 x 0.826] = 1 – 0.686 = 0.314 -> 31.4% chance to finish our straight.
In order to convert this % chance into our hand odds (so we can compare them to the pot odds) we use:
Hand Odds = [(1 / %) – 1]
[(1 / 0.314) – 1] = [3.18 – 1] = 2.18 -> approximately 2.2:1
Keeping these hand odds in mind you will surely understand that we should even call with pot odds as low as 3:1, so even if the pot is a mere €30 you would call with €10.
And now for all of you who have diligently followed our explanations all the way we want to reward you for your patience by giving away a very easy method of calculating your hand odds at the flop as well as at the turn. After the flop simply take your outs and multiply them by 4 in order to receive your % chances of seeing an out. After that you take the already mentioned formula for Hand Odds = [(1 / %) – 1] or if you are more comfortable with whole numbers Hand Odds = [(100 / whole number %) – 1]. If you want to do so at the turn multiply your outs by 2 instead of 4.
Let’s head back to our example one final time:
- We have 8 outs and therefore multiply them by 4 which will result in 32. We can see that these 32% are close to the accurately calculated 31.4%. Now let’s continue with the Hand Odds = [(100 / whole number %) – 1] formula: [(100 / 32) – 1]. 100/32 will roughly result in 3 therefore the end result is 2. And what a nice surprise, our quickly assessed hand odds of 2:1 are very close to the painstakingly calculated 2.2:1 from before.