Poker Odds and Probabilities

During this years World Series Of Poker, my diary documented what I thought was a slightly higher than average amount of times, that I ran into Aces whilst holding Kings. Typically, having waited 5 hours for a major hand to come along, this can be one of the most demoralising situations in NLH tournaments. Last month, I also made the final six of the biggest event on the European Tour: the WPT event at the Aviation Club on the Champs Elysee With 6 players left, and the ESPN cameras rolling, I picked up K,K on Surinder Sunars Big Blind. He sat there with A,A and duly doubled up. Being one of the greatest players of all time, he then proceeded to take the 600,000 euro first prize. But I felt I gave him the lift up that he needed, just at the right time.

So I thought I would churn over the grey matter, and calculate the odds of walking into this confrontation. It’s strange, but this is one statistic I have never seen printed anywhere.

One often published poker statistic is that:

It is 16-1 that you will be dealt a poker pair (go to the back of the classroom if you assumed it was 12-1), and:

It is 220-1 that you will be dealt any specific pair, such as Aces. (I know it can often feel like it is a lot longer odds than that!)

So when you are holding any indiscriminate hand (such as Kings, or 7,2) it is 220-1 that any one of your opponents has Aces. Heads up, it is 220-1. In a six handed WPT final in Paris, it is 220-1 divided by 5 opponents: 44-1. Not an unlucky coup at all! Again, although this probability may be interesting for those of us with dull lives, its usefulness is debatable. It will be a rainy day on the moon before I pass kings pre-flop. (Super-satellites excepted of course!)

A more useful statistic is that K,K is only a 2-1 favourite against A,K. The warning signs are there. An even much more useful statistic is an Ace will flop 23% of the time.

So, if you get cute with pre-flop Kings, the flop will kill your action almost a quarter of the time. The major dangers of slow playing Kings though, are:

An opponent with a pocket pair is about 15/2 to flop a set (or quads.)

Fortunately an opponent with two odd cards is almost 40-1 to flop 2 pair. They may also have straight and/or flush possibilities though.

If your opponent flops a set on a low broken flop, he may well bust you! Early in NLH tournaments especially, you can make a little from pocket Kings, but quiet easily lose your whole stack.

The biggest crime though, is pocket Queens. I often see top players smooth call a pre-flop raise with this hand. I don’t know if they are trying to outplay their opponents on the flop, or are just scared of pocket Kings or Aces. Personally, I think this is suicidal or at least a criminal waste of a good hand. I will always re-raise and try and get my whole stack in the middle before the flop.

As discussed earlier, the odds on pocket Kings or Aces being out there are variable depending on the number of dealt hands. The odds will be at least 12-1 on a full table though.

Again this article has already outlined the dangers of a small pair out-flopping you.

More importantly though, the probabilities that an Ace or a King will flop is 43% of the time.

An Ace or a King on the flop obviously kills your action, prevents you from winning a much bigger pot, and often leads to you losing a medium sized one.

It’s often best to keep the game simple. Just stick the whole stack in, and cross your fingers.