The Odds of That
Published: March 2, 2020
Something incredible has happened.
- Your pocket kings faced an ace on the flop twenty-three times in a row.
- Your flush draw missed fifty-seven times straight.
- You haven’t been dealt aces in thirty bajillion years.
What are the odds of that!?
It already happened. So the probability of it happening is one hundred percent.
It has happened. It always will have happened.
As long as time travel (to the past) is impossible, there is a zero percent chance that something that has already happened will not have happened and there is a hundred percent chance that something that has already happened will have happened.
Probability doesn’t measure the likelihood of something. It measures the likelihood of something happening given what we know or assume.
In hold’em, what are the odds that the player under the gun has pocket aces?
There are fifty-two cards in the deck. Four of those cards are aces. And players are dealt two of those cards at random.
If that’s all you know you can calculate the odds of that player having aces is 220-to-1.
If you also know that the player looked at their hand and then raised, you can say it’s considerably more likely that they have aces.
What if you also know that the player is Petra, and Petra is the most legendary rock in the history of poker? Petra plays sixty hours a week and no one has seen Petra raise with less than pocket kings in the last twenty years.
Now the odds of her having aces is about 2-to-1.
As we acquire more knowledge we use that knowledge to determine the probability of things we don’t know.
This is why it doesn’t make sense to wonder what the probability is of something that you already know happened. You know it happened, so the probability of it is 100%.
Productive hindsight probabilties
Calculating hindsight probabilities can be useful to improve your play.
For example, everyone folds to Valencia who raises all in on the button. The small blind folds. You are the big blind and you call with kings. Valencia turns over aces and wins the pot.
She had aces, but given what you knew at the time, she was equally likely to have queens.
You can calculate the probability of winning the pot given what you knew at the time
As a result, when you are in a situation like that again, you can make the best possible decision with the knowledge you have.
Counter-productive hindsight probabilities
Calculating hindsight probabilities can be detrimental to your play and to your life.
For example, since last month, you’ve raised all-in with a flush draw on the flop and been called twenty-three times and every time you’ve missed your flush.
You can calculate the probability of that happening given what you knew last month.
What would be the result of that?
- You get to spend time relishing in how unlucky you are.
- You have something to complain about to yourself and to others.
- You have something to blame for your poor results.
- You have something you can use to extend your bad luck
- You have something to think about and focus on that isn’t how to best play the current hand.
- If your win rate is negative or your bankroll goes to zero, you can blame bad luck or “variance.”
If that’s what you want to do that’s great. People doing that paid my rent for many years.
If you really want to know how much of your results (good and bad) is due to variance, The Definitive Guide to Poker Bankroll Requirements can show you how to estimate your win rate with 95% confidence.
If you would rather have that done for you, you can sign up for a free account on Neverbust.
If you have any questions, or just want to tell me how awesome this is, you can contact me here.