Quotes About Probability

At one such tournament, I told the audience that one player would win 76% of the time and the other would win 24% of the time. I dealt the remaining cards, the last of which turned the 24% hand into the winner. Amid the cheers and groans, someone in the audience called out, "Annie, you were wrong!" In the same spirit that he said it, I explained that I wasn't. "I said that would happen 24% of the time. That's not zero. You got to see part of the 24%!

For any single decision, there are different ways the future could unfold—some better, some worse. When you make a decision, the decision makes certain paths possible (even if you don't know where they lead) and others impossible. The decision you make determines which set of outcomes are possible and how likely each of those outcomes is. But it doesn't determine which of that set of outcomes will actually happen.

Luck exerts its influence between your decision and which of the possible paths you end up on. It is the element you have no control over that determines which of the possible outcomes you actually observe in the short run.

Poker teaches that lesson. A great poker player who has a good-size advantage over the other players at the table, making significantly better strategic decisions, will still be losing over 40% of the time at the end of eight hours of play. That's a whole lot of wrong. And it's not just confined to poker.

When people complained that Nate Silver did his job poorly because he had Clinton favored, I thought, "Those people haven't gotten all their chips in a pot with a pair against a straight draw and lost." Or, more likely, they've had those things happen throughout their lives and didn't realize that's what 30% or 40% feels like.

An accurate picture of the odds is important when you're choosing a path. But once you've already made your choice, then you should switch into irrational optimism for the execution phase.

In most of our decisions, we are not betting against another person. Rather, we are betting against all the future versions of ourselves that we are not choosing. We are constantly deciding among alternative futures:

Now imagine if you had gone for that night of blackjack a year ago. When you think about the outcomes as having happened in the distant past, it is likely your preference for the results reverses, landing in a more rational place. You are now happier about the $100 win than about the $100 loss. Once we pull ourselves out of the moment through time-traveling exercises, we can see these things in proportion to their size, free of the distortion caused by whether the ticker just moved up or down.

most of our decisions, we are not betting against another person. Rather, we are betting against all the future versions of ourselves that we are not choosing.

When you make a decision, the decision makes certain paths possible (even if you don't know where they lead) and others impossible. The decision you make determines which set of outcomes are possible and how likely each of those outcomes is. But it doesn't determine which of that set of outcomes will actually happen.

When we think probabilistically, we are less likely to use adverse results alone as proof that we made a decision error, because we recognize the possibility that the decision might have been good but luck and/ or incomplete information (and a sample size of one) intervened.

Remember, the likelihood of positive and negative futures must add up to 100%. The positive space of backcasting and the negative space of a premortem still have to fit in a finite amount of space. When we see how much negative space there really is, we shrink down the positive space to a size that more accurately reflects reality and less reflects our naturally optimistic nature

Hindsight bias is the tendency to believe that an outcome, after it occurs, was predictable or inevitable.

Job and relocation decisions are bets. Sales negotiations and contracts are bets. Buying a house is a bet. Ordering the chicken instead of the steak is a bet. Everything is a bet.

Deciding which hands are worth playing and which hands are not is the first and most consequential choice a player makes. And pros are just better at that choice, playing a mere 15% to 25% of the two-card starting combinations they are dealt in Texas Hold'em. Compare that to an amateur, who will stick with their starting cards over half the time. In the battle of whether to hold 'em or fold 'em, amateurs usually hold 'em. Professionals usually fold 'em.

Terms that express likelihoods mean very different things to different people. Using ambiguous terms can lead to confusion and miscommunication with people you want to engage for help. Being more precise, by expressing probabilities as percentages, makes it more likely you'll uncover information that can correct inaccuracies in your beliefs and broaden your knowledge.

So in loose multi-way action games, the math says play tight. In tight games, where the pots are tiny, the math says play loose.

In the short-term, for any single decision, there is only a loose relationship between the quality of the decision and the quality of the outcome. The two are correlated, but the relationship can take a long time to play out.

You can't tell that much about the quality of a decision from a single outcome, because of luck. When you make a decision, you can rarely guarantee a good outcome (or a bad one). Instead, the goal is to try to choose the option that will lead to the most favorable range of outcomes.

As with all the strategies in this book, we must recognize that no strategy can turn us into perfectly rational actors. In addition, we can make the best possible decisions and still not get the result we want.

Over time, those world-class poker players taught me to understand what a bet really is: a decision about an uncertain future.

Thinking in bets starts with recognizing that there are exactly two things that determine how our lives turn out: the quality of our decisions and luck.

Sixty percent of the time, it works every time.

The value of small pocket pairs comes from the possibility of flopping three of kind and winning a sizable pot. To that extent, playing this type of hand is a low risk/high reward proposition.