Quotes About Probability

On the other hand, a discrete event (e.g., a football game, roulette, blackjack, or other casino game) has a defined ending point, which is characteristic of external losses.

gambling creates risk while investing/speculating assumes and manages risk that already exists.

Another reason controls should precede strategy is that, as we learned in chapter 7, you can't calculate the probability of a trade's being profitable; you can only calculate your exposure. So all you can do is manage your losses, not predict profits.

You can almost always find chains of coincidence to disprove magic.

What do the dice say?" Dice say nothing. They are dice." Why roll'em, then?" They are dice. What else would I do with them?

People fly despite knowing that a certain percentage of airplanes crash every year.

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.

Improving decision quality is about increasing our chances of good outcomes, not guaranteeing them.

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. Learning to recognize the difference between the two is what thinking in bets is all about.

When someone asks you about a coin they flipped four times, there is a correct answer: "I'm not sure.

Forcing ourselves to express how sure we are of our beliefs brings to plain sight the probabilistic nature of those beliefs, that what we believe is almost never 100% or 0% accurate but, rather, somewhere in between.

Making better decisions starts with understanding this: uncertainty can work a lot of mischief.

When you are weighing whether to quit something or stick with it, you can't know for sure whether you can succeed at what you're doing because that's probabilistic. But there is a crucial difference between the two choices. Only one choice—the choice to persevere—lets you eventually find out the answer.

To figure out whether a decision is good or bad, you need to know not just the things that might reasonably happen and what could be gained or lost, but also the likelihood of each possibility unfolding. That means, to become a better decision-maker, you need to be willing to estimate those probabilities.

Here's a secret: All guesses are educated guesses because there is almost no estimate you could make about which you literally know nothing.

Andrew Mauboussin and Michael Mauboussin came up with this pretty comprehensive list of these types of terms for a survey they conducted: Almost always More often than not Serious possibility Almost certainly Never Slam dunk Always Not often Unlikely Certainly Often Usually Frequently Possibly With high probability Likely Probably With low probability Maybe Rarely With moderate probability Might happen Real possibility

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.

We process outcomes sequentially, treating each outcome as if it stands alone. We don't sit back and wait to update our beliefs until we have enough data to overcome the uncertain relationship between outcomes and decisions.

Some of these terms had startlingly wide ranges, which I imagine you experienced in your four-person survey. For instance, "real possibility" had a range of about 20% to 80%. A quarter of the people taking the survey thought the term meant 40% of the time or less. A quarter thought it meant 40% to 60%. A quarter thought it meant 60% to 75%. Finally, a quarter thought it meant over 75% of the time.

The same thing happened after Donald Trump won the presidency. There was a huge outcry about the polls being wrong. Nate Silver, the founder of FiveThirtyEight.com, drew a lot of that criticism. But he never said Clinton was a sure thing. Based on his aggregation and weighting of polling data, he had Trump between 30% and 40% to win (approximately between two-to-one and three-to-two against) in the week before the election. An event predicted to happen 30% to 40% of the time will happen a lot.

When we field our outcomes as the future unfolds, we always run into this problem: the way things turn out could be the result of our decisions, luck, or some combination of the two.

information. We

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.

I know viscerally how likely 60–40 and 70–30 favorites are to lose (and, of course, the opposite). 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.