To cultivate a better mind, practice a new and useful way of thinking until its habitual, and then train yourself in yet another good one.
We need this quick and automatic thinking process, even if it isn't perfect. We can't rationally analyze every decision from what to order at the coffee shop to exactly what information to share or withhold from each person we deal with. Even thinking about who to vote for, or whether our assumption that we should be good to others is true, could eat up too much time if we tried to perfectly analyze every aspect. Life moves on, and we don't have the luxury of spending large chunks of it thinking about any one part of it.
But although we develop a particular way of thinking (or ways) largely unconsciously, that doesn't mean we can't do it more consciously. In fact, we can develop habits of mind based on "rules" chosen specifically to give us better results. As an example, I'm going to explain how good poker players understand and think in terms of "investment odds," and why that process might be useful in everyday life.
An example
A poker player is dealt four hearts. He can draw a card if he "calls" the last bet. The probability of drawing a heart to complete his flush is about 19% (.2). He figures that if he draws the heart the probability of winning the hand is 90% (.9), and close to 0 if he doesn't get the heart. The probability of his winning is found by multiplying the probability of drawing the heart times that of winning if he draws it, which gives him an 17% chance of winning (.2 x .19 = .171). So, with roughly a 1 in 6 chance of winning, should he continue?
Ah, but we don't have enough information. Whether he should bet also depends on how much he'll have to bet from that point forward and how much he will make if he wins. The exact amount that he'll have to bet and that will be in the pot is an educated guess based on his knowledge of the game and the other players, but based on his best guesses the potential win has to justify the risk, which is what investment odds are all about. The formula (which ignores what he has already invested, since this is irrelevant at the point of deciding whether to add more):
Multiply the projected pot size by the probability of winning and divide the result by the total of projected bets. If the result is higher than 1, it's a good investment.So if he expects that there will be $300 in the pot at the end, and that he'll have to bet a total of $50 more, we get: ($300 x .17)/$50 = 1.02, which means this is just barely a good bet.
Now throw away the math
Yes, some poker players do the math that carefully, but the good news is that for thinking in general the basic process is more important than one's preciseness with the math (and preciseness is impossible in most situations). The life lesson here, in case you don't see it in the math, is that it isn't just about the odds of success and the value things risked (love, time, money, respects), but also about the balance between the probabilities and the profits.
Should a single man risk saying hello to a pretty woman he would like to know? Hmm... He might have a one in twenty chance of "winning the pot," (getting to know her) but the "bet" which he risks (saying hello) is very small, so yes, the investment odds seem to be better than one. To see it from another perspective, if he wanted to befriend a pretty woman is it worth saying hello to twenty of them? Forty? Sixty? Each is a small bet for a possibly big reward.
What about investing $25,000 to open a small restaurant, knowing that (based on the statistics) there is only a 20% chance of succeeding? Well, if the average success (over the years of ownership) means making $500,000 more than a job would have paid, the answer is clear (investment odds of 4 -- a screamingly good bet). By the way, most successful entrepreneurs fail several times before achieving lasting success, and this little demonstration of investment odds, when contrasted with the advice of the many naysayers in our lives, suggests we are too often scared off from good bets just because losses are more common than wins. We don't see that the big payoff is essentially bought by all those lost bets.
To train yourself in using investment odds as a way of thinking, you look at the potential profit (in dollars, security, pleasure, personal development) multiplied by the rough probability of success, and determine from that if the size of the bet (dollars, time effort, anguish) is justified.
This works in areas of life that are not as quantifiable too. For example, should you believe what you read in a newspaper? It is quick and useful to believe movie schedules, because experience says they are almost always accurate and you lose little when they fail. What about government economic forecasts reported in the news? The potential win multiplied by the small odds of success suggests that you better not bet much on them.
If someone tells me cows have five stomachs and I choose to believe it I "win" a fun bit of trivia to share by "betting" on the probability of this being true. What do I lose (how much am I betting) if it's incorrect? Not much if I do no more than share this "fact" with friends. If, on the other hand, I'm writing a book on animals and my credibility is at stake, I might want to verify this using other sources. (By the way, I think cows have one stomach with four digestive compartments -- but don't quote me on that.)
This may all seem to be common sense, but how often do we over-invest our time in analyzing something for which -- if we arrive at a different understanding -- we will derive very little profit. Time is a valuable investment. And how often do we think something is too risky when all we will lose is small amounts of money and bits of time for a reasonable chance to gain a lot of money (which buys time back if used correctly). Our "common sense" is common, but better sense -- a better way of thinking -- is not. It is cultivated by only a few.
To cultivate a better mind, practice a new and useful way of thinking until its habitual, and then train yourself in yet another good one. I'll have more of them in the future on this website and in The Mind Power Report.
In the flush draw example, he assumes that the odds of drawing the flush are 0.19 and a flush has a 90% chance of winning. But then he gets the formula for figuring the odds of winning wrong, writing "(.2 x .19 = .171)".
By those assumptions, the correct formula would be 0.19 x 0.9 = 0.171. As written, 0.2 x 0.19 = 0.038, not 0.171, so he's not a poker math whiz.
His assumptions are also suspect. He doesn't say what type of poker it is, except to say that the player has to decide whether to call the last bet of the hand. What game is being played would make a big difference to the amount of information available to the player and therefore the odds.
If it was 5-card stud poker, with one more card to be dealt, each player would have three cards showing. The player with four hearts could then count the hearts shown, including those in his own hand, and come up with a reasonable estimate of the number of hearts still remaining in the deck, allowing for a quarter of the hole cards dealt having been hearts.
The same would be true, though with more uncertainty, if the game was
7-card stud, because that starts with two hole cards instead of just one.
He probably based this example on Texas hold-em, however, as given away by his estimate of a 19% or 20% chance of pulling another heart.
In hold-em, each player is dealt two hole cards, then there's a bet, and then three cards are dealt that are shared by all the players, the "flop". After another bet, a fourth card called the "turn" is added to the center. Another bet, then the last card called the "river" is added to the center. After a final bet, players show their hands.
The structure of hold-em makes the calculation of most odds unvarying after the flop, because no matter how many players there are at a table all players know only their two hole cards plus those common cards that are face up in the center, which they all share. Since none of the players know what other players have as their hole cards, they have to assume that all of the cards that are not showing are potentially still in the deck.
That means that after the flop there are still 52-5=47 cards still unseen. If a player has four cards to a flush at that point, then there are nine flush cards still unseen, and thus the odds of making that flush on the turn are 9/47=0.19. Before the river card, there are 46 cards still unseen, and so the odds of filling the flush increase to 9/46=0.20 (actually, it is 0.195+, but it's rounded up). That's where this writer likely got the odds he used.
Texas hold-em is so popular because it's a fast game, in that relatively little time is spent dealing out the cards compared to stud games, and because its structure makes it possible for players to know whether or not good hands like straights and flushes might already be beat by an even better hand. Because those five cards in the center at the end of each hand are shared by all players, and each player has only two hole cards, every final hand must include at least three of the shared cards.
Thus, if a player has a straight, s/he can be certain that there isn't any flush if there aren't at least three cards of any one suit showing. If s/he has a flush, s/he can be certain that there isn't a full house or four of a kind if there isn't at least one pair showing. In either case, depending upon how good that straight or flush might be, the player might be able to know that s/he has "the nuts". At no limit table stakes, this is a killer, and it's how professional players win at tournaments and cash games.
There's a whole lot more to poker, of course, but this article explains the basic concept of risk versus reward estimation, even though this writer probably should study poker odds rather more closely before investing any money in it.