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thought was known to produce electrical activity in the brain and faint but detectable electrical currents in the scalp.
If you do this, what do you want to happen? and If you do this, what do you think will happen? I wouldn’t have liked either answer. These two questions became valuable guides for me in the future.
you start the Martingale by betting $1 on, say, red. After each loss, bet twice as much on the next spin of the wheel, always on red. Eventually you win—red has to come up sometime—and that win covers the previous string of losses, plus a profit of $1. Then start again by betting $1 and repeat the whole process, netting another $1 profit each time when you finally win.
I also believed then, as I do now after more than fifty years as a money manager, that the surest way to get rich is to play only those gambling games or make those investments where I have an edge.
In counting cards, it’s mainly the fraction remaining that matters, not the number.
One of the best compromises between ease of use and profitability was to count the small-value cards (2, 3, 4, 5, 6) as +1 as they are seen during play, intermediate cards (7, 8, 9) as 0, and large-value cards (10, J, Q, K, A) as −1.
For instance, when the dealer has a total of 16 he has to hit. He loses if he draws a big card that puts his total over 21 and survives if he draws a small card. A 5 gives him 21, best of all. So he benefits when the deck is richer in small cards and poorer in big cards.
the complete deck had 36 non-Tens and 16 Tens, so I started counting “36, 16,” which gives a ratio of non-Tens to Tens of 36 ÷ 16 = 2.25.
A ratio below 2.25 meant the deck was Ten-rich, and when a ratio hit 2.0 the player had an edge of about 1 percent. For ratios of 2.0 or less, which meant advantages of 1 percent or more, I bet between $2 and $10 depending on the size of my edge. Otherwise I bet $1.
Another reason to publish quickly is the well-known phenomenon that it is typically much easier to solve a problem if you know it can be solved.
life is a mixture of chance and choice. Chance can be thought of as the cards you are dealt in life. Choice is how you play them.
This plan, of betting only at a level at which I was emotionally comfortable and not advancing until I was ready, enabled me to play my system with a calm and disciplined accuracy. This lesson from the blackjack tables would prove invaluable throughout my investment lifetime as the stakes grew ever larger.
a pair of 8s. They must be split. Why? Because 16 is a terrible hand. Draw and you probably bust, or stand and the dealer probably beats you with 17 or more.
For the second time, the Ten-Count System had shown moderately heavy losses mixed with “lucky” streaks of the most dazzling brilliance. I learned later that this was a characteristic of a random series of favorable bets. And I would see it again and again in real life in both the gambling and the investment worlds
Russell T. Barnhart, a magician and gambling scholar,
His book Danger in the Cards describes his adventures detecting swindles in private games.
Mathematically, interruptions didn’t matter, because my lifetime of playing was just one long series of hands, and chopping it into sessions and playing them at various times and in various casinos should not affect my edge, nor the long-run amount I could expect to win. This principle applies in both gambling and investing.
I chose the best seat for a card counter, known as third base, which is farthest to the left as viewed from the player’s side of the table. Sitting there, I was the last to act, so I would benefit by having seen more cards when it was time to play my hand.
High–Low count sees these cards in the first round of play: A, 5, 6, 9, 2, 3. Then the count, which started with zero, becomes −1 + 1 + 1 + 0 + 1 + 1 = +3.
When the count is positive the player benefits, and when it is negative it helps the casino. The impact of any particular value of the count is greater when fewer cards are left. Good players simply estimate this by seeing how many cards are in the discard tray
For instance, never play at a table where the payoff for getting a two-card 21, or blackjack, has been changed from the original 3:2 to lesser amounts like 6:5 or 1:1.
To start the Labouchère, write down a string of numbers, such as 3, 5, and 7. The total of these, 15, is what you try to win. Your first bet is the total of the first and last numbers in the string, 3 + 7, or 10. If you win, cross off the first and last numbers, leaving only 5. Your next bet is 5, and if you win you have reached your goal. If you lose, add 10 to the string so it becomes, 3, 5, 7, 10 and then bet 3 + 10 or 13. In any case, each time you lose you add one number to the string, and each time you win you cross off two numbers.
In American roulette, the wheel has thirty-eight pockets for the ball to fall into. Thirty-six of these, numbered from 1 to 36, are either red or black, with eighteen of each. The green pockets, 0 and 00 (zero and double-zero), are opposite each other on the rotor and thus split the other thirty-six into two groups of eighteen. A winning bet on a single number pays 35:1,
Thus Aces are 1, 2s through 9s are their numerical value, and 10s, Jacks, Queens, and Kings count as 0, not 10.
As with individual cards, only the last digit of a total counts. For example, 9 + 9 = 18 counts as a total of 8. If the first two cards of a hand total 8 or 9, termed a natural 8 or a natural 9, as the case may be, all bets are settled without any further cards being dealt.
“How do you tell whether a mathematician is an introvert or an extrovert?” Answer: “If he looks at his shoes when he talks to you, he’s an introvert. If he looks at your shoes, he’s an extrovert.”
I am often asked what it takes to be a successful card counter. I’ve found that an academic understanding is not enough. You need to think quickly, be disciplined enough to follow the system, and have a suitable temperament, including the ability to switch your mind into the here and now and stay focused on the cards, the people, and your surroundings. Better still is to have an “act” or persona that makes you seem like a type of player with which casinos are familiar.
By 1995 baccarat in Nevada accounted for half as much casino profit as did blackjack, yet with only one-fiftieth as many tables. A baccarat table was twenty-five times as profitable as a blackjack table.
As I would learn, most stock-picking stories, advice, and recommendations are completely worthless.
Then Vivian remarked on my second mistake in thinking, my plan for getting out, which was to wait until I was even again. What I had done was focus on a price that was of unique historical significance to me, only me, namely, my purchase price.
this error was in the way I thought about the problem of when to sell, choosing an irrelevant criterion—the price I paid—rather than focusing on economic fundamentals like whether cash or alternative investments would serve better.
he joined a limited partnership that itself allocated money to limited partnerships, so-called hedge funds,
Lesson: Do not assume that what investors call momentum, a long streak of either rising or falling prices, will continue unless you can make a sound case that it will.
a common stock purchase warrant is a security issued by a company that gives the owner the right to buy stock at a specified price, known as the exercise price, on or before a stated expiration date.
An option to buy a stock is similar to a warrant, the principal difference being that warrants are typically issued by the company itself and options are not.
Convertible bonds are like ordinary bonds but with the additional feature that they can be exchanged for a fixed number of shares of the issuing company’s stock if the holder so desires.
He evaluated businesses with the aim of buying shares in them, or even the entire company, so cheaply that he had an ample “margin of safety” to allow for the unknown and the unanticipated.
I didn’t judge the worth of various businesses. Instead I compared different securities of the same company with the object of finding relative mispricing, from which I could construct a hedged position, long the relatively undervalued, short the relatively overvalued, from which I could extract a positive return despite stock market ups and downs.
One campaign issue was how to cut California’s budget deficit. The problem was caused largely by the anti-tax measure Proposition 13, adopted by California voters in 1978. This limited the tax on real estate to 1 percent of the assessed valuation with a cap of 2 percent per year on any revaluation upward. With California’s soaring prices, the tax on houses that weren’t traded fell over time to a small fraction of 1 percent of their current value, thus sharply eroding the tax base and expanding the budget deficit.
A hedge fund in the United States is simply a private limited partnership managed by one or more general partners (each of whom risks the loss of their entire net worth should things go badly wrong) and a group of investors, or limited partners, whose loss is limited to the amount they commit.
The other was a discount factor that was applied to the warrant’s uncertain payoff at expiration in order to obtain its present value. This discount factor, or markdown, accounted for the fact that investors tend to value an uncertain payoff less than if it was a sure thing.
In 1972 the company had warrants that sold for 27 cents when the stock traded at $8 share. The warrants were so cheap because they were worthless unless the stock traded above $40 a share. Fat chance. Since our model said the warrants were worth $4 a share, we bought all we could at the unbelievable bargain price of 27 cents each, which turned out to be 10,800 warrants at a total cost, after commissions, of $3,200. We hedged our risk of loss by shorting eight hundred shares of the common stock at $8. When the stock later fell to $1.50 a share, we bought back our short stock for a profit of
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the proposition that what matters in life is how you spend your time.
cognitive dissonance. That’s where you want to believe something enough that you simply reject any information to the contrary.
Lesson: It doesn’t pay to push the other party to their absolute limit. A small extra gain is generally not worth the substantial risk the deal will break up.
The optimal strategy is to wait until you have seen about 37 percent of the prospects, then choose the next one you see who is better than anybody among this first 37 percent that you passed over. If no one is better you are stuck with the last person on the list.