The mathematics of card shuffling is quite easy to explain. To calculate how many arrangements 52 playing cards can have, you must go through all the possible shuffles. If you do the multiplication and round the answer, you will get a number with 67 zeros. That’s more than a quadrillion times as many ways to arrange these cards as there are atoms on Earth.
It is extremely unlikely that two people in the entire history of humanity have ever shuffled a deck of cards the same way. This illustrates how many possibilities there are for arranging 52 cards.
The vastness of 52! is not only inspiring to contemplate—it has also posed some significant practical problems for online game developers. Online poker can involve large sums of money, so it’s critical that these games are as secure and fair as possible. Any flaws or loopholes could be exploited by cheaters or used by the house against players.
Digital cards should be well shuffled and dealt randomly, just like real ones. In an ideal world, an algorithm would randomly select an arrangement from the 52! possible decks. But no computer has enough memory to evaluate all of these possibilities, and a perfect random number generator doesn’t yet exist. Therefore, developers generally rely on algorithms that simulate card shuffling, and the limited number of shuffles created problems for early developers and ones that online poker players could exploit.
Today many online poker sites use the Fisher–Yates algorithm, also called the Knuth shuffle (which sounds delightfully like a dance). Even with continuous improvements over time, random generators simply aren’t good enough to do what people can do with an actual deck.
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The US has one of the highest divorce rates in the world, even though over the past four decades, it has fallen among younger couples. Instead, middle-aged and older adults have taken over. In fact, adults aged 65 and older are now the only age group in the US with a growing divorce rate. Today, roughly 36% of people getting divorced are 50 and older, compared to only 8.7% in 1990. This is known as a “gray divorce”.
This tilt towards later-in-life divorce is happening for a mix of reasons. Lives are longer than they used to be, and older couples may be less willing to put up with unfulfilling marriages than before. Meanwhile, young people are getting married later and have become more selective when choosing a partner. As one researcher puts it, “the United States is progressing toward a system in which marriage is rarer and more stable than it was in the past”.
Amid this trend, one aspect of gray divorce is beginning to receive more attention: the surprisingly deep and wide-ranging impact the split can have on adult children – and on their relationships with their parents, especially, their fathers.
After a divorce, husbands often lose their social networks and have less contact with their children, who often side with their mother. This pattern of children turning towards the mother after a divorce is known as the matrifocal tilt and increases further when a father re-partners. By contrast, when a mother re-partners, it does not seem to change the mother-child contact. Interestingly, women are more likely to file for divorce, and are less likely to remarry after a gray divorce.
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Americans 70 and over have the highest suicide rates of any age group, and their rates of suicide have increased in recent years. During this period, 63,836 older Americans died by gun suicide. Gun suicide is a greater killer of men over 70 than car crashes.
And if older men are in trouble, older white men are especially in trouble. They die by gun suicide at the highest rate—a rate more than triple that of Black and Latino men of the same age, and 19 times the rate of women 70 and over.
Suicide in later life often stays hidden. Many isolated older Americans have no obituary, memorial, or funeral. For those who do, the cause of death often goes unmentioned. But doctors and researchers are sounding the alarm. No single factor drives the high rates, researchers say. But severe illness, pain, financial pressures, isolation, a lack of mental health care, cognitive impairment, and the availability of firearms all play a role. Gun laws also factor in. The US has a substantially higher suicide rate for older adults than neighboring Mexico or Canada, countries with stricter gun laws.
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We know that making money is not the purpose of life. Of course, money won’t fill our inner void. But what will? If you are very good at making money, if it feels satisfying, it is easier to keep doing that than to stop and step into the unknown.
The better you are at making money, the more you leave on the table when you exit the game. The greater your future earning potential, the higher the price of your freedom. Without clarity on what we value, any amount of money can be a prison.
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From a heavily guarded mountain hideout in the heart of the Sierra Madre, 59-year-old Nemesio “Mencho” Oseguera reigns as the new drug king of Mexico, aided in his ascendance by America’s resurging love of cocaine and the Trump administration’s escalating war on fentanyl. Oseguera spent decades building his Jalisco New Generation Cartel into a transnational criminal organization fierce enough to forge a new underworld order in Mexico, displacing the Sinaloa cartel, torn by warring factions, as the world’s biggest drug pusher.
The Sinaloans, Mexico’s top fentanyl traffickers, got caught in the crosshairs of the Trump administration, which promised to eradicate the synthetic opioid. The crackdown has left an open field for Jalisco and its lucrative cocaine trade, elevating Oseguera to No. 1. “‘Mencho’ is the most powerful drug trafficker operating in the world,” said Derek Maltz, who served this year as interim chief of the Drug Enforcement Administration.
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Since 2024, foreign investors have been net sellers of Indian equities in the secondary market (existing stocks), but they have been rushing into India’s primary market, which consists of initial public offerings and follow-on public offers. Overseas investors made net investments to the tune of $14.5 billion in the primary market last year, while redeeming $14.4 billion from the secondary markets.
For global investors, the math is simple. India’s secondary market looks overpriced as compared to other emerging markets. MSCI India index trades at a price-to-earnings ratio of 25.4x as compared to MSCI Emerging Market Index — which includes India — with P/E ratio of 15.41x. The MSCI China index trades at 14.6x while MSCI Korea index is at 12.4x.
Even the U.S. imposing 50% tariffs on Indian exports has not led to any significant correction in the market, preventing investors from entering cheap. In such a scenario, IPOs offer a better play for the Indian markets as managements and bankers price the issue attractively, drawing significant investor interest. Returns from Indian IPOs in 2024 were starkly higher at 37.1%, compared with its stock market returns of just over 7%.
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