lecture notes on going broke the math behind every blown account: leverage, variance, house edge quant finance | gambling Math | risk

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On July 23, 2025, the sister of a murdered Idaho student looked at the killer in court and said, "Sit up straight when I talk to you." When the judge later gave him the chance to explain, he used three words. In the video below, you see her statement. On November 13, 2022, four University of Idaho students were killed in a rented house in Moscow, Idaho. Kaylee Goncalves, 21. Madison Mogen, 21. Xana Kernodle, 20. Ethan Chapin, 20. The killer was Bryan Kohberger, 28, a PhD student in criminology at Washington State University. He left one thing behind: a knife sheath with his DNA on the button snap. Investigators traced it through genetic genealogy, matched it to trash from his family's home in Pennsylvania, and arrested him there six weeks later. In July 2025 he pleaded guilty to avoid the death penalty. He never gave a motive. At sentencing, Kaylee's older sister Alivea stood up. "I won't offer you tears. I won't offer you trembling." She read him the questions he would not answer. Why November 13th. Where the murder weapon is. Then she told him what he was. "You are not profound. You're pathetic." "You spent months preparing and still all it took was my sister and a sheath." When she finished, the courtroom applauded. He didn't move. Judge Steven Hippler asked if he wanted to speak. "I respectfully decline." He got four consecutive life sentences without parole, plus 10 years for burglary. The judge called him a "faceless coward" and said it was time to end his "15 minutes of fame." He took a plea to save his life and kept the one thing the families asked for. Should a guilty plea ever be allowed without the truth?
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In the 1990s, in Angarsk, Siberia, a man in a police uniform would pull over at night and offer a woman a lift home. It was late. He was the police. They got in. Some of them never got home. He kept doing it for almost two decades. At home he had a wife and a daughter. In 2012 investigators took DNA from about 3,500 current and former police officers in the Irkutsk region. On June 23, 2012, they arrested one of them. Mikhail Popkov, 48. In 2015 he was convicted of 22 murders. In 2018, of 56 more. Then two in 2021. Three more in 2023. 83 murders. One man. In a 2019 prison interview he was asked why. Was it revenge? Did he see himself as some kind of cleaner? "I can't explain it." Then he was asked how he stopped. He said it was fear of being caught. And one rule. "On principle, I didn't let anyone in my car." He started by offering women a ride. He says he stopped by never offering one again.
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In 1993 three prison guards walked a 33-year-old man into an interview room in Wisconsin. He was in handcuffs. One guard held each arm. In front of the camera his hands would not stay still. In June 1978, three weeks after his high school graduation in Ohio, he was 18. So was Steven Hicks, a hitchhiker he picked up that summer. Steven never got home. Years later he lived in Milwaukee. He met men in bars and brought them home. The drink was already mixed with sleeping pills. On May 27, 1991, a 14-year-old boy got out of that apartment and was found in the street, naked and bleeding. Three young women called 911. The man told the officers the boy was his 19-year-old lover. The officers walked the boy back inside. On July 22, 1991, Tracy Edwards, 32, ran from the same apartment with a handcuff on one wrist and flagged down a patrol car. That night the police learned the name of the man who lived there. Jeffrey Dahmer. 17 men and boys, killed over 13 years. In 1992 he got 16 life terms. Asked why, he said: "Not because I was angry with them, not because I hated them, but because I wanted to keep them with me." During the interview he asked them to cut the film. On November 28, 1994, another inmate beat him to death. It took three guards to walk him into a room. It took two officers to walk a 14-year-old back to him.
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On September 15, 1873, Jay Cooke had President Grant as a guest at his estate outside Philadelphia. Three days later his bank shut its doors. Cooke was one of the most trusted bankers in America. He had sold the bonds that paid for the Union side of the Civil War. Then he put his bank behind the Northern Pacific, a railroad from Lake Superior to Puget Sound that wasn't finished and wasn't earning. Two weeks later Frank Leslie's Illustrated Newspaper wrote that the Northern Pacific had already swallowed "at least $40,000,000." And this line, which I keep rereading: "Men who a few days ago were worth millions are to-day penniless." The New York Stock Exchange closed for ten days. It had never closed before. The same page has a drawing of Grant meeting the bankers at the Fifth Avenue Hotel. The caption: "The President refusing to use the U.S. Treasury." About 18,000 businesses went bankrupt. 121 railroads. Unemployment hit 14% nationally and around 25% in New York, and the depression lasted more than five years. Cooke himself came back. He made a new fortune in a Utah silver mine and died rich in 1905. That part bothers me more than the crash. The man who borrowed against an unfinished railroad got a second chance. The people queuing outside the Fourth National Bank on Nassau Street mostly didn't. Was Grant right to keep the Treasury shut?
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I found the front page of the Indianapolis Times for October 29, 1929. Across the top: "Stock Crash Greatest in History." Further down, in small type, my favourite line: "Assurance That Bottom Is Reached Brings Only Brief Halt." The bottom came in 1932. 89% below the peak. On September 3, 1929, the Dow stood at 381. Economist Irving Fisher was talking about "a permanently high plateau." On October 24, a record 12.9 million shares changed hands in a day. Bankers met at Lamont's office, and their man Richard Whitney walked onto the floor and loudly bid $205 for 25,000 shares of US Steel. The market calmed down. For one day. Monday, October 28: down 12.8%. Tuesday the 29th: down 11.7% on 16.4 million shares. Down 23% in two days. By noon the paper was reporting nearly $50 billion in market value gone. This is where I disagree with how the story usually gets told. The crash didn't ruin anyone. The debt did. By August 1929 brokers had lent small investors more than $8.5 billion, often more than two thirds of what a stock cost. If you bought with your own money, October was a painful number on paper. If you bought on margin, you got the call, sold at any price, and pushed the market lower for everyone else. Whitney's bid was theatre. It bought one day, not three years. The scariest number for me isn't even 89%. It's 1954. The Dow got back to its September 1929 level on November 23, 1954. Twenty-five years. Buy the top at 40, break even on the index at 65. So when someone tells me "the market always comes back," I want to ask: in whose lifetime? Today 100x leverage is one tap away. The next crash isn't the question. The question is who will be carrying a loan that Tuesday.
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FANDUEL SAYS ITS MEDIAN BET IS $5. ONE VIP WAGERED $18.5 MILLION, LOST $1.5M AND GOT A BRYCE HARPER VIDEO. It published the number the same week Congress's 20 October deadline on its VIP videos ran out. Here is the math the median hides ↓ -> Now FanDuel publishes "Fast Facts": median bet $5, median bettor about $63 a month. No sample size, no method. The bettor behind the inquiry, Terry Thompson, wagered $18.5 million on FanDuel since 2020 and lost $1.5 million, The Philadelphia Inquirer reported. In November 2024 his VIP host arranged a 21-second Harper video that greeted him and his son by name. The $63 comes from a NerdWallet/Harris poll of 458 sports bettors. In the same poll the median bettor spent $750 a year. The average spent $3,284. 4.4 times the median. That gap is the tail. Harper: "I did not know FanDuel would do this, I did not consent to it, and FanDuel had no right to do it." FanDuel says the videos were a "token of appreciation for a customer's loyalty" and were not used to induce gambling. Caveat: Thompson's losses are allegations in a lawsuit against FanDuel and DraftKings, filed March 2026. A $5 median can be true and still miss the point. Turnover pays the house, and one VIP brought $18.5M of it ↓ Which number should regulators look at: the median bettor, or the top 1%?
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1 MISSED FILE ON 1 OF 8 SERVERS COST KNIGHT CAPITAL $460 MILLION IN 45 MINUTES august 1, 2012. knight was the biggest trader in us stocks: 17.3% of nyse volume. the code that killed it had been dead for 9 years ↓ -> Now the SEC order reads like a post-mortem, line by line. In 2003 Knight retired a function called Power Peg. It never deleted the code. In July 2012 it reused the flag that once switched Power Peg on, for NYSE's new Retail Liquidity Program. One technician copied the new code to 7 of 8 servers. On the 8th, the old flag woke up 2003 code. 212 customer orders came in. More than 4 million orders went out. 397 million shares, 154 stocks, 45 minutes. By the time it stopped: $3.5 billion long in 80 stocks, $3.15 billion short in 74. 97 automated warning emails were sent. None were acted on. Day 1 the stock fell 33%. By day 2, 75% of its value was gone. On August 5 investors led by Jefferies put in about $400 million. By July 2013 Knight was folded into Getco. What it showed: the new code worked. The deployment failed. No second technician, no written procedure. The SEC counted the loss at more than $460 million and fined Knight $12 million. Knight's own pre-tax figure was $440 million. A single skipped server is no longer an IT ticket. At market speed it is a balance sheet ↓
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BILL HWANG'S ARCHEGOS HAD $36 BILLION AND WENT TO ZERO IN UNDER A WEEK. BANKS LOST AT LEAST $10.4B. The usual story: one terrible week in the market. The numbers tell a different one. It fits in one line of math ↓ 2013: Hwang launches Archegos as a family office. March 2021: $36B of capital, $160B of stock exposure through swaps. 23 March 2021: buys nearly a billion dollars more of ViacomCBS and other stocks. Within a week: wiped out. 6 reasons it went to zero: 1. LEVERAGE. $160B on $36B is about 4.4x. A 22.5% fall across the book erases all of it. 2. CONCENTRATION. The exposure sat in a handful of stocks. Concentrated names can fall 22.5% in days. 3. OPACITY. Through swaps, each bank saw only its own slice of the $160B. 4. TIMING. On 23 March it added nearly $1B more, days before the fall. 5. COUNTERPARTIES. Credit Suisse lost $5.5B, Nomura $2.9B, Morgan Stanley $911M, UBS $774M. 6. LAW. Losing money is legal. Hwang got 18 years and $9B+ in restitution for fraud. Control group: LTCM, 1998. More than 25-to-1, lost over 90% of its capital. 14 firms put in $3.625B. No criminal charges. The one difference: nobody was convicted of lying. formula: Δp* = 1/L. Everything else is how long it takes. sources: US DOJ SDNY, CNN, NBC News, The Daily Upside, Federal Reserve History Which killed Archegos: the leverage, or the secrecy?
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JAMES WYNN MADE $87M ON HYPERLIQUID IN 70 DAYS. A 3.6% BITCOIN DIP TOOK $99M AT 40X LEVERAGE. May 24, 2025: a 40x Bitcoin long worth $1.25 billion. Entry $107,993. May 26: he posts that he is leaving the "casino". Here is the 40x leverage math nobody checks ↓ At 40x leverage you put up 2.5% of the position. The other 97.5% is borrowed. So a 2.5% move against you wipes the whole margin. Not 25%. Not 10%. 2.5%. May 29: 94 BTC liquidated at $106,330. May 30, hours after he wrote "I strongly advise people against what I'm doing!": 527 BTC liquidated at $104,950. Then 422 BTC at $104,150. 949 BTC gone. About $99.3 million. BITCOIN LIQUIDATION MATH AT 40X LEVERAGE $107,993 → $104,950 is a 2.82% drop. Multiply by 40: that is 113% of the starting margin. Bitcoin did not crash. It slipped under $105,000 after tariff comments from Trump. What it showed: the edge worked for 70 days. The leverage let one ordinary dip decide everything. His own words afterwards: "I was basically gambling. I got greedy and stopped taking the numbers seriously." Caveat: analyst Dethective later alleged Wynn ran equal longs and shorts against himself, so part of the losses may have been hedged or unrealized. A single bad call is no longer the risk. 40 times a normal day is. $87M in profit on May 26: cash out, or one more 40x long?
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RYO GAKUCHO, 40 MIN, 257K VIEWS: STOP YOUR NISA AT (SPENDING − PENSION) × 25. JGB AND ¥100M RULES INSIDE. ryo gakucho packed his aug-sep 2026 money lectures into 1 video. 4 topics, 6 rules. the strangest one: you can stop investing decades before you start withdrawing ↓ the idea: money has a finish line, and most people run past it. NISA, JGB, SIDE HUSTLE, ¥100M: THE 6 RULES 1. NISA STOP LINE (0:47): (yearly spending − pension and other income) × 25. spend ¥5M, pension ¥2M, gap ¥3M × 25 = ¥75M. the 25 comes from the trinity study 4% rule. for early retirement he uses 3.5% 2. STOP ≠ WITHDRAW (2:16): ¥15M at age 40, left alone at 7%, is about ¥81M at 65. ¥6M (NISA ¥1.2M × 5 years) at 5%+ passes ¥20M in 25 years. stop adding early, start spending late 3. PENSION MATH (4:54): single, ¥110k/month gap → line ¥33M (¥75M with no pension). couple, ¥70k/month gap → ¥21M (¥90M with no pension). fire at 45 on ¥3M a year at 3.5% → about ¥86M 4. SIDE HUSTLE NG 5 (11:01): copying no one, too little volume, volume as the goal, no review, missed timing. his fix: 5 posts a day at 70/100 quality minimum, double down on the top 10%, kill the bottom 10% 5. JGB TRAP (21:20): retail floating 10y pays 1.87% (10y JGB yield × 0.66, principal protected). shin-madohan fixed 10y pays ~2.7-2.8% at market price. drop ≈ rate rise × years left: +1.2% with 7 years left = −8.4%, ¥1M → ¥916k. his call: not while rates are rising 6. ¥100M AND STILL WORKING (29:45): 7 reasons. a 70/30 portfolio gives ¥70M × 4% = ¥2.8M, not ¥4M. 7% doubles ¥100M to ¥200M in 10 years. a ¥10M salary is hard to drop. plus family, a higher fire target, social ties, nothing else to do spending gap × 25 → stop adding → let 7% compound → withdraw 4% from 65 alone each rule is basic. together they answer one question: how much is enough, and what happens after you get there. bookmark this before your next NISA top-up. the lecture is in japanese with auto-captions, link in the first reply. are you still adding past your line, or not there yet?
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