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@dhyaa_khaled: مشروع مجاري الهندية #كربلاء #كربلاء_المقدسه_بين_الحرمين #الهندية #الحسين #العراق #محمد_شياع_السوداني

ضياء خالد
ضياء خالد
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Sunday 21 January 2024 20:03:18 GMT
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➡️Quant Finance From Scratch, part 1: expected value, with 12 lines of Python you can follow line by line. Two questions guide the video: what exactly is an edge, and why does a tiny edge turn into near certainty? Step 1, probability. The wheel has 37 pockets and 18 of them are red, so a bet on red wins with a probability of 18 out of 37, just under half. Step 2, expected value. A win pays one dollar and a loss costs one dollar. Weighted by their chances, that averages out to minus 2.7 cents per bet. Step 3, one player. A single spin pays plus or minus one dollar, so a balance jumps around. Our example player was 11 dollars ahead after 47 spins and still ended 22 dollars down. Step 4, a thousand players. Their balances spread out like stock charts, and 181 of the 1,000 walked away with a profit. Step 5, the casino. It takes the other side of all one million bets and earns $27,288, within one percent of the expected $27,027. Step 6, the law of large numbers. The more bets you add up, the closer the average gets to the expected value. The casino's profit per bet settles at 2.7 cents. Step 7, the reason. The edge grows with every bet, while luck only grows with the square root of the number of bets. After about 1,400 bets the edge is bigger than one standard deviation of luck. The same idea runs insurance companies, market makers and quant funds: they look for a small edge and repeat it many thousands of times. Even the casino was 44 dollars down after its first 2,000 bets, which is why measuring risk matters as much as measuring the edge. The honest part: the wheel is simulated with a fixed seed and nothing was downloaded. Every number in the video comes from a real run of the code, and the video checks its own numbers before it renders. This video is for education only, and nothing in it is financial advice. The house edge works exactly as shown, which is why gambling loses over time. #quantfinance #probability #python #expectedvalue #statistics
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