Mathematics · the experiment
Turn $1 into $1,000 with fair bets, then see who gets ruined
You run an imaginary finance company that only makes fair bets. Replay the article's leverage game step by step, and recover its numbers.
1 · Without borrowing
You start with $1 and aim for $1,000. Every bet is fair, and you can only stake what you have.
At best, what is your chance of getting there before going bankrupt?
2 · Find the right step
You can now borrow up to 9 times your fortune: leverage of 10. Which strategy gives the best chance of reaching ×1,000?
Check it: set the gain aimed for on each bet, from a single bet to tiny steps, and run the 1,000 gamblers, until about one in two reaches $1,000.
3 · Replay Lehman
With leverage of 20, how far can you aim while keeping a one-in-two chance of getting there?
Lehman Brothers multiplied its equity by 8. Aim for ×8 with fair bets, and raise the leverage until nine gamblers in ten get there.
4 · Who gets ruined?
When the rare bet is lost, where does the gambler's fortune land?
Game played
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