Q&A: Gambling.
Originally published:
This is an English translation (via GPT-5.4). Read the original Hebrew version.
Gambling.
Question
Given that I have the ability to borrow an unlimited amount of money for gambling, and when I stop gambling I am required to repay the loan, would it be worthwhile for me to gamble on something whose payout is tenfold but whose odds are one in twenty, using the following strategy: each time I bet ten times as much as the previous time. I would stop gambling when I win, and with the amount of my winnings I would cover the previous losses. Presumably yes, so why doesn’t every billionaire use a strategy like this?
Answer
Because he doesn’t have infinite money
With the orders of magnitude that you yourself gave (increasing the amount by a factor of 10 each time, and winning odds of 1 in 20), it’s easy to illustrate why this doesn’t work: if it takes you 15 bets to win, you’ll reach a sum of one quadrillion, which according to Google is the amount of money all the people in the world have combined. Long before that, you’ll reach an amount that no person can possess, and long before that, an amount that no casino could pay back to you.
Honestly, I thought about this question myself as a kid with doubling the amount each time (so that in the end each win earns one shekel), before I discovered that this is a well-known question in game theory. I didn’t manage to calculate the probabilities all that much, but I came up with an amusing objection — it turns out that for that rich person, it’s more worthwhile to work for minimum wage than to gamble using this method.