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To expand on this further, and to plug the Kelly Criterion which the author mentions having written a former blog post on: Suppose instead of betting all your
by vitus 6y ago
To expand on this further, and to plug the Kelly Criterion which the author mentions having written a former blog post on:
Suppose instead of betting all your money every round, you instead decide to bet 10 cents each time. Now, instead of being essentially guaranteed long-term ruin, you can and most likely will be able to continue making money indefinitely. (In fact, your chance of ever dipping below, say, $0.50 is finite even when extending your rounds played arbitrarily.)
The Kelly Criterion for this scenario actually dictates that you should bet 25% of your money each round. Using this betting strategy, somewhere around 70% of people end up making money off this game when run for 100 rounds (1% end up ending up with a respectable $25 or more, while about as many end up with <$0.15). You even have an opportunity for redemption -- when we drag out the horizon to 5000 rounds played, somewhere around 90% of individuals become billionaires, even as 30% of people were behind after 100 rounds (so 2/3 of those redeemed themselves).
On the other hand, with the all-or-nothing solution outlined in the article, about 13% of the population coming out ahead (around 1% of the population gets really rich, ending up with >$200, while more than half end up with less than a penny). Meanwhile, the odds get worse as the game goes on, as at just 500 rounds, >80% of players have been reduced to less than a penny.
That's a long-winded way of saying that the amount you bet is really important.