The Temptation of Risk-Altering Gambling Systems
Picture this: you’re sitting in a coffee shop getting ready to write some code, and your friend walks in claiming to have made 0.4 BTC just from running software on his laptop.
When this happened to me, my first thought was immediately that he got lucky day trading. Maybe he even wrote a program to do it for him that was somehow miraculously working.
The answer was actually far simpler. The Bitcoin was merely a vehicle for performing thousands of bets per on an online gambling site. The premise of the site was simple. You can wager any amount of bitcoin, and there’s a 49.5% chance you double it but a 50.5% chance you lose it. The website is the digital equivalent of betting on a coin flip except for the fact that the site takes an advantage. Software allows users to make thousands of bets per minute with various strategies.
My gut reaction was that there was no way he could possibly be making money off of this, so I pleaded with him to stop the software. However, in the hour we debated it, he made another 0.1 BTC. How did he get these consistent returns?
Enter the Labouchère system. This is the algorithm the ran on the laptop and made 0.1 BTC sitting in a coffee shop. The idea is simple. A gambler picks an amount of money he desires to win and must keep track of his losses along the way. This way, as long as he plays for long enough, he will always win the amount he decided at the beginning.
For example, consider a player who desires to make $6 from a round of betting. To begin the Labouchère system, he will write a sequence of arbitrary integers with a sum of $6. For instance, he might pick the sequence [$1, $2, $3]. The system dictates that he then must make a bet equal to the sum of the outer integers of the sequence. With a sequence of [$1, $2, $3], he would bet $4 since the sum of $1 and $3 is $4. If he wins, he gets to remove $1 and $3 from the sequence. If he loses, he must add $4 to the right side of the sequence. Then, he starts again. This ensures that he will always make back his losses and win the amount of money he desires.
However, the system has a fatal flaw. It could take an arbitrarily high number of bets, or in other words an arbitrarily high amount of capital, to win a round. By running repeated Labouchère, one can make very consistent returns if one has a large amount of available capital to do so. As a result, one running this system risks all available capital every time they play.
By running the software in the coffee shop, my friend was risking his entire 1 BTC wallet, which was available to the gambling site. Most rounds of Labouchère will return $6, or whatever amount a player decided ahead of time, but once in awhile, it will result in a much larger loss.
This makes the system very psychologically tempting. Graphs of a player’s returns will show a very clear upwards linear trend. However, it will always crash to $0 given a long enough amount of time because no player has infinite available capital to bet with.
This article is a much more condensed version of a paper I wrote, which examines the simulated outcomes of this system in great detail.
Checkout the abstract and full paper on my website:
