Sun 21 Sep 2008
I’m not much of a gambler myself, but I know lots of people who enjoy casino gambling from time to time. It seems to be the consensus opinion that these (non gambling-addict) people set a limit for how much they are willing to lose during their visit, to avoid getting in seriously over their heads.
In a random game such a limit actually encourages people to consistently exit the game at a loss — even in a game where the odds are 50%. Due to simple probabilities, even in a the most fair game possible you can quickly build up swings of wins and losses that will compound your balance far from its starting point. By having a fixed exit point on the losing side, one can guarantee that given enough time you will eventually hit that point.
Example: let’s say you went to Vegas and set a limit of $150 maximum loss. In a simulated 50% game repeated 10000 times, you would have finished with about $400 positive balance. But thanks to your loss limit, you would have been out before the random positive swings took you there.

My hypothesis then was to leverage this effect in reverse: what if you didn’t set an loss limit, but instead set yourself up for a success limit? I wrote a simple perl script to test this out. The results were disappointing, though not really surprising.
The short answer to my hypothesis is that it’s correct, except that you will often need an incredible amount of iterations until you get to your target. And during that time it is unfortunately unlikely that you will have to have a lot of money in the bank just to get out of the nearly inevitable random holes.
With “reasonable” options (like 2000 iterations, $100 target, and $500 maximum loss) I can simulate a day of virtual gambling. By running a whole bunch of these days consecutively, I found (unsurprisingly) that in the long term net result ends up being close to zero. In the end, for random games your results simply match the odds of the game you are playing. In a casino where the odds are never going to be 50%, that means you lose.
This whole exercise reminds me of a kid, when I independently invented what is known as the Martingale Betting System. I thought I was a frigging genius until I charted it in Excel and realized that at some point you’d need an infinite bankroll just to win $1.



September 21st, 2008 at 2:50am
Of course that simulation assumes a 50% chance of winning, and absolutely no game in Las Vegas gives that. The closest is Roulette color betting, which gives you 47.4% in the American variant and 48.6% in the European variant.
Also, that graph could have very easily been inverted vertically and still been a reasonable outcome for the exact same game. All you really know going in is that after N steps, you will be, on average, sqrt(N)/N units away from 0 in some direction. The chances of it being a positive or negative outcome are 50% - so even in the long-run aggregate game your overall chances are still the same as for a single play, so you’d might as well just bet your maximum loss amount up-front.
September 21st, 2008 at 7:06am
Indeed fluffy, that is why I both noted that the odds are never going to be 50%, and why my script uses rand*(36/37).
Oh and also… of course that graph was just one of thousands of simulations run. There is nothing special about it other than the fact that it happened to illustrate my point.
September 23rd, 2008 at 1:44pm
Somehow, you forgot to factor in the value of free drinks and the cost of tips to the dealer and cocktail waitress.
This leads me to believe that either it’s been too long since you’ve been to Vegas, or you’re looking at Internet gambling.
A crying shame, no matter how you chart it.
September 24th, 2008 at 4:45pm
Ah, I didn’t actually look at the script. Yeah, that models European Roulette correctly.