This blog entry was originally written by Jay Jacobs (@jayjacobs), I am just migrating the post to the new SIRA site.
With this year’s RSA conference still close in the rear view mirror, I felt I had to write about something that stuck in my mind as I went through the week. I found repeated confirmation to something Doug Hubbard wrote, “I have never seen a single objection to using risk analysis in any profession that wasn’t based on ignorance of what risk analysis is and what it can do.” Keep in mind, ignorance isn't meant to be derogatory or insulting. It simply means a lack of knowledge or uninformed. Many of the people I heard object to risk analysis were incredibly smart in many ways, yet they were presenting objections from an uninformed position of risk analysis. It makes me wonder if we have to reduce ignorance about this field before we are able to successfully reduce uncertainty around our exposure to loss.
One such objection I encountered was during a conversation I had on the first night I was in San Francisco. After some lively back-n-forth with a colleague on the efficacy of risk management and some healthy skepticism from this person, I received this challenge: “suppose I go into a casino with $100,000, what am I going to come out with?” The assumption on his part was that analysis would provide a single number (perhaps an average loss) and whatever the answer was, it’d be wrong. But my response was simply, “what if I produce a distribution?” And so, for this challenge I have whipped out the first graph. It is based on some very specific assumptions though. I made the assumption that the gambler would chose a (single) game for their visit and they were consistent in their gambling. Not that it mirrors reality, it just makes this example much easier (and this is just an example).
Here are the other assumptions:
- American Roulette (with the “0” and “00”)
- Bets were one of the red/green, even/odd options (which wins about 47.3% and pays 1 to 1)
- The gambler played for about 4 hours at a lively pace of 60+ games per hour (for a total of 250 rounds)
- The gambler consistently wagered $5 per round
I know these would probably not match reality, but that’s okay. The assumptions are clear and the analysis could be updated as the assumptions are updated. Point being, it only matters that the analysis matches the assumptions and that we can update the the assumptions (and the model). The analysis could be redone with the odds from any game, or the analysis could combine multiple games played during a casino visit. I’m just trying to keep this simple.
My answer to the original question would start out with “given the assumptions…” and say something like this:
- The gambler would leave with less money than they started with around 78% of the time
- About half the time, the gambler would lose more than $70
- 10% of the time, the gambler would lose more than $170
- 10% of the time, the gambler would win more than $40
Since we have to answer similar questions regardless of methods used (everyone makes risk-based statements regardless of what they call it), I challenged my skeptical colleague to answer the question in his way and his answer was simple. He would advise the gambler to look at the casino itself, because it logically means they take more money than they give out. While true, there is a large amount of uncertainty in that statement and lacks any feedback or ability to learn over time. We can do better.
A Better Gambling Story
Pure games of chance (like roulette) have loads of variability and almost zero uncertainty since it’s in the house’s interest to make the games as unbiased as possible. This makes them ripe for some simple models and allows us to create a better story. Plus, by telling a gambler that they’ll lose more than they win isn’t very helpful, and may erode (or fail to build) trust, especially when the gambler walks away with money.
My solution is to model visits the casino repeatedly and see how the gambler does (a method known as Monte Carlo). I set up the model to play Roulette 250 times per visit, betting on the 1 to 1 payout options, and record the offset in cash for the gambler over the visit, then I set the model to run 10,000 times. Finally, I made a pretty picture (with red, yellow and green of course) that showed the trends over the 250 iterations (left to right). By looking at this we can get a sense of the individual stories here. For example, there’s a red line that hovers around $50 early in the visit (around rounds 40-70) and then ends up dipping down for a loss around $200 (sound familiar?) Overall though, this should help inform the simple roulette gambler
So, can I tell my colleague exactly how much he’ll walk out of the casino with? Absolutely not, nobody can. But given the correct assumptions we can make some statements of probability that reduce the gambler’s uncertainty better than other methods (including the de facto unaided intuition). This is an important point: it’s not that statistics and math is going to convert lead into gold, but it will be better and more consistent than alternatives. We cannot lose sight of that. It will always be possible to poke the models (and some really deserve to be poked), but we should not tear down a solution just to replace it with something worse.