Risk of Ruin

[fnord_too]

I don't think 30 sessions is enough in most, if not all, cases. People have some pretty major differences in BB/100 from 100k block to 100k block. The variance here is pretty wild.

Moreover, the game truly is dynamic, both your play and the play of the table you are sitting at. Consider mutual funds for a second. Their mantra is "past performance is no gurantee of future results", and these are institutions who employ a lot of quants to minimize risk and/or maximize expectation. I think there is a lot more predictability in poker than in protfolio management, but the point is that trying to quantify these things to fine levels is, I don't believe, feasible for all the reasons that phzon points out.

(I just realized you linked something to trading, but I don't have time to read that right now. I am reasonably well versed in portfolio management, though.)

(This post is getting into rambling but I have a lot of random thoughts to share.)

Let's look at your stop loss idea though. IF you always play your best game, and exercize good game selection, and can accurately assess the level of competion, and leave when it the game is not sufficiently profitable, then stop losses make no sense. Of course, no one can do all these things, though many may think they can. So stop losses are interesting from a Baysean perspective.

Consider your expectation is 2BB/100, with a 15BB/100 standard deviation. You can figure out the likelyhood that you will be N BB from even in either direction if you assume a normal distribution. (This gets into the central limit theorem and a bunch of statistics that I don't want to think about right now, and that are not really germane to what I am trying to get at.) Further say that you realize your EV varries due to how well you are playing and how the rest of the table is playing against you. Now say you have notionalized some discrete EV's and their likelihoods:
+4 BB/100 25%
+3 BB/100 35%
+2 BB/100 10%
+1 BB/100 5%
0 BB/100 5%
-1 BB/100 5%
-2 BB/100 5%
-3 BB/100 5%
-4 BB/100 5%

(That is actually 1.85BB/100, but I don't feel like playing with the numbers any more).

Now, those prior probabilities are a big assumption, but you can figure the liklihood you are at one of those discrete nodes (another simplification, the discrete part) depending on where you are after so many hands.

For instance, say you are at -20BB after 200 hands, you can work out the liklihood that you are in each mode via conditional probability. Working this stuff out in advance may give you some reasonable stop loss numbers. That is you can set an arbitrary confidence, such as "I will not play if there is a 20% chance I am not in a +2BB/100 or better situation."

So, if you believe you can come up with good prior probabilities, you can do some math to come up with stop losses that suit you. There is going to be a lot of uncertainty in those prior probabilities, but that might be fine.

Of course if you know you start to play like crap after you drop a buy in regardless of the game or your level of fatigue, then you really have no need for math in establishing stop losses, just self awareness and dicipline.

This sort of Baysean inference could result in some interesting RoR math, but its impact may be too small taking all the uncertainties into account.

That is kind of what I was originally trying to say, that the cascading errors in measurement leave you with really broad confidence intervals.

(To paraphrase TJ, I appologize for the long winded rambling nature of this reply, I did not have time to write a short one.)