[TNixon]

[ QUOTE ]
Having a downswing of a particular size is very different from losing that amount in a fixed number of hands.

[/ QUOTE ]
Ok, I think I understand why you pointed this out, and either my thinking is severely off, but I still don't understand why (likely, like I said, I'm way over my head here, just trying to figure things out), or you didn't take much more time examining what I was trying to do in that example than you did explaining why it was wrong and missed out on the fact that I knew it would only be an approximation that actually answers a different question. (not quite so likely, but it's entirely possible that I didn't sufficiently explain what I was trying to do).

So let me try to be as thorough as possible in explaining my thought process, to make it as easy and as painless as possible to poke the relevant holes:

First of all, in the interest of what appears to be a fairly simple approximation, I'm willing to modify the problem from chance of an absolute downswing to the chance of being a certain amount below expectation.

For a string of 2,-4,-2,3,-6,2,4,2,4,-3, the average expectation is 0.2/hand. At hand 1, we would be 1.8 above expectation, at hand 2, 2.4 below expectation, at hand 3, 4.66 below expectation, and at hand 5, 6.2 below expectation.

This is obviously only a very loose approximation to what most people think of as a "downswing", since at hand 2 we're at a "downswing" of -4, at hand 3, a swing of -6, and hand 5, a swing of -9, but I'm willing to find 6.2 instead of 9, and 4.6 instead of 6.

It's a very rough approximation, but the question itself isn't exactly a precise one to begin with, and this is better than nothing at all.

My thought was that by changing the question in this way, it could be simplified to a level where I was actually capable of figuring out an answer, by trying to determine the probability of being a certain distance away from expectation instead of the actual size of the swing, and I *believe* the example I laid out did just that. It obviously didn't solve the original problem, but I think it did solve this modified version of the problem. If you disagree, feel free to do so with a little more substance than "that doesn't work."

Of course, people far smarter than me seem to have already solved the original problem. Thanks for that link, jason1990. [img]/images/graemlins/smile.gif[/img]