[koolmoe]

[ QUOTE ]
Here is another example that illustrates how likely a 300BB downswing is. Lets say I have a 5% risk of ruin with a 300BB bankroll.

Let also assume that every time I win 100BB, I cash out and round my bankroll down to 300BB.

Each time I do this I start out with a 5% risk of ruin. What happens if I do this 30 times?

The chance of my not going broke each time is .95, so the chance that I don't go broke in all 30 trials is .95 to the 30th power which equals .21.

So there is a 79% chance that I will go broke (and experience a downswing of 300BB or more) during one of the 30 trials. Wow, that is depressing.

[/ QUOTE ]

This is a nice example, but there is a slight problem with it. In each trial, the endpoint is either +100 BB or -300 BB. The ROR = 5% would necessarily include some examples which include an initial swing of +100 BB or more eventually ending at net -300BB. So for the trials as you have set them up, the chances of -300 BB should be slightly less than 5%. A decent estimate of the true percentage might be ROR(300 BB) - ROR(400 BB), though that would probably be too small.

Now, the one thing missing in each trial is the number of hands it takes to reach the end of the trial. So even if we compute that we are 79% (or however) likely to experience a -300BB downswing over 30 trials, we have no idea from this approach how many hands are included (on average slightly less than 10000 for each +100 BB trial).

However, it should be clear that as we play more hands, the likelihood of experiencing a -300 BB downswing are increased to the point of almost certainty, even for a winning player (by construction).

It is a really interesting way to look at the question.