Hey, anyone knows the formula to calculate how likely you are to go on a X bi downswing having a Y long term ROI? I've seen this somewhere but can't find it anymore =p
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I think Augustus Caesar had something going on like this, might have been in the blog section.
If you play long enough, you will see every size of downswing with probability 1. However, it's reasonable to ask questions like, "If I play 10,000 tournaments, what is the average size of the largest downswing I will see?" or "How long will I have to play to see a downswing of 50 buy-ins?" These questions can be answered if you assume that the games stay the same and that you don't tilt, and formulas for both are in the book Collin Moshman and I are writing on practical poker math. I'll just give an answer to the second question here.
The average amount of time it takes for you to see a downswing of size D when your win rate is WR and your standard deviation is SD is about
1/2 (SD/WR)^2 * (Exp(2 * D * WR / (SD^2))-1) - D / WR.
For example, if your ROI is 5% = 0.05 buy-ins per tournament, and your standard deviation is 1.55 buy-ins per tournament, then the average times before you see downswings of size 10, 30, and 100 buy-ins are
10 buy-ins: 48 tournaments
30 buy-ins: 594 tournaments
100 buy-ins: 28,400 tournaments
These are based on a Brownian motion model which isn't perfect, but which should still be accurate. A bigger question is whether you really know your ROI, and whether you can be sure you will still be playing your A-game after dropping 80 buy-ins.
There's a program called ROI simulator...
You can download it here...
http://www.zshare.net/download/70886672f9227868/
It's very interesting! Hope it helps!