# Downswing odds

• Black
Joined: 26.05.2007
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
• 6 replies
• Bronze
Joined: 08.10.2006
I think Augustus Caesar had something going on like this, might have been in the blog section.
• Bronze
Joined: 08.10.2006
• Black
Joined: 26.05.2007
Thanks!
• Bronze
Joined: 17.06.2010
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

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.
• Bronze
Joined: 11.03.2008
There's a program called ROI simulator...