300BB downswings are not normal. PERIOD!

[stevepa]

Ok, let's try to do some math (Disclaimer: I make no guarantees I do this right)

Say we have a player with a winrate of 1bb/100. We'll use the previously quoted 15bb/100 SD for full ring games. Now, we want to know the probability of a 300bb downswing (so #of100hands * observed win rate over those hands = -300)

So, starting from Z = (E - o)/(SD/sqrt(n)),
where Z = # of standard deviations away from expected
E = expected win rate
o = observed win rate
SD = standard deviation
n = # of 100 hands played
Writing out the rest isn't worth the effort, but substitute o=300/n, then set dz/dn = 0 and solve for n. Then substitute that to get z. I get that the most likely 300bb downswing occurs over ~30,000 hands with probability 1.04%.

So, for someone having played 300k hands of no-tilt, constant 1bb/100 poker, the probability of having had a 300bb downswing is ~ 1-(0.9896^10) = 10%.

Again, no guarantees that this is right.

Edit: I messed up the shorthanded calculation...Fixed now.

Also, if you're interested, for the short handed # quoted (17bb/100 SD), the same player would have a 300bb downswing over 30,000 hands about 2.08% of the time. So after 300k hands, prob of at least 1 300bb downswing = 19.0%.

Steve

[CardSharpCook]

To add another useless personal anecdote:

In 250K hands at one level I've had 2 -250BB swings. One of them was the first 4K hands played at this level. The other... I was clearly tilting in many of my sessions and thought myself to be "not in a correct state of mind". Add in a little real life problem (about a girl...), and I lost 250BB over 21K hands. Outside of that, I have lost 100BB in several sessions, and my third biggest downswing was 150BB over 12K hands of what I thought to be great poker on my part. I don't see 300BB as unreasonable, but I think Rigaletto is correct in saying we often dismiss the downswing instead of fixing the problem. However, the corralary to that is players who try to convince themselves that they are in control. That is, that they can prevent downswings by superior play.

CSC