bad luck downswings don't exist?

[btmagnetw]

using excel, i entered 200 cells of =NORMINV(RAND(),3,30)

i believe that generates a random distribution of numbers which would imitate that of a player who's winrate is 3bb/100 and has a variance of 30bb/100. i'm not sure if that variance is accurate for a typical player, its what i remember mine to be.

200 cells means 20,000 hands. the average winrate after that many hands is 600bb. here's a list of trials of actual wins:

648
1659
1357
730
1117
1000
707
-394
1421
494
356
371
826
919
1393
523
209
767
717
240

that's ONE losing streak after 20,000 hands out of 20. how can people say that good players still have 100k hand breakeven stretches?

so is this experiment not accurate for some reason? or are all downswings a result of bad play moreso than bad luck?

[AaronBrown]

First of all, you got a little lucky in your numbers. On average you have 1.6 20,000 hand downswings under your assumptions (although 30 is the standard deviation, not the variance).

Second, you're looking at fixed runs of 20,000 hands. That's not the longest run of hands with a net loss. You could have added hands from the series before and after the -394 on, maybe there would have been a run of 25,000 or 30,000. You could also have a run of 25,000 or 30,000 with net losses, but it's hidden because it crossed over a boundary and was preceeded and followed by winning streaks.

Finally, people don't say 100,000 hand downswings are common, just that they're reasonably possible, even if you are a long-term winning player. So the fact that a random simulation turns up only 25,000 or 30,000 hand downswings doesn't prove that if you did a lot of these you would see some longer negative runs.

[tarheeljks]

i see your point aaron and agree, but i still think that people just incorrectly attribute their downswings to variance.

[btmagnetw]

lets say i do the same thing over 1,000 cells or 100,000 hands. how many 10 buy in downswings (or 1,000bb) should i see, on average?

[BruceZ]

[ QUOTE ]
using excel, i entered 200 cells of =NORMINV(RAND(),3,30)

i believe that generates a random distribution of numbers which would imitate that of a player who's winrate is 3bb/100 and has a variance of 30bb/100. i'm not sure if that variance is accurate for a typical player, its what i remember mine to be.

200 cells means 20,000 hands. the average winrate after that many hands is 600bb. here's a list of trials of actual wins:

648
1659
1357
730
1117
1000
707
-394
1421
494
356
371
826
919
1393
523
209
767
717
240

that's ONE losing streak after 20,000 hands out of 20. how can people say that good players still have 100k hand breakeven stretches?

so is this experiment not accurate for some reason? or are all downswings a result of bad play moreso than bad luck?

[/ QUOTE ]

You would expect about 1.6 out of 20 on average, so your results are just a little lucky, but still in line with expectations. The average win rate for 20,000 hands is 3*200 = 600, and the standard deviation for 20,000 hands is 30*sqrt(200) =~ 424. So being negative after 20,000 hands is about 600/424 standard deviations below average, which corresponds to a probability of 1 - NORMSDIST(600/420) =~ 7.85%, or about 1.6 in 20.

Repeating this for 100,000 hands would that show being behind after that many hands would be more than 3 standard deviations below average, and the probability comes out to about 1 in 1278. So while rare, this is still possible.



[ QUOTE ]
also, if my variance is 30bb/100, what's my variance per hand? do you just divide by 100?

[/ QUOTE ]

That is the standard deviation, not the variance, and you would divide by sqrt(100) = 10.

The variance is the square of the standard deviation, 900 bb^2 for 100 hands, and if you wanted the variance per hand for some reason, then you would divide this by 100 hands.

EDIT: Changed NORMSINV to NORMSDIST

[btmagnetw]

ok i repeated it with 100,000 hands, and i see where i went wrong before. there were lots of 20k, 30k, and even 50k breakeven stretches.

what i'm curious about now, is how many downswings i should see per 100,000 hands? i've yet to see a 1000bb downswing, but i'm not sure if 1000bb is a buy in or if its 500bb. my 30bb came from my PT stats. assuming a buy in is 500bb, i've yet to see a 20 buy in downswing, but i think its common belief that these are common?

[Thremp]

30PTBB/100 is v v low. Move it to 65PTBB/100 an rerun.

[AaronBrown]

<< i see your point aaron and agree, but i still think that people just incorrectly attribute their downswings to variance. >>

That's certainly true. While long downswings are possible by bad luck, they're much easier to create with bad play, or even just high variance play.

It's a highly unrealistic assumption that you have a constant win rate and standard deviation over 100,000 hands. Any significant downswing should lead to a rigorous assessment of your play.

The reason to emphasize the chance long downswings is so people accept the need for large bankrolls (or small stakes) and careful management, even if they are very good players.

[TheJared]

your std deviation # is wayyyy too low for real life.

I've seen 35 at lower stakes, 45-55 at midstakes and higher then that at HSNL. If you adjust this you will see the hell that poker is.

My last 65k hands at 2/4 NL are at 57 std dev BB/100.

[Some9]

this is very neat:

http://www.google.com/url?sa=t&ct=re...Mp18WCZEgpFz1Pw