winrates and downswings

[DavidC]

Hey guys,

Assume that you have a winrate of 2/100 and a SD of X.

You go up a limit.

Your winrate drops to 1/100 while maintaining the former X SD.

Will your downswings be:

1) Twice as deep
2) Twice as long
3) Neither
4) Both

?

Edit: DOWNSWING SIZE TO BE CALCULATED IN BB. Sorry guys.

[tiltaholic]

in dollar amount? or in bb? if dollar amount, then what is the relation in bb size between limits?

[UATrewqaz]

Well it's all about %'s really.

These are just test numbers to show you my train of thought

if you are a 2/100 winner you have an X% chance of having a Y BB downswing

I believe if you are now a 1/100 winner you'd have an X * 2% chance of having a Y BB downswing.

Thus you will experience downswings like you are used to twice more often and have a twice greater chance of experiencing a mega downswing.

[milesdyson]

the swinginess will be the same in terms of length/big bets, but at the end of 10 billion hands your winrate will be less by 1 bb/100.

imagine just fitting your graph with a straight line. just drop the slope of the line to fit your new winrate, but the difference between your actual graph and your "winrate line" at any given hand # would be the same (in big bets). bleh, i need to draw a picture but i'm at work.

[DavidC]

[ QUOTE ]
in dollar amount? or in bb? if dollar amount, then what is the relation in bb size between limits?

[/ QUOTE ]

Shite, good point... op edited.

[DavidC]

[ QUOTE ]
the swinginess will be the same in terms of length/big bets, but at the end of 10 billion hands your winrate will be less by 1 bb/100.

imagine just fitting your graph with a straight line. just drop the slope of the line to fit your new winrate, but the difference between your actual graph and your "winrate line" at any given hand # would be the same (in big bets). bleh, i need to draw a picture but i'm at work.

[/ QUOTE ]

No no, this works, thanks.

Something else that I was thinking of is that if you were to graph bb/100 over time rather than bb over time, your graph would look like a huge amount of static over your first 5k-10k hands or whatever, and then would start to settle into a nearly flat line near your true winrate. If you improved from 1/100 to 2/100, you'd see a gradual slope going up from the 1 line to the 2 line, but never quite getting to the 2-line, because of the history at 1/100 (other than when statistical blips took it over).

Good answer, bro. Thanks. I probably should have known. /images/graemlins/frown.gif

--Dave.

[deception5]

This (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=3044308&page=&view=&sb=5& o=&fpart=all&vc=1) is the best post I've seen on the subject and can probably answer your questions better than I can.

[NateDog]

[ QUOTE ]
[ QUOTE ]
the swinginess will be the same in terms of length/big bets, but at the end of 10 billion hands your winrate will be less by 1 bb/100.

imagine just fitting your graph with a straight line. just drop the slope of the line to fit your new winrate, but the difference between your actual graph and your "winrate line" at any given hand # would be the same (in big bets). bleh, i need to draw a picture but i'm at work.

[/ QUOTE ]

No no, this works, thanks.

Something else that I was thinking of is that if you were to graph bb/100 over time rather than bb over time, your graph would look like a huge amount of static over your first 5k-10k hands or whatever, and then would start to settle into a nearly flat line near your true winrate. If you improved from 1/100 to 2/100, you'd see a gradual slope going up from the 1 line to the 2 line, but never quite getting to the 2-line, because of the history at 1/100 (other than when statistical blips took it over).

Good answer, bro. Thanks. I probably should have known. /images/graemlins/frown.gif

--Dave.

[/ QUOTE ]

Pokergrapher does this under options > plot converging bb/100

[Doc7]

and it looks just like you suspected it would too : )

[Hojglad]

I think the answer to the question you posted is:
5) More frequent.

The variance associated with poker is inversely proportional to your winrate as a player. So, if your winrate drops from 2bb/100 to 1bb/100, then your variance must increase. Homer made a post about this some time ago. Search around for a bit and you'll find it.

[deception5]

[ QUOTE ]
So, if your winrate drops from 2bb/100 to 1bb/100, then your variance must increase.

[/ QUOTE ]

I don't believe this is correct. I think that what happens is that your variance is exactly the same but your starting point is lower. If the bulk of your sessions were from -2BB to 6BB they would now be from -3BB to 5BB. Still an 8BB spread, but lower average gains. If you mean you'd have more evenly split winning and losing session then yes, I agree with that.

[Shillx]

What you have to understand about a downswing is that it is anything less then the mean and not anything less then 0 BB/100.

Let's say that you have an expert card cheat who can beat poker for 20 BB/100 with an SD of 5 BB/100. A terrible downswing for him would be 18 BB/100 over 10k hands eventhough he is making tons of $$$ over that span. If he found himself in a game where he was making 19 BB/100 with the same SD, a 17 BB/100 over 10k hands would be just like the former. So losing 1 BB/100 on your winrate makes downswings 1 BB/100 worse. It also makes upswings 1 BB/100 worse.

It is very easy to see that the answer is (C)

[DavidC]

[ QUOTE ]
and it looks just like you suspected it would too : )

[/ QUOTE ]

Yeah... I'm living in the old days:

I use Vern's graphing tool, it always works, and it's kinda grown on me. /images/graemlins/smile.gif

It took me a LONG time to get used to finally accept Windows 95... At the time, I could do most things much faster in DOS.

These days, the only thing that I can do faster in dos than windows is renaming lots of files according to a standard naming format, which I do rarely (i.e. changing a list of mp3 file names to match an artist name or something).

[DavidC]

[ QUOTE ]
What you have to understand about a downswing is that it is anything less then the mean and not anything less then 0 BB/100.

Let's say that you have an expert card cheat who can beat poker for 20 BB/100 with an SD of 5 BB/100. A terrible downswing for him would be 18 BB/100 over 10k hands eventhough he is making tons of $$$ over that span. If he found himself in a game where he was making 19 BB/100 with the same SD, a 17 BB/100 over 10k hands would be just like the former. So losing 1 BB/100 on your winrate makes downswings 1 BB/100 worse. It also makes upswings 1 BB/100 worse.

It is very easy to see that the answer is (C)

[/ QUOTE ]

You mean #3, right? /images/graemlins/cool.gif

Thanks, Shill. Your point about downswings being less than the mean rather than less than zero is well taken.

--Dave.

[Bankuri]

[ QUOTE ]
What you have to understand about a downswing is that it is anything less then the mean and not anything less then 0 BB/100.

Let's say that you have an expert card cheat who can beat poker for 20 BB/100 with an SD of 5 BB/100. A terrible downswing for him would be 18 BB/100 over 10k hands eventhough he is making tons of $$$ over that span. If he found himself in a game where he was making 19 BB/100 with the same SD, a 17 BB/100 over 10k hands would be just like the former. So losing 1 BB/100 on your winrate makes downswings 1 BB/100 worse. It also makes upswings 1 BB/100 worse.

It is very easy to see that the answer is (C)

[/ QUOTE ]

Another way to see this is to look at the statistical gaussian distribution. The standard deviation is a measure of how far you are likely to move from your mean. Since it is the same in both cases, you have the same likelihood of moving X BB/100 from your mean winrate. This means your downswings (or upswings) have the same probability of happening thus neither longer or deeper.